From τὰ φυσικά (ta physika) to physics – XVIII

During the Middle ages Islamicate scholars analysed, studies, criticised and developed a wide range of academic disciples that they had adopted from their Greek, Persian, Chinese, and India predecessors before passing them back into Europe during the twelfth-century Scientific Renaissance. One of the disciples where their endeavours had the biggest impact was in the science of optics. 

As we saw in an earlier episode, as opposed to the popular cliché, the Ancient Greeks propagated a wide range of theories of vision ranging from the Atomist intromission theory, over the Platonist combined extramission/intromission theory, the pure extramission theory in the geometric optics of Euclid, Heron, and Ptolemaeus, to the Aristotelian intromission theory and finally the Stoic pneuma based theory shared by Galen. All of these reached the medieval Islamic society in translation and each of them found their critics, supporters, and propagators.  

Already in the ninth century Abū Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī (c. 801–873), an Arabic Muslim polymath, who was born in Kufa, in what is now south-central Iraq, the son and grandson of the governor. Originally educated in his home town he moved at some point to Baghdad to complete his education and where he would go on to serve three ‘Abbāsid Caliphs.

An Iraqi postage stamp issued in 1962 on the occasion of the millennium anniversary of the founding of the city of Baghdad and in memory of the philosopher Yacoub bin Ishaq Al-Kindi. Source: Wikimedia Commons

His interests were wide-ranging and he is said to have written at least two hundred and sixty books, which, as is often the case, have mostly been lost. Of major interest for his contributions to optics is his De radiis stellarum, a work that only exists in Latin translation, the Arabic original being lost. Here al-Kindī presents a central element of his general philosophy:

It is manifest that everything in this world, whether it be substance or accident, produces rays in its own manner like a star … Everything that has actual existence in the world of the elements emits rays in every direction, which fill the whole world.^[1]

De radiis, manuscript, 17th century. Cambridge, Trinity College Library, Medieval manuscripts, MS R.15.17 (937). Source: Wikimedia Commons

Of course, given this general statement optics with its light rays and visual rays is a central area for al-Kindī. He wrote several works on optics of which On the Causes of Differences in Perspective or De aspectibus, to give it its Latin title, is the most important but like De radiis stellarum, the Arabic original is lost. In this work al-Kindī comes down in favour of the Euclidian theory of geometrical optics with its pure extramission theory of vision but not without criticism. To start he summarises the various alternative theories he has inherited from antiquity:

Therefore I say that it is impossible that the eye should perceive its sensibles except [1] by their forms travelling to the eye, as many of the ancients have judged, and being impressed in it, or [2] by power proceeding from the eye to sensible things, by which it perceives them, or [3] by these two things occurring simultaneously, or [4] by their forms being stamped and impressed in the air and the air stamping and impressing them in the eye, which [forms] the eye comprehends by its power of perceiving that which air, which light mediates, impresses in it.^[2]

One is obviously the atomists, two is Euclid and Ptolemaeus, three is clearly Plato, and four is the mediumistic theory of Aristotle. Through argument al-Kindī eliminates all but Euclid by attacking the basic principle of intromission. He argues that a circle viewed edgewise, should in an intromission theory still appear as a circle but in reality it appears as a straight line:

Therefore it remains that the power proceeds from the observer to the visible objects, by which they are perceived . this power proceeds from the eye in straight lines and falls only on the edges of the circles, perceiving them as straight lines.^[3]

Having established that Euclid is the only valid model of perception he now takes him to task. He presents six propositions at the beginning of his work that demonstrate that luminous rays are rectilinear, although he is not intending to replace Euclid’s visual rays with luminous rays. He also differs from Euclid on the constitution of the visual cone. Whereas Euclid conceives it to consist of single rectilinear rays, al-Kindī sees it as a continuous whole. He goes further and argues that rays issue in all directions from every point on the surface of the eye. He bases this claim on the analogous behaviour of external light. al-Kindī argued that light reflects from every point on an object in every direction. He appears to have been the first to explicitly  state this simple concept which would go on to be an important element in theories of vision and optics in general. Although Euclid’s extramission theory of vision would prove to be wrong in the long run al-Kindī’s De aspectibusremained popular amongst Islamic scholars and together with his De radiis stellarum would have a major impact in Europe following the twelfth-century Scientific Renaissance. 

al-Kindī’s Arabic, Nestorian Christian, contemporary Ḥunayn ibn ʾIsḥāq al-ʿIbādī  (808–873), who was born in al–Hirah, near Kufa in what is now south-central Iraq, but moved to Baghdad where he worked as a translator and physician. Ḥunayn ibn ʾIsḥāq had studied medicine under Yuhanna ibn Masawaih (c. 777–857), a Persian or Assyrian, East Syriac Christian physician, the first to write in Arabic over ophthalmology  and the student would come to outperform his teacher in this area of medicine. His medicine is principally Galenic, who was for the Arabic physicians the “Prince of Physicians”, so it comes as no surprise that his ophthalmology is basically Galenic and his theory of vision Galenic and Stoic. He wrote two works on ophthalmology, Ten Treatises on theEye and the Book of the Questions on the Eye.

Hunayn ibn Ishaq 9th century CE description of the eye diagram in a copy of his book, Kitab al-Ashr Maqalat fil-Ayn (“Ten Treatises on the Eye”), in a 12th century CE edition Source: Wikimedia Commons

In his Ten Treatises on the Eye, Ḥunayn ibn ʾIsḥāq gives a detailed description of the structure and function of the eye that closely parallels that of Galen.

The eye according to Hunain ibn Ishaq. From a “Book of the Ten Treatises of the Eye” manuscript dated c. 1200.

Lindberg p. 35

His theory of vision is also that of Galen, which he specifically choses over alternatives, he writes: 

We say: the object of vision can be seen only in one of the following three ways: [i] by sending out something from itself to us by which it indicates its presence so that we know what it is; [ii] by not sending anything out but remaining steady and unchanged in its place; then the faculty of perception goes out from us to it, and we recognise what it is through this medium; [iii] by there being another thing  … intermediate between us and it; it is this which gives us information about it, so that we learn what it is. And we shall now see which of these three [theories] is the right one.^[4]

Alternative one covers both the intromission theories of the atomist and Aristotle, which Ḥunayn rejects with the old argument, how can a perceived mountain enter the eye? The second alternative covers the extramission theories of Euclid and Ptolemaeus, which Ḥunayn also dismisses thus:

It is not possible that the visual spirit extends over all this space [between the eye and a distant visible object] until it spreads round the seen body and encircles it entirely.^[5]

The third alternative turns out to be that of Galen and the Stoic in which pneuma coming out of the eye triggers the air that already exists between the object and the eye creating a connection along which the visual perception takes place. This is according to Ḥunayn the right one.

Ḥunayn’s Ten Treatises on the Eye was very widely read both in Islamicate culture and later in Latin translation in medieval Europe. It was in the latter case for many people their introduction to the theories of Galen, whose own work was first translated into Latin much later.

The work of both al-Kindī and Ḥunayn ibn ʾIsḥāq were widely read and highly influential and both of them dismissed the intromission theory of vision of Aristotle. However, Aristotle had two heavyweight champions, who defended and propagated his theory in Ibn  Sīnā (980–1073), Latin Avicenna, and Ibn Rushd (1126–1198), Latin Averroes, probably the two must influential medieval, Islamic philosophers. I have included brief biographical sketches of both in the episode on Islamic theories of motion so I won’t repeat myself here.

Ibn  Sīnā, who was incredibly prolific, wrote about the theory of vision is a number of still extant works including the Kitab al-Shifa (The Book of Healing, also known as Sufficientia), Kitab al-Najat (The Book of Deliverance), Maqala fi ’l-Nafs (Epistle or Compendium of the Soul), Danishnama (Book of Knowledge), and Kitab al-Qanum fi ‘l-Tibb (Liber canonis of Canon of Medicine). 

Portrait of Avicenna on a Iranian postage stamp Source: Wikipedia Commons

Ibn  Sīnā doesn’t so much defend Aristotle’s intromission theory of vision as demolish the extramission theory in its various forms. I’m not going to go into detail, just say that his arguments are convincing. His main argument is that the rays going out to the object do not perceive the object but the object is perceived by something returning to the eye. This being the case we perceive by something entering the eye so we don’t need the rays going out from the eye. Against the Galenic theory he basically argues convincingly that either air as a medium can convey perception or it can’t and if it can it doesn’t need to be activated by pneuma. This naturally leaves him with just Aristotle’s theory as acceptable. Both Ibn  Sīnā and Ibn Rushd take over the basic Galenic  structure and function of the eye from Ḥunayn. 

Ibn Rushd is, of course the most avid Aristotelian during the Islamic Middle Ages, which earned him the title of “The Commentator” when his works were translated into Latin. He refutes the theories of visual perception of Euclid, Ptolemaeus, Galen, and al-Kindi arguing that they would all imply the ability to see in the dark. He also says that an extramission theory would imply that the eye produces enough rays to fill a hemisphere of the world every time somebody opened their eyes which was just absurd. In general, Ibn Rushd is more concerned with what happens to the image once it enters the eye, which is physiology and/or psychology and not physics, so doesn’t concern us here. 

Detail of Averroes in a 14th-century painting by Andrea di Bonaiuto Source: Wikimedia Commons

We now turn our attention to Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham, Latin Alhazen or Alhacen, (c. 965–c. 1040), a Persian or Arabic mathematician, astronomer, and physicist, who was born in Basra and spent a large part of his life in Cairo. Ibn al-Haytham is one of the most important figures in the history of optics before the seventeenth century and he worked a revolution in the discipline. In his From Sight to Light: The Passage from Ancient to Modern Optics (University of Chicago Press, 2015) Mark Smith titles his chapter on Ibn al-Haytham Alhacen and the Grand Synthesis, which is a pretty good summary in five words. 

Cropped version of the frontispiece of Johannes Hevelius, Selenographia, depicting Ibn al-Haytham (Alhacen) Source: Wikimedia Commons

Amongst Ibn al-Haytham’s extant works eleven deal wholly or partially with aspects of optics. Amongst the no longer extant works another six deal with the topic in one way or another. However, there is one work that is in the history of optics dominant and that we will look at briefly here, that is his Kitab al-Manazir (Book of Optics) which was translated into Latin by an unknown translator in the twelfth century as De aspectibus or Perspectiva. 

Ibn al-Haytham rejects the extramission theories basically taking over the arguments of Ibn  Sīnā. He also notes that strong light entering the eyes causes pain and prolonged staring at strong light sources produced after images when the eyes are returned to the dark, so the eyes are sensible to light, which comes in, not goes out. Interestingly and also very important to the future development of optics, although he dismisses the extramission theory he doesn’t dismiss the geometric optics of Euclid and Ptolemaeus. He accepts their cone of vision, and as we will see even utilises it himself, but on the condition that their rectilinear rays are merely geometrical constructs and not real visual rays. Thus, making Euclid’s and Ptolemaeus’ geometrical optics independent of the extramission theory. A seemingly trivial but highly significant redefining. 

Having followed Ibn  Sīnā in dismissing the extramission theory he doesn’t follow him in adopting Aristotle’s intromission theory but develops an entirely new one. Adopting al-Kindī’s theory that every point on an illuminated object reflects light rays in every direction, Ibn al-Haytham states that it is these reflected light rays that transmit the colour and luminosity of the object to and into the eye. This is truly a radically new concept. The theories of Plato, Aristotle, and the Stoic all required the presence of light to facilitate visual perception but Ibn al-Haytham says quite simply that all it requires is light, anything else is superfluous. 

Ibn al-Haytham sees a problem with his intromission theory, if light rays are meeting the eye from every possible direction how does the eye form a distinct image of the viewed object? He offers up a fairly refined solution to this problem. Firstly, although the structure of the eye that he adopts is that of Galen/ Ḥunayn for Ibn al-Haytham the surface of the cornea, in his model, is a perfect sphere. He then hypothesises that only those rays that meet the surface of the eye perpendicularly can actually enter the eye. All the other light rays slide or veer off. 

He justifies this with an analogy. He says, consider an iron ball thrown at a wooden plank. If it hits the plank perpendicularly it rebounds or if thrown hard enough breaks the plank, If the ball hits the plank at an angle it slides or veers off. Ibn al-Haytham argues perpendicular rays are strong and penetrate the eye, whereas rays that meet to eye at an angle are weak and veer off. 

Because his cornea is perfectly spherical this means that all the perpendicular rays meet at the centre of this sphere and this is where the image of the object is formed. The rays coming from the viewed object to the centre of the sphere form a visual cone like that of Euclid and Ptolemaeus but with the rays going from object to eye and not from the eye to the object. This explains or justifies his retention of their geometric optics. Alongside making vision purely based on light this justification of a geometric optics within an intromission theory is Ibn al-Haytham’s second major contribution to the evolution of optics.

Lindberg p. 72

Ibn al-Haytham’s visual cone from object to eye

You will often come across the claim that Ibn al-Haytham established his theory of vision experimentally and empirically, this is simply not true. The theory of vision is argued entirely philosophically without any experimentation involved. The experiments appear first in the later chapters of his Kitab al-Manazir where he deals with the mathematics of reflection and refraction, in both cases building on and extending the work of Ptolemaeus in his Optics.

The structure of the human eye according to Ibn al-Haytham showing optic nerve transmitting image to brain —Manuscript copy of his Kitāb al-Manāẓir (MS Fatih 3212, vol. 1, fol. 81b, Süleymaniye Mosque Library, Istanbul) Source: Wikimedia Commons

Because of these false claims, Ibn al-Haytham, like Galileo, is often credited with being the inventor of modern science, or the inventor of empirical experimental science, or the inventor of the scientific method, or the inventor of mathematics based science, all of which claims are total rubbish. It is in particular rubbish because almost everything he did was a copy and extension of the empirical, experimental work done by Ptolemaeus. There are even people who make these claims for both Ibn al-Haytham and Galileo! Are they really one and the same scientist cursed to travel through time inventing modern science  over and over again?

In the section on reflection Ibn al-Haytham describes a very complex and sophisticated experimental set up to investigate reflection in plane, concave, and convex mirrors. As already noted these experiments are more complex version of the ones that can be found in Ptolemaeus’ work, so not as ground-breaking as they are very often painted. However, having  described in great detail the set up and how it supposedly worked Mark Smith has the following to say:

Indeed, given its obvious unfeasibility as actually described–with all the planes perfectly aligned and all measurements perfectly reproduced–the test appears to have been an elaborate thought experiment designed to confirm what Alhacen already took for granted, that is, that light reflects at equal angles. The experiment is therefore intellectually but not physically replicable.^[6]

Ibn al-Haytham does, however, go on to subject the topic of reflection to a detailed, very accurate, high level mathematical analysis. 

As already mentioned following on to his analysis of reflection Ibn al-Haytham now handles the topic of refraction, once again taking Ptolemaeus as his inspiration and role model. Once again we get a complex experimental set up and once again, this time for different reasons, Mark Smith doubts whether they were ever carried out:

We are therefore led to raise the same doubt about feasibility that we did with the reflection experiment, and in this case the doubt is deepened by Alhacen’s failure to acknowledge the problem posed by critical angle for the tests for refraction from glass to air and glass to water. In short, there is good reason to believe that he did not carry out the experiment as described, which helps explain his failure to provide any values. That in turn raises serious doubt about the experiment’s replicability and, therefore, its “modernity.” Furthermore, its originality is questionable in that it is clearly based on Ptolemy’s experimental derivation of the angles of refraction.^[7]

As with the section on reflection there is extensive mathematical analysis.

Although Ibn al-Haytham building on the work of others very clearly laid the foundations of modern optics, it would be a mistake to think that his work immediately established itself as the go to theory of the discipline. The rival theories of al-Kindī, Ibn  Sīnā, and Ibn Rushd continues to have their supporters almost all the way down to the seventeenth century.

I have now sketched the full spectrum of theories of vision presented by scholars during the Islamic Middle Ages. All of these theories would be translated into Latin during the twelfth century and as we will see in a later episode would have a major impact. 

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^[1] David C. Lindberg, Theories of Vision: From Al-Kindi to Kepler, University of Chicago Press, 1976, p. 19

^[2] Lindberg, pp. 21-22

^[3] Lindberg, p. 23

^[4] Lindberg, p. 38

^[5] Lindberg, pp. 38-39

^[6]A. Mark Smith, From Sight to Light: The Passage from Ancient to Modern Optics, University of Chicago Press, 2015, p. 199

^[7] Smith, p. 218

From τὰ φυσικά (ta physika) to physics – XVII

As I explained in episode XII of this series where I introduced the work of the ancient Greek engineers and their machines, the discipline mechanics derives its name from the study of machines.

Greek μηχανική mēkhanikḗ, lit. “of machines” and in antiquity it is literally the discipline of the so-called simple machines: lever, wheel and axel, pulley, balance, inclined plane, wedge, and screw. 

Just as some scholars during the ‘Abbāsid  Caliphate studies, absorbed, criticised, and developed the works of Aristotle and John Philoponus on motion, and those of Aristotle and Ptolemaeus on astronomy, so there were others who took up the translated works of the Greek engineers such as Hero of Alexandria and Philo of Byzantium, extending and improving their work on machines. The Islamic texts on machines have an emphasis on timekeeping and hydrostatics.

For the earliest Islamic book on machines, we turn once again to the translation power house, the Persian Banū Mūsā brothers  Abū Jaʿfar, Muḥammad ibn Mūsā ibn Shākir (before 803 – February 873); Abū al‐Qāsim, Aḥmad ibn Mūsā ibn Shākir (d. 9th century) and Al-Ḥasan ibn Mūsā ibn Shākir (d. 9th century), the sons of the astronomer and astrologer on the court of the ‘Abbāsid caliph al-Maʾmūn, Mūsā ibn Shākir. Amongst their approximately twenty books, of which only three survived, the most famous is Kitab al-Hiyal al Naficah (Book of Ingenious Devices), which draw on knowledge of the works of Hero and Philo but also on Persian, Chinese, and Indian sources but which goes well beyond anything achieved by their Greek predecessors.  

It contains designs for almost a hundred trick vessels and automata the effects of which, “were produces by a sophisticated, if empirical, use of the principles of hydrostatics, aerostatics, and mechanics. The components used included tanks, pipes, floats siphons, lever arms balanced on axles, taps with multiple borings, cone-valves , rack-and-pinion gears, and screw-and-pinion gears.”^[1]

A thirsty bull gets to drink. Courtesy of Library of Topkapi Palace Museum, Istanbul, manuscript A.3474, model 6.

How a thirsty bull gets to drink. From D. Hill, The Book of Ingenious Devices, model 6.

(Right) Lamp with a perpetual wick. Courtesy of Staatsbibliothek zu Berlin, Preußischer Kulturbesitz, arabischen Handschriften, manuscript 5562, model 96. (Left) Inner workings of a lamp with a perpetual wick. From D. Hill, The Book of Ingenious Devices, model 96.

In the ninth century the ‘Abbāsid caliph al-Mustaʿīn (c. 836 – 17 October 866) commissioned the philosopher, physician, mathematician, and astronomer Qusta ibn Luqa al-Ba’albakki (820–912) to translate Hero’s Mechanica, a text in which Hero explored the parallelograms of velocities, determined certain simple centres of gravity, analysed the intricate mechanical powers by which small forces are used to move large weights, discussed the problems of the two mean proportions, and estimated the forces of motion on an inclined plane, which has only survived in the Arabic translation. 

Ibn Khalaf al-Murādī

In al-Andalus in the eleventh century, the engineer Ibn Khalaf al-Murādī about whom we know almost nothing authored Kitāb al-asrār fī natā’ij al-afkār (The Book of Secrets in the Results of Ideas), which describes 31 models consisting of 15 clocks, 5 large mechanical toys (automata), 4 war machines, 2 machines for raising water from wells and one portable universal sundial.

When I looked at the science of engineering and saw that it had disappeared after its ancient heritage, that its masters have perished, and that their memories are now forgotten, I worked my wits and thoughts in secrecy about philosophical shapes and figures, which could move the mind, with effort, from nothingness to being and from idleness to motion. And I arranged these shapes one by one in drawings and explained them.

Al-Muradi, The Book of Secrets in the Results of Ideas

Page from The Book of Secrets in the Results of Ideas

Page from The Book of Secrets in the Results of Ideas

Page from The Book of Secrets in the Results of Ideas

The most spectacular of all the Islamicate text on machines and mechanics is the Kitab fi ma’rifat al-hiyal al-handasiya, (The Book of Knowledge of Ingenious Mechanical Devices) commissioned in Amid (modern day Diyarbakir in Turkey) in 1206 by the Artuqid ruler Nāṣir al-Dīn Maḥmūd (ruled 1201–1222) and created by the artisan, engineer artist and mathematician Badīʿ az-Zaman Abu l-ʿIzz ibn Ismāʿīl ibn ar-Razāz al-Jazarī (1136–after 1206).

All that we know about al-Jazarī comes from his book. He was born in 1136 in Upper Mesopotamia the son of the chief engineer at the Artuklu Palace, the residence of the Mardin branch of the Artuqids the vassal rulers of Upper Mesopotamia, a position he inherited from his father. Al-Jazarī was an artisan rather than a scholar, an engineer rather than an inventor. 

The book, which al-Jazarī wrote at the command of Nāsir al-Dīn, is divided into fifty chapters, grouped into six categories; I, water clocks and candle clocks (ten chapters); II, vessels and figures suitable for drinking sessions (ten chapters); III, pitchers and basins for phlebotomy and ritual washing (ten chapters); IV, fountains that change their shape and machines for the perpetual flute (ten chapters); V, machines for raising water (five chapters); and VI, miscellaneous (five chapters): a large ornamental door cast in brass and copper, a protractor, combination locks, a lock with bolts, and a small water clock. Donald R. Hill, DSB

A Candle Clock from a copy of al-Jazaris treatise on automata

Al-Jazari’s “peacock fountain” was a sophisticated hand washing device featuring humanoid automata which offer soap and towels.

His work was clearly derivative and he cites the  Banū Mūsā, the mathematician, astronomer, and astrolabe maker Abū Ḥāmid Aḥmad ibn Muḥammad al‐Ṣāghānī al‐Asṭurlābī (died, 990), Hibatullah ibn al-Husayn (d. 1139), and a Pseudo-Archimedes as sources. Many of his devices are improved models of ones described by Hero of Alexandria and Philo of Byzantium. He probably also drew on Indian and Chinese sources. 

The book is clearly written in straightforward Arabic; and the text is accompanied by 173 drawings, ranging from rudimentary sketches to full page paintings. On these drawings the individual parts are in many cases marked with the letters of the Arabic alphabet, to which al-Jazarī refers in his descriptions. The drawings are usually in partial perspective; but despite considerable artistic merit, they seem rather crude to modern eyes. They are, however, effective aids to understanding the text. Donald R. Hill, DSB

Diagram of a hydropowered perpetual flute from The Book of Knowledge of Ingenious Mechanical Devices by Al-Jazari in 1206.

The elephant clock was one of the most famous inventions of al-Jazari

The book was obviously fairly widespread in Islamicate culture judging by the number of surviving manuscripts but unlike the work of the Banū Mūsā it was first translated from the Arabic into a European language in modern times. 

Our last Islamic engineer is the Ottoman Turk polymath Taqi ad-Din Muhammad ibn Ma’ruf ash-Shami al-Asadi (1526–1585), who as we saw in the last episode designed, built, and managed the observatory in Istanbul for Sultan Murad III (1546–1595). Taqī al-Dīn is famous for his mechanical clocks about which he wrote two books. 

1. The Brightest Stars for the Construction of Mechanical Clocks (al–Kawākib al–durriyya fī waḍ ^ҁ al–bankāmāt al–dawriyya) was written by Taqī al-Dīn in 1559 and addressed mechanical-automatic clocks. This work is considered the first written work on mechanical-automatic clocks in the Islamic and Ottoman world. Taqī al-Dīn mentions that he benefited from using Samiz ‘Alī Pasha’s private library and his collection of European mechanical clocks.
2. al–Ṭuruq al–saniyya fī al–ālāt al–rūḥāniyya is a second book on mechanics by Taqī al-Dīn that emphasizes the geometrical-mechanical structure of clocks, which was a topic previously observed and studied by the Banū Mūsā and al-Jazarī.

Mechanical clock of Taqī al-Dīn. Image taken from Sifat ālāt rasadiya bi-naw’in ākhar.

He also wrote The Sublime Methods in Spiritual Devices (al-Turuq al-saniyya fi’1-alat al-ruhaniyya) a treatise in six chapters 1) clepsydras, 2) devices for lifting weights, 3) devices for raising water, 4) fountains and continually playing flutes and kettle-drums, 5) irrigation devices, 6) self-moving spit. 

Sixteenth-century Ottoman scientist and engineer Taqi al-Din harnessed surging river water in his designs for an advanced six-cylinder pump, publishing his ideas in a book called ‘The Sublime Methods of Spiritual Machine’. 
The pistons of the pump were similar to drop hammers, and they could have been used to either create wood pulp for paper or to beat long strips of metal in a single pass.

The self-moving spit in part six uses an early steam turbine as motive power:

“Part Six: Making a spit which carries meat over fire so that it will rotate by itself without the power of an animal. This was made by people in several ways, and one of these is to have at the end of the spit a wheel with vanes, and opposite the wheel place a hollow pitcher made of copper with a closed head and full of water. Let the nozzle of the pitcher be opposite the vanes of the wheel. Kindle fire under the pitcher and steam will issue from its nozzle in a restricted form and it will turn the vane wheel. When the pitcher becomes empty of water bring close to it cold water in a basin and let the nozzle of the pitcher dip into the cold water. The heat will cause all the water in the basin to be attracted into the pitcher and the [the steam] will start rotating the vane wheel again.” 

Naturally by Taqī al-Dīn’s time the Renaissance was in full swing in Europe and European artist-engineers were already writing their own books on machines and mechanics. 

As can be seen Islamic engineers knew of and built on the work of their Greek predecessors and the work of the Banū Mūsā and Ibn Khalaf al-Murādī became known in Europe exercising an influence on the European developments in machines and mechanics. There was also an information flow in the 16^th century between the observatory in Istanbul and Europe.

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^[1] E. R. Truitt, Medieval Robots: Mechanisms, Magic, Nature, and Art, University of Pennsylvania Press, 2015 p. 20 quoting Donald Hill, “Medieval Arabic Mechanical Technology,” in Proceedings of the First International Symposium for the History of Arabic Science, Aleppo, April 5–12 1976, Aleppo: Institute forb the History of Arabic Science, 1979.

From τὰ φυσικά (ta physika) to physics – XV

Over time, the translation movement stated by the ‘Abbāsid Caliph al-Manṣūr (714–775) translated a large part of the works of Aristotle into Arabic. His philosophy was warmly welcomed by the Islamic philosophers, who didn’t just read it but analysed it with great care and wrote long and deep commentaries on it. The works of Aristotle were from this source reintroduced into Europe in the twelfth century, together with the, often critical, commentaries of the Islamic scholars, this time translated from Arabic into Latin, sometimes via Hebrew. This led, thanks largely to the work of Albertus Magnus (c. 1200–1280) and his pupil Thomas Aquinas (c. 1225–1274), to the acceptance of Aristotle on the then still comparatively young, medieval European universities and the beginnings of scholasticism. All of this, of course, lies in the future and we first want to look at how Islamic scholars accepted and reacted to Aristotle’s theories of motion, fall and projectile motion. This reception was influenced by the writings on the subject of John Philoponus (c. 490–c. 570), which had also been translated into Arabic, and which, whilst largely ignored in late antiquity and the early European Middle Ages, enjoyed a strong reception under Islamic scholars. 

Working our way forward chronologically, our first Islamic scholar who took up the works of Aristotle was Abū Naṣr Muḥammad al-Fārābī (c. 870–950/951), known in Latin as Alfarabius. al-Fārābī, a polymath, was born in Trasoxiana (modern Turkestan) the son of a military soldier.

Iranian stamp with al-Farabi’s imagined face Source: Wikimedia Commons

Whether his was Turkic or Persian is not known. Little is known of his childhood but he went to Harran to study under the Nestorian Christian Yuhanna ibn Haylan. Later he moved to Baghdad to continue his studies under Ibn Haylan and also studied logic with Abu Bishr Matta ibn Yunus (d. 940) and Arabic grammar with Abu Bakr ibn al-Sarraj (c. 875–c. 928).

al-Farabi on the currency of the Republic of Kazakhstan Source: Wikimedia Commons

Later in life he moved to Damascus and then to Alexandria before returning to Damascus, which is where he probably died. His importance for the history of physics is not direct. However, he attempted to reconcile the philosophies of Plato and Aristotle in the tradition of the Neoplatonists. Drawing attention to their works for other Islamic scholars. In his work he provided the first comprehensive Arabic classification of the sciences in his Kitab al-ibsa al ‘Ulum (Catalog of Sciences). It is a largely Aristotelian in nature and was adopted, amongst others, by Ibn al-Haytham (c. 965–1039) and Ibn Rushd (1126–1198). His only direct contribution to physics was a new argument in his On Vacuum on  the nature of the existence of void, concluding that air’s volume can expand to fill available space, and he suggested that the concept of perfect vacuum was incoherent.

Our next Islamic scholar is Abū Rayhān Muhammad ibn Ahmad al-Bīrunī (973–after 1050) possibly the most polymathic of all Islamic scholars.

An imaginary rendition of Al Biruni on a 1973 Soviet postage stamp Source: Wikimedia Commons

He was born in an outlying district of Kath the capital of the Afrighid Kindom of Khwarazm, part of the Persian Empire before it was conquered by the Muslims, now in Uzbekistan. Depending who is doing the describing he is described as Khwarezmian, Persian, or Uzbeki. He led a very complex life, which would turn this post into a book if I tried to describe it. He is reputed to have written 146 books on a very wide range of subjects., although his main areas of study were astronomy, mathematics, and geography. He lived for a time in India studying the land, its cultures, and its peoples. The book he wrote on India is his most well-known work. His only real contribution to physics was his use of a hydrostatic balance to experimentally determine the density of many different substances. “He reports very precise specific gravity  determinations for eight metals, fifteen other solids (mostly precious or semiprecious stones), and six liquids.” (DSB). He carried out a major dispute with Ibn Sīnā (980-1073) in which he rejected Aristotle’s claim that the Earth is eternal.

Abū ʿAlī al-Ḥusayn bin ʿAbdullāh ibn al-Ḥasan bin ʿAlī bin Sīnā al-Balkhi al-Bukhari (980-1073), known in Latin as Avicenna, was one of the most influential of all Islamic philosophers within the Islamic Empire and one of the two most important Islamic philosophers, when translated into Latin during the twelfth century Scientific Renaissance. Born into a Persian family in Transoxiana near the city of Bukhara, today in Uzbekistan. He had a comprehensive and wide-ranging education and became a physician. 

Portrait of Avicenna on a Iranian postage stamp Source: Wikipedia Commons

Although he wrote books on almost all subjects, his two most important works are Kitāb al-Shifāʾ (The Book of Healing) an encyclopaedia of science and philosophy, intended to cure the souls and the five volume al-Qānūn fī al-Ṭibb (The Canon of Medicine) and encyclopaedia of medicine. The latter an Aristotelean take on the works of Hippocrates and Galen became a standard work in Europe during the Middle Ages and Renaissance and was still in use in the seventeenth century. Avicenna’s philosophical work, a Neoplatonic Aristotelianism came to overshadow and replace the philosophical work of al-Fārābī, Farabism. 

In The Book of Healing, probably influenced by John Philoponus, Ibn Sīnā developed a theory of motion in which he distinguished between the inclination or tendency to motion and the force of a projectile. Projectile motion was the result of an inclination (mayl) transferred to the projectile by the thrower. He concluded that projectile motion in a vacuum would not cease. For him inclination was a permanent force whose effect was dissipated by external forces such as air resistance. 

Abu’l-Barakāt Hibat Allah ibn Malkā al-Baghdādī (c. 1080–1164) was born Baruch ben Malka into a Jewish family in Balad on the Tigris north of Mosul in modern Iraq. He only converted to Islam late in life. He is regarded as a follower of Ibn Sīnā and was like him a physician. He was an Aristotelian but heavily criticised Aristotle’s theories of motion. 

al-Baghdādī ??

He showed, in his theories, that velocity and acceleration are two different things and that force is proportional to acceleration and not velocity.  He “proposed an explanation of the acceleration of falling bodies by the accumulation of successive increments of power with successive increments of velocity. ( A. C. Crombie Augustine to Galileo v.2, p.67). He further developed Philoponus’ theory of impetus, stating that the mover imparts a violent inclination (mayl qasri) on the moved and that this diminishes as the moving object distances itself from the mover. (  Gutman, Oliver (2003), Pseudo-Avicenna, Liber Celi Et Mundi: A Critical Edition, Brill,  p. 193) He further suggested that “there is motion only if the relative positions of the bodies in question change.” He also stated that “each type of body has a characteristic velocity that reaches its maximum when its motion encounters no resistance.  ( Langermann, Y. Tzvi, “al-Baghdadi, Abu ‘l-Barakat (fl. c.1200-50)”, Islamic Philosophy, Routledge Encyclopedia of Philosophy 1998) ,

Abū Bakr Muḥammad ibn Yaḥyà ibn aṣ-Ṣā’igh at-Tūjībī ibn Bājja (c. 1085–1138), known in Latin as Avempace, was an Arab born in Zaragoza in al-Andalus, today’s Spain. Another polymath he made important contribution to botany in his Kitāb an-Nabāt (“The Book of Plants”).

An imaginary sketch representing Muslim polymath Ibn Bājja. Source: Wikimedia Commons

Much of what we know about his theories of motion comes from the extensive criticism of them by Ibn Rushd, (1126–1198). The philosopher Ernest A. Moody identifies four main reasons for regarding Ibn Bājja as a major figure in the development of the theory of impetus:

1. “For Avempace…V = P – M, so that when M = 0, V = P. This opposes Aristotle’s (supposed use of) V = P / M.” 

2. “Internal coherence with this “law of motion” requires, Moody believes, also a defence of the theory of an impressed force – as we find for example in Philoponus himself.” 

3. “Avempace’s appeal to an ‘impressed force’ was also reflected in the fact that ‘if we use modern terms, it might be said that the force of gravity, for Avempace, is not determined essentially as a relation between the masses of different bodies, but is conceived as an absolute indwelling power of self-motion animating the body like a soul.” 

4. “The theory of an ‘impressed force’ appears to have been upheld by al-Bitruji, who was influenced ins ideas by Avempace’s disciple Ibn-Tofayl.”

Ibn Bājja argued that even in a void a body would move with finite velocity because, although there was no resistance, the body would still have to traverse distance. (( A. C. Crombie Augustine to Galileo v.2, p.67). 

We turn briefly to ʾAbū Bakr Muḥammad bin ʿAbd al-Malik bin Muḥammad bin Ṭufayl al-Qaysiyy al-ʾAndalusiyy (c. 1105–1185), Latin Abubacer Aben Tofail. Born in al-Andalus in Guadix near Granada into an Arabic family, he was as stated above in 4. a student of Ibn Bājja. He is notable for having agitated to reject Ptolemaic astronomy and return to a purer Aristotelian homocentric astronomy.

An imaginary sketch representing Muslim polymath ʾAbū Bakr Muḥammad Ibn Ṭufail. Source: Wikimedia Commons

Ibn Tufayl in turn influenced Nur al-Din Ibn Ishaq al-Betrugi (died c. 1204), known in Latin as Alpetragius, about whom almost nothing is known except that he probably came from near Cordoba. He adopted both an impetus theory of projectile motion and an Aristotelian homocentric astronomy model from Ibn Tufayl, combining the two to suggest, like Philoponus, impetus as the form of motion of the planets. 

Nur ad-Din al-Bitruji

Ibn Tufayl was heavily involved in politics and was a secretary for the ruler of Granada, and later as vizier and physician for Abu Yaqub Yusuf (1135–1184), the Almohad caliph. The Almohad Caliphate ruled over Southern Spain and Northern Africa from 1121 to 1269. Ibn Tufayl named Abū l-Walīd Muḥammad Ibn ʾAḥmad Ibn Rushd; (1126–1198), Latin Averroes. Ibn Rushd was together with Ibn Sīnā the second of the two most important Islamic philosophers, when translated into Latin during the twelfth century Scientific Renaissance.

Ibn Rushd was born in Cordoba into a family well known in the city for their public service, especially in the legal and religious fields. He was probably of mixed Muladí and Berber ancestry. The Muladí were the native population of the Iberian Peninsula before the Muslim conquest. He was a strict adherent of Aristotelian philosophy rejecting the Neoplatonic interpretations of al-Farabi and Ibn Ibn Sīnā. He came to be regarded as the greatest of the Islamic Aristotelians and acquired the title of The Commentator in medieval Europe. 

Detail of Averroes in a 14th-century painting by Andrea di Bonaiuto Source: Wikimedia Commons

He followed Ibn Tufayl in rejecting the deferent and epicycle models of Ptolemy in favour of the homocentric spheres of Aristotle. However, he also rejected the impetus theory that Ibn Tufayl had inherited from Ibn Bājja. 

In his commentary on Aristotle’s Physics, Ibn Rushd launches a detail attack on Ibn Bājja’s theory of motion, which includes quotes from Ibn Bājja’s lost work on physics. This debate between the two theories, Aristotle contra Philoponus, as presented by Ibn Rushd was taken up again in Europe in the thirteenth century as part of the Scientific Renaissance with European medieval scholars taking up arms respectively for Averroes or Avempace. 

All of these Islamic polymathic philosophers, spread out over nearly two centuries, had the philosophy of Aristotle at the core of their own work. The majority, however, in a modified Neoplatonic version. When dealing with Aristotle’s concepts of motion, the ideas of John Philoponus came to play a central modifying role, with the notable exception of the work of Ibn Rushd. Through the discussion and adoption of Philoponus’ proto-impetus theory meant that when the big twelfth century, Scientific Renaissance translation movement was up and running this alternative to Aristotle’s concepts became once again available in medieval Europe. 

Magnetic Variations – V William Gilbert

We have now reached the pinnacle of investigations into magnetism and the magnetic compass, during the Early Modern Period, with the publication of William Gilbert’s De magnete in 1600. I will be handling it in four separate posts–a biography of Gilbert, a presentation of the book, a possible/probably co-author, and the dispute of the disciples. It is interesting to look at Gilbert as a whole and not just as the author of De magnete, because he had a long and successful career as a physician, which would make him a figure of interest in the histories of science and medicine if he had never carried out his research into magnetism. All of which tends to get overlooked because of the significance of De magnete. I found it wrong when somebody changed the title of his Wikipedia article from William Gilbert (physician) to William Gilbert (physicist) arguing This guy seems way more noticeable as a physicIST than as a physicIAN. Correct, in my opinion would be William Gilbert (physician) because that is what he was and did. His magnetic investigations were secondary in his life. 

William Gilbert artist unknown Welcome Library vis Wikimedia Commons

Gilbert^[1] was born into a rising, middle-class family that had only recently acquired its well-to-do status. His great-grandfather, John Gilbert, had married Joan Tricklove, the only daughter of a wealthy merchant from Clare, Suffolk. Their son, William Gilbert of Clare, became a weaver and eventually sewer [server] of the chamber to Henry VIII. This William married Margery Grey, and among their nine children was Jerome Gilbert. Jerome, who had some knowledge of law, moved from Clare to Colchester in the 1520’s became a free burgess and recorder there, and married Elizabeth Coggeshall. The oldest of their four children was William Gilbert of Colchester. (DSB)

Timperleys, the 15th-century home of the Gilbert family in Colchester. Source: Wikimedia Commons

By 1558 Jerome Gilbert had married for the second time to Jane Wingfield, who bore him a further nine children. There are no real records of Williams life before he matriculated from St John’s College, Cambridge in May 1558. There is no record of his birth or baptism, but a later nativity listed 2:20 pm, 24 May 1544. However, the monument erected by his stepbrothers Ambrose and William in Holy Trinity Church in Colchester states that he was born in the town of Colchester but gives his age at death in 1603 as sixty-three, placing his birth in 1540. 

Source: Welcome Collection via Wikimedia Commons

Local tradition says that he attended Colchester Royal Grammar School founded in 1128 and granted a royal charter by Henry VIII in 1539. It would be granted a second royal charter by Elizabeth I in 1584. However, there is no proof of his having attended the grammar school and his family was wealthy enough that he could have had a private tutor. In Cambridge he graduated BA  and was admitted to a fellowship of St John’s in 1561. He graduated MA in 1564. He served in the junior position of mathematical examiner in 1565 and 1566, graduating MD in 1569. He was senior bursar in January 1570, then left Cambridge to set up a medical practice in London. 

The inscription on his monument states that he practiced for more than thirty years in London. He was obviously successful acquiring a clientele amongst the gentry and aristocracy. He obtained a grant of arms in 1577 and was moving in court circles by 1580. 

Source: Wikimedia Commons

The most important body for medical practitioners was the London College of Physicians. It was established with a royal charter by Henry VII in 1518, although it didn’t start being called the Royal College of Physicians until late in the seventeenth century. 

Charter of incorporation for the College by Henry VIII under the Great Seal, 1518

It was set up as the first official licencing body for physicians in England but only for the City of London and an area of seven miles around it. Up until the sixteenth century there were no controls on who could practice as a physician in England. Previously in the sixteenth century there had been an Act of Parliament in 1511, which gave bishops the power to licence physicians for their dioceses. The setting up of the College of Physicians was the next set in establishing control in the matter, but as noted it only had authority in and around London. The whole thing was set up upon the initiative of Thomas Linacre (c. 1460–1524), who was its first president and benefactor, bequeathing his house and his library to the college.

Portrait of Thomas Linacre (or Lynaker) (c.1460-1524), copied by William Miller (College Beadle and amateur painter), 1810, from a painting at Windsor Castle. This is the usually accepted image of Linacre. However the identification has been challenged and the original at Windsor is now catalogued as An Elderly Man. Source: Wikimedia Commons

In 1523 an Act of Parliament extended their licensing powers to the whole of England, but the licensing was to be carried out in London. There are only very few cases of physicians outside of London, who had been licensed by the college. 

As well as his social climb as a physician Gilbert made a successful career within the College of Physicians. Around 1580 he was elected to one of the about thirty fellowships of the college holding the post of censor, regulating standards of practice, between 1581 and 1590. He held the post of treasurer to the college twice from 1587 to 1594 and again from 1597 to 1599, he was consiliarius from 1597 to 1599 and finally elected president in 1600. 

Between 1589 and 1594 Gilbert was involved in the college’s first, controversial, and aborted attempts to produce a pharmacopoeia. The Pharmacopoeia Londinensis finally saw the light of day in 1618  backed up by a royal proclamation from King James I. The proclamation enabled the Royal College of Physicians to create an officially sanctioned list of all known medical drugs, their effects, and directions on their use. No one was allowed to concoct any medicine or sell any substance if it did not appear in the Pharmacopoeia Londinensis. Of historical interest in the fact that Nicholas Culpeper’s legendary Herbal was a deliberate attempt to break the college’s monopoly on medical treatments. 

Pharmacopoeia Londinensis in facsimile RCP

His social status continued to rise in the same period adding the powerful Cecil family to his patrons. He attended the death of Mildred Cecil, Lady Burghley (née Cooke)in 1589 and that of William Cecil, Lord Burghley, Elizabeth I chief counsellor, in 1598. His social climb reached a peak with his formal appointment for life as a physician to Elizabeth I in April1601. He was re-appointed royal physician to James I & VI shortly before his own death in 1603.

Very little in known about his personal life. He remained unmarried but seems to have maintained close relations to his family, especially his half brothers and sisters. By 1595 Gilbert had acquired and moved into Wingfield house in St Peter’s Hill, a large property near St Paul’s Cathedral.

Site of St Peter’s Hill Source: Wikimedia Commons

This was possibly inherited from his stepmother Jane Wingfield. Here he developed an informal intellectual circle. This included the famous correspondent  John Chamberlin (1553–1628), who possessed a large circle of notable intellectual friend such as Sir Henry Wotton (1568–1639) and Thomas Bodley (1545–1613), and who lodged in Wingfield House. The physician and magnetic philosopher, Mark Ridley (1560–c. 1624), of whom we will hear much more in a later episode, also lodged in Wingfield House. Thomas Blundeville (c. 1522–c. 1606) author of Exercises (1594) covering a wide rang of cosmographical and navigational topics was a close friend, as was Lancelot Browne (c. 1545–1605) another royal physician, co-author with Blundeville of The Theoriques of the Seuen Planets (1602), an astronomy book that also published research of William Gilbert on magnetism, and which contained work by Henry Briggs (1561–1630) and Edward Wright (1561–1615), who we have met before and will meet again. William Harvey (1578–1657) married Lancelot Browne’s daughter Elizabeth. William Barlow (1544–1625) another magnetic philosopher whom we have met before and will meet again was also a member of this circle. 

As a physician Gilbert came into contact with London’s maritime community. In 1588, he and Lancelot Browne were approached by the privy council to administer drugs to sailors struck down by an epidemic, being two of four, ‘very fytt persons to be employed in the said Navye to have care of the helthe of the noblemen, gentlemen and others in that service.’ Gilbert was also proud of his conversations with the circumnavigators Francis Drake (c. 1540–1596) and Thomas Cavendish (1560–1592). Gilbert offered to write a book on tropical medicine for the chronicler of English exploration Richard Hakluyt (1553-1616) and advised Sir Francis Walsingham, Elizabeth’s security chief, on health issues during the hostilities with Spain.

At his death in 1603, Gilbert donated his library to the College of Physicians but his library, the college and Wingfield were all destroyed in the Great Fire of London in 1666.

Gilbert’s high social status, his status as a leading London physician, and his close circle of prominent intellectual friends almost certainly guaranteed a warm reception for De magnete when it was published in 1600. This was not the product of some unknown projector^[2] but the work of a man of substance with an excellent reputation.

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^[1] This biographical sketch relies heavily, but not exclusively, on the writings of Stephen Pumfrey, Gilbert’s best modern biographer. I just wish that Icon Books would reissue his Latitude & The Magnetic Earth: The True Story of Queen Elizabeth’s Most Distinguished Man of Science (2003) with footnotes, or even endnotes, and an index!

^[2] In the Early Modern and Enlightenment periods the figure of the projector was as vital as it was common. Daniel Defoe famously nicknamed his era the “Projecting Age.” Decades earlier scholars were already commenting on the “rampant passion for schemes”. Projectors were inventors or entrepreneurs ‘who set out to gain the trust and backing of a powerful patron such as a ruler or potential investor, for what he claimed was a financially profitable and generally prestigious original venture which would yield practical benefits.’

From τὰ φυσικά (ta physika) to physics – XIII

Just as the period of dominance of Aristotelian philosophy in antiquity was succeeded by the rise to dominance of Stoicism and Epicureanism, as I documented in the fifth episode of the series, so they too began to lose their hold on the world of thought in late antiquity. From the middle of the third till the middle of the seventh century CE thought in the ancient world was dominated by Neoplatonism. The term Neoplatonism is a neologism created to describe a renaissance of nominally Platonic thought that took place in this period. The term itself is to some extent misleading, whereas the terms Stoic, Peripatetic or Platonic signify a single school founder by a single philosopher with a set of doctrines developed by that founder, Neoplatonism doesn’t.  To quote the Stanford Encyclopedia of Philosophy:

Late antique philosophers now counted among “the Neoplatonists” did not think of themselves as engaged in some sort of effort specifically to revive the spirit and the letter of Plato’s dialogues. To be sure, they did call themselves “Platonists” and held Plato’s views, which they understood as a positive system of philosophical doctrine, in higher esteem than the tenets of the pre-Socratics, Aristotle, or any other subsequent thinker. However, and more importantly, their signature project is more accurately described as a grand synthesis of an intellectual heritage that was by then exceedingly rich and profound. In effect, they absorbed, appropriated, and creatively harmonized almost the entire Hellenic tradition of philosophy, religion, and even literature—with the exceptions of Epicureanism, which they roundly rejected, and the thoroughgoing corporealism of the Stoics. The result of this effort was a grandiose and powerfully persuasive system of thought that reflected upon a millennium of intellectual culture and brought the scientific and moral theories of Plato, Aristotle, and the ethics of the Stoics into fruitful dialogue with literature, myth, and religious practice. In virtue of their inherent respect for the writings of many of their predecessors, the Neoplatonists together offered a kind of meta-discourse and reflection on the sum-total of ideas produced over centuries of sustained inquiry into the human condition.

Plotinus (c. 204/5–270 CE) is regarded as the first of the Neoplatonists. Central to his philosophy and in fact to all of the Neoplatonists is monism expressed through the concepts of the One and Henosis.

Head in white marble. Ostia Antica, Museo, inv. 436. Neck broken through diagonally, head broken into two halves and reconstructed. Lower half of nose is missing. One of four replicas which were all discovered in Ostia. The identification as Plotinus is plausible but not proven. Source: Wikimedia Commons

Plotinus taught that there is a supreme, totally transcendent “One”, containing no division, multiplicity, or distinction; beyond all categories of being and non-being. His “One” “cannot be any existing thing”, nor is it merely the sum of all things (compare the Stoic doctrine of disbelief in non-material existence), but “is prior to all existents”. Plotinus identified his “One” with the concept of ‘Good’ and the principle of ‘Beauty’. (Wikipedia)

Henosis is the word for mystical “oneness”, “union”, or “unity” in classical Greek. In Platonism, and especially Neoplatonism, the goal of henosis is union with what is fundamental in reality: the One the Source, or Monad. (Wikipedia)

Plotinus was succeeded by his pupil Porphyry of Tyre (c. 234–c. 305 CE),

Porphire Sophiste, in a French 16th-century engraving Source: Wikimedia Commons

who was in turn succeeded by his pupil Iamblichus (c. 245–c. 325 CE).

Source: Wikimedia Commons

Both Theon of Alexandria (c. 335–c. 405 CE) and his daughter Hypatia (c. 360–c. 415 CE) were Neoplatonists but their philosophy differed from that of the acolytes of Iamblichus, which dominated Neoplatonic thought in Alexandria during their time. 

The Neoplatonic philosopher-mathematicians produced commentaries on and annotated editions of the major Greek mathematical works. Theon was a textbook editor, who produced annotated edition of Euclid’s Elements, Euclid’s Data, his Optics and Ptolemaios’ Mathēmatikē Syntaxis. Theon’s edition of the Elements was, until the nineteenth century, the only surviving edition.

Theon of Alexandria is best known for having edited the existing text of Euclid’s Elements, shown here in a ninth-century manuscript Vatican Library via Wikimedia Commons

We have no surviving works by Hypatia but the Suda, a tenth-century Byzantine encyclopaedia of the ancient Mediterranean world lists three mathematical works for her, which it states have all been lost. The Suda credits her with commentaries on the Conic Sections of the third-century BCE Apollonius of Perga, the “Astronomical Table” and the Arithemica of the second- and third-century CE Diophantus of Alexandria. Alan Cameron, however, argues convincingly that she in fact edited the surviving text of Ptolemaeus’ Handy Tables, (the second item on the Suda list) normally attributed to her father Theon as well as a large part of the text of the Almagest her father used for his commentary.  Only six of the thirteen books of Apollonius’ Conic Sections exist in Greek; historians argue that the additional four books that exist in Arabic are from Hypatia, a plausible assumption. So once again, what we have is that Hypatia was like her father a textbook editor.

Proclus Lycius (412–185) wrote a commentary on Euclid’s Elements. According to Thomas Heath in volume one of his edition of The Thirteen Books of Euclid’s Elements:

It is well known that the commentary of Proclus on Eucl. Book I is one of the two main sources of information as to the history of Greek geometry which we possess, the other being the Collection of Pappus.

First Latin edition of one of the major works by Proclus Lycaeus (412-485), founder and head of the neo-Platonic school of Athens: a commentary on the first book of Euclid’s “Elements of Geometry”, Source: Wikimedia Commons

Pappus of Alexandria (fl. 320) produced an encyclopaedic compendium of ancient Greek geometry, astronomy , and mechanics in eight books entitled, Synagoge (Συναγωγή) or Collection. This work, whilst highly important as a record of the history of Greek mathematics, remained virtually unknown until the sixteenth century when it was translated and published by Federico Commandino (1509–1575) in 1588. It became influential in the seventeeth century. The Suda credits him with a commentary on the first four books of Ptolemaios’ Mathēmatikē Syntaxis, now lost. He also wrote commentaries on Euclid’s Elements fragments of which are preserved in Proclus and on Ptolemaios’ Ἁρμονικά (Harmonika), now lost.

Title page of Pappus’s Mathematicae Collectiones, translated into Latin by Federico Commandino (1588). Source: Wikimedia Commons

Apart from small odds and ends, such as Pappus’ hexagon theorem in projective geometry, these Neoplatonic philosopher-mathematicians produced very little original work. However, their role in recording and conserving Greek mathematical works should not be underestimated.

The non-mathematical Neoplatonic philosophers also contributed almost nothing new to the roots of the discipline of physics that I have sketched in the previous episodes of this series but their obsessively inclusive, eclectic agglomeration of the works of earlier Greek philosophers, in particular Plato and Aristotle, meant that these works that had slid into the background during the dominance of Stoicism and Epicureanism was once again brought into the foreground and passed on down to future generations. 

All three of the monotheistic religions, Judaism, Christianity, and Islam took a strong interest in Neoplatonism because of its strongly monist core and often became first acquainted with the works of Plato, Aristotle, and other earlier Greek philosophers through Neoplatonic sources rather than through the originals. In the history of science transmission of sources often takes indirect roots.

Above I said that Neoplatonic philosophers also contributed almost nothing new to the roots of the discipline of physics, however, there is one very notable exception, the sixth century Christian, Neoplatonist John Philoponus (c. 490–c. 570) of Alexandria. Philoponus was a pupil and sometime amanuensis of the Neoplatonist philosopher Ammonius Hermiae (C. 440­–c. 520),who was also from Alexandria but had studied in Athens under Proclus before returning to Alexandria to teach. He lectured on Plato, Aristotle and Porphyry of Tyre, as well as on astronomy and geometry. As is often the case most of his supposed numerous writings have not survived. He is known to have lectured and written extensively over Aristotle as did Philoponus his pupil. However, whereas Ammonius seems to have been positive in his assessments of Aristotle, Philoponus was highly critical. 

Amongst his voluminous writings Philoponus wrote extensive critiques of almost all of Aristotle’s texts of which in our context a couple are of great importance. As a Christian Philoponus rejected Aristotle’s concept of an eternal cosmos, replacing it with a cosmos created by God in its entirety in one moment. Because his cosmos was a single unified whole he rejected Aristotle’s division of the cosmos into supralunar and sublunar regions. The cosmos was overall the same and subject to the same laws. In this he was following the Stoics, and his philosophy is heavily influenced by Stoic concepts. Philoponus also anticipates Descartes in stating that bodies have extension in space.

Most important in the history of physics Philoponus rejects both Aristotle’s concept of fall and his concept of projectile motion. It seems that, unlike Galileo, Philoponus really did drop objects of differing weight from a tower and concluded that they fall almost at the same speed:

“if one lets fall simultaneously from the same height two bodies differing greatly in weight, one will find that the ratio of their times of motion does not correspond does not correspond to the ration of their weights, but that the difference in time is a very small one” (In Physica, 683, 17).^[1]

He dismisses Aristotle’s theory of projectile motion and produces what would later become known as the theory of impetus an important precursor to the theory of inertia.

“some incorporeal kinetic power is imparted by the thrower to the object thrown “and that” if an arrow or a stone is projected by force in a void, the same things will happen much more easily, nothing being necessary except the thrower” (ibid, 641, 29).

Denying Aristotle’s distinction between sublunar and supralunar motion, Philoponus also applied his impetus concept to the motion of the planets.

Because of his deviant religious views on the nature of the Trinity, Philoponus was declared anathema at the Third Council of Constantinople, which limited the reception of his anti-Aristotelian dynamics in late antiquity, but his works were translated into Syriac and Arabic where they would have a significant influence as we shall see in future episodes.

Philoponus was the first philosopher to go beyond the dynamics of Aristotle and his concepts are the beginnings of the path that would eventually lead to the modern theories of that branch of physics.

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^[1] In Physica, H. Vitelli, ed. (Berlin, 1887)

From τὰ φυσικά (ta physika) to physics – XII

As I explained at the very beginning of this series the Greek concept ta physika was very different from what we envision when we hear the word physics today. In fact, this series is an attempt to sketch the path from the ta physika of Greek antiquity to the emergence of our modern physics in the Early Modern Period. We can find fragments of the roots of physics is various different areas of thought in antiquity and I have already looked at the philosophers, the mathematicians, the astronomers, ancient Greek optics, and statics. Today, I will turn my attention to the engineers, which means basically the first century BCE Roman architect, Vitruvius (c. 75–after c. 15 BCE)

A 1684 depiction of Vitruvius presenting De Architectura to Augustus. Source: Wikimedia Commons

and the first century CE Greek engineer and mathematician, Hero of Alexandria (fl. 60 CE).

Image of Hero of Alexandria from a 1688 German translation of Hero’s Pneumatics Source: Wikimedia Commons

Although there are other aspects to their work the principal reason for including them is their work on machines, as I pointed out in the last episode, mechanics comes from study of machines.  

Greek μηχανική mēkhanikḗ, lit. “of machines” and in antiquity it is literally the discipline of the so-called simple machines: lever, wheel and axel, pulley, balance, inclined plane, wedge, and screw. 

As I explained in my series on Renaissance Science the re-emergence of the works of Vitruvius and Hero in the Renaissance triggered a whole culture of artist engineers and of machine books, both of which played a significant role in the cross over between the theoretical book knowledge of the scholastics and the practical knowledge of the artisans or better said the dissolving of the boundary between them creating a meld between the two types of knowledge that would over the next two and a half centuries lead to the modern concept of knowledge or science. Whereas the early knowledge of machines consisted of how they function and how to construct them, the emerging modern physics explained why they work.

Both Vitruvius and Hero of Alexandria were building on a long tradition of machine-building, Ancient Greek engineers, most of whose work has not survived but who are referenced by later authors such as Vitruvius, Hero, and Pliny. We have the fourth century BCE military engineer Polyidus of Thessaly, who served under Philip II of Macedon (382–336) and his two students Diades of Pella and Charias, all three of whom are referenced by Vitruvius in his own section on siege engines in Book X of De architectura.

Polyidus of Thessaly is credited with the Helepolis siege tower, shown as model above Source: Wikimedia Commons

They are also included in a list of “those who have written about machines” in the preface to Book VII on Finishing:

…those who have written about machines like Diades, Archytas, Archimedes, Ctesibios, Nymphodoros, Philo of Byzantium, Diphilos, Democles, Charias, Polyidos, Pyrrhos, and Agesistratos. 

Taken from Vitruvius Ten Books on Architecture Ed. Ingrid D Rowland & Thomas Nobel Howe

Nymphodoros, Diphilos, and Democles are not otherwise known. Pyrrhos (318–272 BCE), King of Epirus, was a renowned military strategist, who wrote a thesis on siegecraft.

A marble bust of Pyrrhos from the Villa of the Papyri at the Roman site of Herculaneum, now in the National Archaeological Museum of Naples, Italy Source: Wikimedia Commons

I have a separate post on Archimedes (c. 287–c. 212 BCE), who is without doubt the most well-known engineer in antiquity. Archytas (c. 420–c. 355 BCE) was a mathematician associated with the Pythagoreans. He is thought to have been a pupil of the Pythagorean, Philolaus (c. 470–c. 385 BCE) and to have been the teacher of Eudoxus of Cnidus (c. 390–c. 340 BCE). Like many figures in antiquity much was written about him but none of his own writings have survived. He is credited with the creation of the concept of the quadrivium–arithmetic, geometry, music, astronomy–which became the basis of mathematical education first on the Latin schools and later the universities in the Middle Ages. Vitruvius’ Book X Chapters 13, 14, and 15 are almost identical to chapters on siegecraft from the Περὶ μηχανημάτων Perì mēchanēmátōn (On Machines) by Athenaeus Mechanicus (fl. mid-to-late 1^st century BCE) and the, no longer extant book, of Agesistratos (late 2^nd century BCE), about whom almost nothing in known, is thought to be the common source. 

This just leaves Ctesibios and Philo of Byzantium from Vitruvius’ list. Ctesibios (fl. 285–222 BCE) wrote extensively on compressed air, i.e. pneumatics, but none of his work survives. However, he is referenced by Athenaeus, Vitruvius, Pliny, Proclus, and Philo of Byzantium.

Hydraulic clock of Ctesibius, reconstruction at the Technological Museum of Thessaloniki Source: Wikimedia Commons

Philo of Byzantium (c. 280–c. 220 BCE), also known as Philo Mechanicus, only gets referenced by Vitruvius, Hero, and the mathematician Eutocius of Ascalon (c. 480s–c. 520s CE), who discussed his method for doubling a cube. Almost nothing is known about him, other than that he spent most of his life in Alexandria. He left only one known work is an encyclopaedic book on mechanics the Syntaxis (Μηχανική Σύνταξη, Mēkhanikḗ Sýntaxē). This only survives in fragments, but internal references allow us to recreate the titles of all nine sections:

•  Isagoge (Εἰσαγωγή, Eisagōgḗ) – Introduction (general mathematics)
• Mochlica (Μοχλικά, Mokhliká) – Leverage (mechanics)
• Limenopoeica (Λιμενοποιικά, Limenopoiiká) – Harbour Construction
• Belopoeica (Βελοποιικά, Belopoiiká) – Siege Engine Construction
• Pneumatica (Πνευματικά, Pneumatiká) – Pneumatics
• Automatopoeica (Αὐτοματοποιητικά, Automatopoiētiká) – Automatons (mechanical toys and diversions)
• Parasceuastica (Παρασκευαστικά, Paraskeuastiká) – Preparations (for sieges) 
• Poliorcetica (Πολιορκητικά, Poliorkētiká) – Siegecraft
• Peri Epistolon (Περὶ Ἐπιστολῶν, Perì Epistolō̂n) – On Letters (coding and hidden letters for military use)

Belopoeica, Parasceuastica, and Poliorcetica are extant in Greek, as are fragments of Isagoge and Automatopoeica. For a long time only the first sixteen chapters of Pneumatica were known in a Latin translation of an Arabic text but in the early twentieth century three new fuller Arabic manuscripts were found, one in the Bodleian and two in the library of the Hagia Sophia.

Philo of Byzantium. Pneumatica: Facsimile and Transcript of the Latin … 534, Bayerische Staatsbibliothek Munchen

As can be seen Vitruvius and Hero are part of a tradition of Greek mechanics that extends over more than five centuries but it is only with the two of them that we have complete books that were rediscovered, translated, and printed in the Early Modern Period, contributing significantly to the practical turn that was an important feature of the emergence of modern science.

Once again with Vitruvius, we have a figure from antiquity about whom we know very little. He seems to have worked in some capacity for Julius Caesar (100–44 BCE) and as a military engineer for Caesar’s grandnephew and adopted heir, Gaius Octavius (63 BCE–14 CE), later the Emperor Augustus. Upon retirement he came under the patronage of Augustus’ sister Octavia Minor (c. 66­–11 BCE). 

He is, of course, renowned as the author of De Architectura Libri Decem, (Ten Books on Architecture), which is actually a description not a title, signifying ten parchment scrolls on the subject of architecture. As with the Elements of Euclid, there is a discussion as to whether Vitruvius actually wrote all ten books or merely brought together and edited the contents produced by several authors. The ten books are:

• Book 1: First Principles and the Layout of Cities
• Book 2: Building Materials
• Book 3: Temples
• Book 4: Corinthian, Doric, and Tuscan Temples
• Book 5: Public Buildings
• Book 6: Private Buildings
• Book 7: Finishing
• Book 8: Water
• Book 9: Astronomy, Sundials and Clocks
• Book 10: Machines

Viewed from our standpoint a peculiar mixture of themes but in antiquity there existed no division between architecture and mechanical engineering. In fact, service as a military engineer, like Vitruvius, was one of the two available sources for architectural training. The other was an apprenticeship as a builder. Although this seems strange to us now, we should remember that Leon Battista Alberti (1404–1472), who wrote the first architectural treatise in the Renaissance, De re aedificatoria (On the Art of Building) based on Vitruvius, written between 1443 and 1452 but published in 1485 as the first printed book on architecture, was a mathematician, who considered mathematics as the foundation of the arts and the sciences.  Also following the Great Fire of London in 1666, the two architects who rebuilt London were Christopher Wren (1632–1723), astronomer, mathematician and physicist, and Robert Hooke (1635–1703), a polymath, who was predominantly a physicist Neither of them was a trained architect. 

Of the ten books, it is the last three that in the Early modern period had an influence on the emergence of physics. Book 8, which deals with the practical side of water supplies is in some respects a treatise on applied hydrostatics. 

All illustration from Vitruvius taken from Vitruvius Ten Books on Architecture Ed. Ingrid D Rowland & Thomas Nobel Howe, CUP, ppb. 2001 There are many more and I heartily recommend this book

Book 9 deals with time a central theme in physics and the water clocks that he describes also, like parts of Book 8, an application of hydrostatics, with the more complex ones also involving the construction of machines.

It is Book 10 he opens up the full panoply of mechanics, the construction of machines. We find pully systems, cranes for building sites, cranes for ships and harbours, methods for hauling large blocks, winches, water wheels, bucket chains, the water screw, water pumps, hydraulic organs, hodometers (a mileometer) on land and on water, and to close a wide range of military weapons and siege engines. All of these machines are on a theoretical level examples of applied physics and explaining how and why they worked in terms of forces was a natural consequence of the Renaissance machine culture that Vitruvius’s book helped to inspire.

Note the aeolipile in the middle of the second row under Pneumatic

Included amongst Vitruvius’ machines is the toy steam engine, the aeolipile, which is most commonly associated with Hero of Alexandria to whom we now turn.

Illustration accompanying Hero’s entry in Pneumatica, published in the first century AD. “No. 50. The Steam-Engine. PLACE a cauldron over a fire: a ball shall revolve on a pivot. A fire is lighted under a cauldron, A B, (fig. 50), containing water, and covered at the mouth by the lid C D; with this the bent tube E F G communicates, the extremity of the tube being fitted into a hollow ball, H K. Opposite to the extremity G place a pivot, L M, resting on the lid C D; and let the ball contain two bent pipes, communicating with it at the opposite extremities of a diameter, and bent in opposite directions, the bends being at right angles and across the lines F G, L M. As the cauldron gets hot it will be found that the steam, entering the ball through E F G, passes out through the bent tubes towards the lid, and causes the ball to revolve, as in the case of the dancing figures.” Source: Wikimedia Commons

Unlike Philo of Byzantium and Vitruvius, who each only wrote one book, Hero left us with several works and that is all that he left us. As one source put it, apart from his works we know nothing at all about him. The earliest mention of his works is by Pappus around 300 CE and he himself quotes Archimedes making c. 250 BCE another terminus. He has been dated from 150 BCE to 250 CE, but Otto Neugebauer demonstrated that a lunar eclipse that Hero describes, in his Dioptra, having observed took place in 62 CE, hence flourished c. 60 CE.

Hero was a mathematician and an engineer and based on his texts he is judged by historians to have been a practical man rather than a scholar, although some of his texts appear to be the lectures of a teacher. His work also shows him to have carried out much in the way of experiments. His surviving works are:

• Pneumatica (Πνευματικά), a description of machines working on air, steam or water pressure, including the hydraulis or water organ 
• Automata, a description of machines which enable wonders in banquets and possibly also theatrical contexts by mechanical or pneumatical means (e.g. automatic opening or closing of temple doors, statues that pour wine and milk, etc.) 
• Mechanica, preserved only in Arabic, written for architects, containing means to lift heavy objects
• Metrica, a description of how to calculate surfaces and volumes of diverse objects
• On the Dioptra, a collection of methods to measure lengths, a work in which the odimeter and the dioptra, an apparatus which resembles the theodolite, are described
• Belopoeica, a description of war machines 
• Catoptrica, about the progression of light, reflection, and the use of mirrors 

Automata by Hero of Alexandria (1589 edition) Source: Wikimedia Commons

Spiritali di Herone Alessandrino ridotti in lingua volgare da Alessandro Giorgi da Vrbino. – In Vrbino : appresso Bartholomeo, e Simone Ragusij fratelli, 1592. – [4], 82 c. : ill. ; 4º Source: Wikimedia Commons

Modern reconstruction of wind organ and wind wheel of Heron of Alexandria (1st century AD) according to W. Schmidt: Herons von Alexandria Druckwerke und Automatentheater, Greek and German, 1899 (Heronis Alexandrini opera I, Reprint 1971), p. 205, fig. 44; cf. introduction p. XXXIX Source: Wikimedia Commons

There are other works attributed to him, but the attributions are considered doubtful. As can be seen, apart from the Catoptics, which I dealt with separately in the episode on optics, his surviving work covers much of the same territory as the mechanical chapters of Vitruvius Like Vitruvius, Hero was a major influence on the evolution of the anti-scholastic scientific thought, when his texts became known in the Early Modern Period. 

From τὰ φυσικά (ta physika) to physics – XI

Having in the last two episodes dealt with the first two of the three so-called mixed sciences, astronomy and optics, I shall now deal with statics^[1]. Although receiving far less attention in antiquity that the other two, statics received much attention in the Middle Ages and the Early Modern Period and went on to become a constituent of modern physics, defined thus:

Statics is the branch of classical mechanics that is concerned with the analysis of force and torque acting on a physical system that does not experience an acceleration, but rather, is in equilibrium with its environment. (Wikipedia) 

In antiquity and the Middle Ages, the concept of force did not exist, so we here find the discipline developed around the concept of weight. Statics is one half of the discipline of mechanics from the ancient Greek μηχανική mēkhanikḗ, lit. “of machines” and in antiquity it is literally the discipline of the so-called simple machines: lever, wheel and axel, pulley, balance, inclined plane, wedge, and screw. 

Given that statics plays a major roll in engineering it is not surprising to find that Archimedes wrote one of the two principal texts on the subject in antiquity. 

Archimedes (c. 287–c. 212 BCE), whose work on the topic was his On the Equilibrium of Planes (Ancient Greek: Περὶ ἐπιπέδων ἱσορροπιῶν, Romanised: perí epipédōn isorropiôn) was not the first to tackle the subject.

Archimedes’ first suppositio: On plane equilibrium, Heiberg 1881, p. 142.  

His work was preceded by a text known in Latin as the Questiones Mechanicae (Mechanical Problems), which in the Middle Ages was attributed to Aristotle (384­–322 BCE) but is now considered to actually be by one of his followers or by some to be based on the earlier work of the Pythagorean Archytas (c.420–350 BCE).

Greek edition of the Questiones Mechanicae printed in Paris: Andreas Wechel, 1566.

There was also a On the Balance attributed, almost certainly falsely to Euclid (fl. 300 BCE), which won’t play a further role here. Later than Archimedes there was the Mechanica of Hero of Alexandria (c. 10–c. 70 CE), unknown in the phase of the Renaissance we shall be reviewing but discussed along with the work of Archimedes in Book VII of the Synagoge or Collection of Pappus (c. 290–c. 350 CE).

The two major texts are the pseudo-Aristotelian Questiones Mechanicae and Archimedes’ On the Equilibrium of Planes, which approach the topic very differently. The Questiones Mechanicae is a philosophical work, which derives everything from a first principle that all machines are reducible to circular motion. It gives an informal proof of the law of the lever without reference to the centre of gravity. The pseudo-Euclidian on the Balance contains a mathematical proof of the law of the lever, again without reference to the centre of gravity.

Pages from the Questiones Mechanicae

Pages from the Questiones Mechanicae

In Archimedes’ On the Equilibrium of Planes the centre of gravity plays a very prominent role. In the first volume Archimedes presents seven postulates and fifteen propositions using the centre of gravity to mathematically demonstrate the law of the lever.

Diagram to P6, 7. Two magnitudes, whether commensurable[Prop. 6] or incommensurable [Prop. 7], balance at distances reciprocally proportional to the magnitudes. Archimedes. “On the Equilibrium of Planes or The Centres of Gravity of Planes, Book I”. 
In The Works of Archimedes. Ed. T.L. Heath. Cambridge UP, 1897.

The volume closes with demonstrations of the centres of gravity of the parallelogram, the triangle, and the trapezoid. Centres of gravity are a part of statics because they are the point from which, when a figure is suspended it remains in equilibrium, that is unmoving. In volume two of his text Archimedes presents ten propositions relating to the centres of gravity of parabolic sections. This is achieved by substituting rectangles of equal area, a process made possible by his work Quadrature of the Parabola (Greek: Τετραγωνισμὸς παραβολῆς).

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^[1] This very short post is largely a repeat of the longer post on statics that I wrote in my Renaissance Science series of blog posts. However rather than simply refer to the earlier text by direct link I decided to include it here in this series for completeness sake.

From τὰ φυσικά (ta physika) to physics – VII

No figure looms larger in the history of ancient mathematics than Archimedes, a name surrounded by a dense cloud of stories, myths, and legends. However, one should never lose sight of the fact that behind all the marvellous narratives about setting fire to enemy ships with burning mirrors and overturning others with giant levers, the real Archimedes was one of the greatest mathematicians who ever lived, and his work had a major impact on the newly emerging sciences in the sixteenth and seventeenth centuries. 

Bronze statue of Archimedes in Syracuse Source: Wikimedia Commons

Literally millions of words have been written over the centuries about Archimedes but if you ignore the posthumous hagiography, nearly all of which should be taken with a very large pinch of salt, then in realty we know almost nothing about the man. His supposed life dates c. 287–c. 212 BCE are based on something written by the Byzantine Greek historian, John Tzetzes (c.1110–1180 CE), so approximately fourteen hundred years after he lived. We do know that he was born in Syracuse on the island of Sicily, at the time a self-governing Greek city, and that he tells us in the Sand-Reckoner that his father was Phidias, an astronomer. Here, the reliable or solid facts end, the rest is just speculation. However, unlike Euclid nobody has ever doubted his existence.

Based on his surviving writings, Archimedes is credited with being a mathematician, engineer, astronomer, and inventor. He is usually referred to as a physicist, and although anachronistic, as I pointed out in the first episode of this series, the term in its modern usage was a nineteenth century minting by William Whewell, it is justified as several of his texts definitely fall withing the scope of modern physics, which played a significant role in his influence during the sixteenth and seventeenth centuries. 

I shall ignore all of the war machines that Archimedes, the engineer, created for the defence of Syracuse, as described in the posthumous hagiographies, and concentrate instead on his know contributions to mathematics and science. Of course, the most popular presentation of Archimedes is the story of the crown, the bathtub, and running down the street shouting Eureka (Ancient Greek: εὕρηκα, Romanised: héurēka).

There is nothing remotely like this story in Archimedes own writings. It is also thought not to be real because the water displacement method of determining density that it supposedly led to, would be extremely difficult to realise due to the problems of accurately measuring the volume of water displaced. We will come to what he probably did later but first, feeling frivolous, I can’t resist repeating a terrible joke I first heard in my dim and distant youth:

Archimedes running down the street:  Eureka! Eureka! …

Man, he passes: You dona smella too gooda youselfa!

The so-called Archimedean Screw, which as the name suggests was named after him, a widespread method of raising water deserves at least a mention although there is no direct proof that he actually invented it.

As with other figures from antiquity there are works referenced by other writers that are no longer extant, in Archimedes’ case seven such works are recorded. The works that still exist, in the currently assumed order in which they were written, are Measurement of a Circle, The Sand Reckoner, On the Equilibrium of Planes, Quadrature of the Parabola, On the Sphere and Cylinder, On Spirals, On Conoids and Spheroids, On Floating Bodies, Ostomachion, The Cattle Problem, and The Method of Mechanical Theorems.

The Ostomachion is a geometrical puzzle similar to Tangram and The Cattle Problem is algebraic puzzle that requires the solution of a number of simultaneous Diophantine equations. The Cattle Problem was addressed to Eratosthenes and other Alexandrian mathematicians. The puzzles need not detain us here, but it is interesting to note that Archimedes had a playful side.

Measurement of a Circle is only a short fragment containing three propositions: 

1) The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference of the circle. 

2) The area of a circle is to the square on its diameter as 11 to 14.

3) The ratio of the circumference of any circle to its diameter is greater than

 but less than .

.

Proposition three is his approximation of π and proposition two is actually derived from it, so the order can not be original. Both propositions one and three are examples of Archimedes using the method of exhaustion.

Source: Wikimedia Commons

On the Equilibrium of Planes is in two books. Book one proves the law of the lever and contains propositions on the centre of gravity of the triangle and the trapezium. Book two has ten propositions on the centre of gravity of parabolic segments. This text would prove very important in the development of statics in the Early Modern Period.  

Quadrature of the Parabola has twenty-four propositions and culminates in the poof that the area enclosed by a parabola and a straight line is 4/3 the area of a triangle with equal base and height. He provides two proofs. The first proof is achieved by an application of the method of exhaustion The second s the dissection of the parabolic segment into infinitely many triangles, as shown in the figure below and then summing the infinite series. A very clear demonstration of Archimedes’ mathematical genius

Archimedes’ second proof dissects the area using an arbitrary number of triangles. Source: Wikimedia Commons

On the Sphere and Cylinder contains Archimedes’ famous proof that a sphere has 2/3 the volume and surface area of its circumscribing cylinder. It contains the earliest know explanation of how to find the volumes and surface areas of the two solids. Once again, he uses the method of exhaustion to achieve his results.

A sphere has 2/3 the volume and surface area of its circumscribing cylinder including its bases. Source: Wikimedia Commons

On Spirals defines what is now known as the Archimedean spiral, although it had been previously discussed by the astronomer and mathematician, Conon of Samos (c. 280–c. 220 BCE), as Archimedes acknowledges. He defines it thus:

If a straight line one extremity of which remains fixed is made to revolve at a uniform rate in a plane until it returns to the position from which it started, and if, at the same time as the straight line is revolving, a point moves at a uniform rate along the straight line, starting from the fixed extremity, the point will describe a spiral in the plane.

The Archimedean spiral with three 360° turnings on one arm Source: Wikimedia Commons

He uses the spiral to trisect and angle and also to square a circle. The Archimedean spiral is often confused in popular writing with the Golden spiral and the Fibonacci spiral.

In thirty-two propositions in On Conoids and Spheroids, Archimedes calculates the areas and volumes of sections of cones, spheres, and paraboloids. Once more making extensive use of the method of exhaustion. 

On Floating Bodies could be said to be the most important of Archimedes’ surviving text, or at least the one with the most impact. It is the earliest known text on hydrostatics. Once again in two books, it investigates the position that various solids will assume went floating in a fluid, according to their form and the variations in their specific gravities. The second book is devoted to the floating properties of various paraboloids. The book contains the first statement of Archimedes’ Principle:

Any object, totally or partially immersed in a fluid or liquid, is buoyed up by a force equal to the weight of the fluid displaced by the object.

One page of Archimedes Palimpsest, On Floating Bodies The only know Greek manuscript of the text Source: Wikimedia Commons

It is probably through the application of the principle utilising a hydrostatic balance, that is a balance with the pans resting in containers of fluid, that Archimedes actually solved the problem of whether the crown was pure gold or an alloy. This was the suggestion put followed by a young Galileo in his first ever original work, sent to Guidobaldo del Monte in 1586 in order to win his patronage. 

As we will see later On Floating Bodies would go on to have a massive influence in the Early Modern period, when there was a major renaissance in interest in Archimedes’ work.

The brief sketches above demonstrate that Archimedes was a brilliant mathematician in what we would now term pure and applied mathematics or mathematical physics. There are two works that I haven’t dealt with yet, each of which is of a different nature to the works described above.

In The Sand Reckoner Archimedes develops a system for naming large numbers in order to determine the number of grains of sand needed to fill the cosmos. The normal Greek alpha-numerical number system being totally inadequate for the task. He proceeded by producing powers of the myriad (μυριάς — 10,000), nominally the largest number in the Greek counting system, so a myriad myriads (10⁸) became the next step in his system followed by myriad-myriad myriad-myriads (10¹⁶). He then proceeded to potentiate ( and so on… Having calculated a figure for the then accepted geocentric system, he went on to calculate a new lager figure for the heliocentric system of Aristarchus of Samos (c. 310–c. 230 BCE). This is one of the few references to Aristarchus’ system. Archimedes writes:

You are now aware that the “universe” is the name given by most astronomers to the sphere the centre of which is the centre of the earth, while its radius is equal to the straight line between the centre of the sun and the centre of the earth. This is the common account (τὰ γραφόμενα) as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the “universe” just mentioned. His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun on the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of the fixed stars, situated about the same centre as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface.

The other text The Method of Mechanical Theorems, which was first discovered in 1906 on a palimpsest, a parchment scraped off and reused. The Method is a letter that he wrote to Eratosthenes in Alexandria. In this work Archimedes explains how to use indivisibles (geometrical equivalents of infinitesimals) to calculate areas and volumes. Archimedes did not consider that this method produced rigorous proofs, so having determined the solution using it he then redetermined using the method of exhaustion. 

… certain things first became clear to me by a mechanical method, although they had to be proved by geometry afterwards because their investigation by the said method did not furnish an actual proof. But it is of course easier, when we have previously acquired, by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge.

Although Archimedes was already a legend in antiquity because of his inventions his mathematical works received comparatively little attention. Isidore of Miletus (born c. 475 CE) produced the first comprehensive collation of them in Constantinople c. 530 CE. Also, in the sixth century, Eutocius of Ascalon (c. 480–c. 520) wrote commentaries on several of his mathematical works making them available to a wider readership. 

Although his works were translated and known in the medieval period, it was first during the Renaissance that Archimedes’ mathematical works, in particular, On the Equilibrium of Planes and On Floating Bodies, began to have a major influence on the development of physics. Galileo was by no means the first or the only natural philosopher to consciously replace the qualitative physics of Aristotle with the mathematical physics of Archimedes setting in motion the mathematisation of science that is regarded as a key characteristic of the so-called scientific revolution. 

From τὰ φυσικά (ta physika) to physics – V

In the last episode I outlined those aspects of Aristotle’s philosophy that would go on to play a significant role of the history of physics in later centuries. Because Aristotelian philosophy came to play such a central role in medieval thought in the High Middle Ages, there is a strong tendency to think that it also dominated the philosophical scene throughout antiquity. However, this was not the case. Although his school, the Lyceum, survived his death in 332 BCE and under the leadership of Theophrastus (c. 371–c. 287 BCE) enjoyed a good reputation. Theophrastus produced some good science, but it was natural history–biology, botany–not physics as indeed the majority of Aristotle’s scientific work had been. After Theophrastus died the Lyceum went into decline. However, the school was in no way dominant, the main philosophy of Ancient Greek following Aristotle being Stoicism and Epicureanism. Both of these philosophical directions “shared the aim of attaining tranquillity or freedom from worry (ataraxia), yet their explanations of the world were often radically different, even opposed.”^[1]

Epicurus (341–270) had a rather negative attitude towards natural philosophy:

Epicurus was content for his followers to have an ‘in principle’ approach to understanding the world. He explained that it is not necessary to become too caught up in details. In fact, he argues that less is more, because knowing less can prevent confusion and worry. In Epicurus’ view, there is a distinct possibility of being blinded by science, and this is to be avoided. While Epicurus indicates that he had himself worked out the details of his views more fully, he advocates that a summary is sufficient. A physical theory that can withstand objections and leads to peace of mind should be accepted.^[2]

Portrait of Epicurus, founder of the Epicurean school. Roman copy after a lost Hellenistic original. Source: Wikimedia Commons

Epicurean natural philosophy was retrograde, it rejected the developments made by Empedocles, Plato, Eudoxus, and Aristotle and returned to the views of the Atomists. There existed only bodies and space and the bodies were composed of atoms. Because space, the void was infinite and had no centre they rejected Aristotle’s arguments for a spherical earth at the centre of a spherical cosmos and supported a flat earth floating in the void. As with so many of these figures, Epicurus supposedly wrote a large number of books of which only a few short works survive. However, the Roman poet and philosopher, Lucretius (c. 99–c. 55 BCE) presented the Epicurean philosophy and physical theory in his poem, De rerum natura (On the Nature of Things), This would go on to play a role in the introduction of a particle theory of matter in the Early Modern Period. 

Opening of Pope Sixtus IV’s 1483 manuscript of De rerum natura, scribed by Girolamo di Matteo de Tauris Source:Wikimedia Commons

Unlike Epicureanism, Stoicism did not have a single direction determining founder, although Zeno of Citium (c. 334–c. 226) BCE, is regarded as the first Stoic.

Zeno of Citium. Bust in the Farnese collection, Naples. Photo by Paolo Monti, 1969. Source: Wikimedia Commons

He developed his ideas out of the philosophy of the Cynics being, for a time, a pupil of Crates of Thebes (c. 365–c. 285 BCE). However, equally important in the early phase of Stoicism were, Zeno’s pupil Cleanthes of Assos (c. 330–c. 230 BCE) and his pupil Chrysippus of Soli (C. 279–c. 206 BCE).

Chrysippos of Soli, third founder of Stoicism. Marble, Roman copy after a lost Hellenistic original of the late 3rd century BC. Source: Wikimedia Commons

As with almost all major Greek philosophers in this period, according to hearsay, they all wrote lots of books but only fragments of their actual writings have survived. Most of the reports on what they actually believed and practiced come from writers active centuries after they lived. As opposed to Epicurus and Epicureanism, Stoic philosophy is thought to be the result of a collective of writers rather than one dominant individual.

The Stoic philosophy has three major pillars logic, physics (natural philosophy), and ethics. As this series is about the history of the evolution of physics I shall ignore the ethics, although it was the ethics that made, and still makes, Stoicism attractive to many people. The Stoics, like Aristotle, placed a strong emphasis on logic but whereas Aristotle laid his emphasis on logical deductive reasoning using the syllogism, which is a logic of classes, the Stoics are credited with developing the earliest European logic of proposition or predicative logic. This development is usually attributed to Chrysippus but we have little or nothing of his original texts and rely on later reports by Diogenes Laëtius (fl. 3^rd century CE), Sextus Empiricus (2^nd century CE), Galen (129–c. 216 CE), Aulus Gellius (c. 125–after 180 CE), Alexander of Aphrodisias (fl. 200 CE), and Cicero (106–43 BCE). 

Stoic physic is interesting both for its similarities with and differences to Aristotle. Unlike Epicurus, the Stoics accepted the basic Platonic-Aristotelian model of the cosmos as a sphere with a spherical Earth at its centre. They were in fact mainly responsible for the acceptance of this model by the Roman. They also largely accepted the existing astronomical model of the planets revolving around the Earth on circular orbits. However, their cosmology had a major difference to that of Aristotle that would become highly significant when Stoicism was revived in the Early Modern Period.

The Stoics were pandeists, that is they believed that god was the cosmos and everything in it and the cosmos and everything in it was god. As a result, their matter theory was radically different to that of both Plato and Aristotle. To quote Wikipedia:

According to the Stoics, the Universe is a material reasoning substance (logos), which was divided into two classes: the active and the passive. The passive substance is matter, which “lies sluggish, a substance ready for any use, but sure to remain unemployed if no one sets it in motion.” The active substance is an intelligent aether or primordial fire (pneuma) which acts on the passive matter:

The universe itself is God and the universal outpouring of its soul; it is this same world’s guiding principle, operating in mind and reason, together with the common nature of things and the totality that embraces all existence; then the foreordained might and necessity of the future; then fire and the principle of aether; then those elements whose natural state is one of flux and transition, such as water, earth, and air; then the sun, the moon, the stars; and the universal existence in which all things are contained.

— Chrysippus, in Cicero, De Natura Deorum, i. 39

For their cosmology, a major consequence of this philosophy was that the Stoics rejected Aristotle’s division of the cosmos into the supralunar and sublunar spheres, they were both the same for the Stoics, and they considered comets, which as I said in the last episode played a major role in the emergence of modern astronomy, to be a supralunar phenomenon as opposed to Aristotle who regarded them as a meteorological or atmospheric phenomenon.

Both Epicureanism and Stoicism were very popular amongst educated Romans, such as Cicero and Seneca (c. 54 BCE­–c. 39 CE), and the later Greek philosopher Plutarch (c. 46–119 BCE), who quoted and discussed Epicurean and Stoic philosophers in their writings. They remained so until about 300 CE when they in turn faded into the background and were replaced by the Neoplatonist. However, those writers who paid the most attention to them were those Latin stylists who were most popular amongst the Humanist philosophers of the Renaissance and so their ideas experienced a revival in the Early Modern Period and there had an impact on the evolution of science. 

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^[1] Liba Taub, Ancient Greek and Roman Science: A Very Short Introduction, OUP, 2023 p. 

^[2] Taub p. 70

From τὰ φυσικά (ta physika) to physics – IV

There is very little doubt that Aristotle (384–§22 BCE) is the predominant figure in the narrative of the history of European science in the twenty-two centuries from 400 BCE to 1800 CE, and even after that he remains a central figure in the discourse. The general literature on Aristotle as a philosopher would fill a sizable library and the specific literature on his contributions to the history of science would fill a whole wing of that library. In this post, I will be limiting myself to a brief description of those aspects of his philosophy that had an impact on the history of physics. 

As already explained in the first episode of this series, although Aristotle gave us the word physics in his book title τὰ φυσικά (ta physika), what he means with this is very different from what is meant by the modern use of the term physics. As this series is actually about the evolution of modern physics in the early modern period, I shall here only deal with various aspects of Aristotle’s philosophy that relate to that evolution and they are by no means confined to his τὰ φυσικά (ta physika). 

Before I start, a brief biographical note on Aristotle. Born in Stagira in Northern Greece, the son of the prominent physician Nicomachus (fl. c. 375 BCE), who died whilst he was still young, he was brought up by a guardian. In his late teens he joined Plato’s Academy in Athens, where he remained until the death of Plato in 347/348 BCE. Around 343 BCE he left Athens at the request of Philip II of Macedon to become the tutor to his son Alexander (356–323 BCE), the future Alexander III of Macedon, better known as Alexander the Great.  Around 340 BCE he returned to Athens and set up his own school of philosophy, the Lyceum. Having, for so long, been a pupil of Plato much of his philosophy was formed either by acceptance or rejection of Plato’s teaching.

Bust of Aristotle. Marble, Roman copy after a Greek bronze original by Lysippos from 330 BC; the alabaster mantle is a modern addition. Source: Wikimedia Commons

One major area of acceptance, that would have consequences up to the seventeenth century, was his adoption of the cosmological and astronomical theories of Plato and Eudoxus, together with the four element theory, originally expounded by Empedocles. Aristotle took over the basic two sphere model from Plato. The cosmos is a sphere, which would become the sphere of the stars in astronomy, and the Earth is a sphere at its centre. Unlike Plato, Aristotle explains why the Earth is a sphere and also gives empirical evidence to show that it is truly a sphere. He argued that if something with gravitas falls then it falls towards the centre of the cosmos until it stops. The natural consequence of everything falling towards a centre from all direction is a sphere. This fall was not due to a force but to the tendency for objects to return to their natural or proper place. So, objects that have gravitas i.e., those predominantly consisting of earth or water, return to the Earth. Those with levitas, consisting predominantly of air or fire rise up into the atmosphere. 

Of course, he has to explain why the celestial objects don’t fall to the Earth. Aristotle divides the cosmos into two zones, everything below the orbit of the Moon i.e., sublunar and everything above the orbit of the Moon i.e., supralunar. The sublunar zone consists of the four elements and is subject to change and corruption, whereas the supralunar zone consists of a fifth element, the aether or quintessence, which is unchanging and incorruptible. Natural motion in the supralunar zone is, once again following Plato and Empedocles, uniform circular motion. 

One consequent of Aristotle’s insistence that the supralunar sphere was eternal and incorruptible was that he assigned both meteors and comets to the sublunar zone and considered them to be terrestrial phenomena. As I have documented in a series of posts my The emergence of modern astronomy–The debate on comets in the sixteenth century, Tycho Brahe and new astronomical data, The comets of 1618, Comets in Europe in the 1660s, Comets in Europe in the 1680s, Edmond Halley and the Comets–the unravelling of the true nature of comets played a significant role in the establishment of modern astronomy.

Unlike his predecessors, Aristotle provides empirical arguments to demonstrate that the Earth is actually a sphere, to quote James Hannam:

Aristotle concluded his discission by showing how the theory of the Globe explained observations that might seem otherwise inexplicable. In the first place, he said that when there is a lunar eclipse the shadow of the Earth on the Moon is always curved. This corroborates what he had already shown from his first principles. The umbra during a lunar eclipse follows from the shape of the Earth. If it is a ball, its shadow must always be an arc. 

His second piece of empirical evidence is the way the visible stars change as we travel north or south. He noted that some stars, which are visible in Egypt and Cyprus, can’t be seen in the north. He is almost certainly referring to Eudoxus’ observations of Canopus. It is bright enough to be hard to miss in Egypt, albeit usually low in the sky. Its absence from view in Athens would have been obvious to anyone who had seen it further south. This is only explicable if the Earth is rounded, if it were a flat plane, everyone would see the same stars. Since it is spherical, it’s inevitable that our view of the heavens will change with latitude.^[1]

Hannam closes his section on Aristotle with the following:

By any conventional standards he [Aristotle] knew the Earth was a sphere, and he was probably the first person who did. On that basis, he discovered the theory of the Globe. As we will see in the remainder of this book, everyone today who knows the Earth is round indirectly learnt it from Aristotle. This makes the Globe the greatest scientific achievement of antiquity. It’s only because we take it as obvious that we don’t give Aristotle the credit he deserves.^[2]

For the planets Aristotle takes over the concentric or homocentric spheres of Eudoxus and Callippus but adds more spheres filling out the spaces between the planets making a complete set of spheres within spheres from the Moon to the stars. All motion within the heavens is driven by a sort of friction drive by the outer most sphere. This in turn is driven by an unmoved mover, a concept that appealed to the Church in the medieval period, who simply assumed that the unmoved mover was God. Although more scientific in his explanations than any of his predecessors, Aristotle can, at times, also be totally metaphysical. What motivates the unmoved mover? The spheres have souls, and it is the love of those souls for the unmoved mover that motivates it. The origin of the phrase, “love makes the world go round.”

As is generally well known, having defined fall as natural motion, Aristotle now goes on to elucidate his laws of fall, which, of course, everybody knows were wrong being first brilliantly corrected by Galileo in the seventeenth century. Firstly, Aristotle’s laws of fall are not as wrong as people think, and secondly, they were, as we shall see in later episodes, challenged and corrected much earlier than Galileo. 

Aristotle’s laws of fall are actually based on simple everyday empirical observation. If I drop a lead ball from an oak tree it evidently falls to the ground faster than an acorn that I dislodge whilst dropping the ball. In real life not all objects fall at the same speed. It is only in a vacuum that this is the case. People tend to ignore the all-important “vacuum” when praising Galileo’s enthronement of Aristotle’s laws of fall. Naturally if I drop a two lead balls of different weights, they do fall at approximately the same speed but even here the heavier ball will hit the ground a split second earlier than the lighter one. 

Aristotle argued that the rate of fall was directly proportional to the weight of the falling object and indirectly proportional to the resistance of the medium through which it falls.

Aristotle’s laws of motion. In On the Heavens he states that objects fall at a speed proportional to their weight and inversely proportional to the density of the fluid they are immersed in. This is a correct approximation for objects in Earth’s gravitational field moving in air or water. Source: Wikimedia Commons

This is a good first approximation for objects on the Earth falling through air or water. Having established this Aristotle then argued that the void (a vacuum) could not exist because in the void a falling object would accelerate to infinity and that was an absurdity. Interestingly he also argues that in a vacuum all objects would fall at the same speed, an absurdity! Galileo anyone? It is quite common to express his laws of fall either symbolically or even mathematically, but Aristotle never did either.

As already said, although Aristotle gave us the word physics, he uses it in a very different way. For Aristotle physics is the study of natural things, which he sees as the study of the general principles of change. Change is for Aristotle universal, plants grow and then die, there is quantitative change with respect to size and number and so forth. Most important from our point of view is that he considers motion to be change of place. 

In Aristotle’s theories of motion, having dealt with natural motion he now had to define and deal with unnatural motion. Of course, there was only natural motion in the uncorruptible supralunar area. On Earth beyond natural motion there was voluntary motion and unnatural motion. Voluntary motion is such as animals moving and need not concern us here. Unnatural motion requires a cause, and it is here that Aristotle’s whole theory of motion ran into difficulties. 

If I have a horse and cart or I push a wheelbarrow, then the cart only moves if the horse pulls and the wheelbarrow only moves if I push. If the horse stops pulling or if I stop pushing then the motion stops, no real problems here, although it is difficult to fit this type of motion into the laws of motion that applies to the falling object. Aristotle’s real problems start with projectile motion. If I fire an arrow with a bow or throw a ball, why does the arrow after it has left the bow string or the ball after it has left my hand continue to fly through the air? There is now apparently nothing propelling the arrow or ball. Aristotle’s escape from this impasse is, to say the least, dodgy. He argued that the air displaced by the flying object rushed around to the back and pushed it further along its course. This weak point in his theory was exploited comparatively early by his critics, i.e., long before the seventeenth century.

Aristotle rejected atomism arguing there was no limit to how far one could divide something, so no smallest particles, atoms. His own theory of matter was that there is primal material. Objects consist of two things material and form. This is important because it plays a role in his fourfold theory of cause that dominated his whole philosophy of nature.  

According to Aristotle everything in nature has four causes:

• The Material Cause: The material out of which it is composed.
• The Formal Cause: The pattern or form that makes the material into a particular type of thing.
• The Efficient Cause: In general that which brings an object about
• The Final Cause: The purpose for the existence of the object in question

The four causes also apply to abstract concepts such as motion, each motion has a material, a formal, an efficient, and a final cause.

Aristotle argued by analogy with woodwork that a thing takes its form from four causes: in the case of a table, the wood used (material cause), its design (formal cause), the tools and techniques used (efficient cause), and its decorative or practical purpose (final cause). Source: Wikimedia Commons

Today, we regard the final cause, for which the technical term is teleology, as bizarre. Since at least the nineteenth century it is not thought that most things have an intrinsic purpose for their existence, they just exist. However, in the Middle Ages, the high point of Aristotelian thought in science, it would have chimed with Christian thought, “everything has a place in God’s great plan. 

Introducing Aristotle’s four causes takes us along to, perhaps Aristotle’s greatest contribution to the development of science his methodology and his epistemology, i.e., his theory of knowledge. In six works, collectively known as the Organon, he laid out the earliest known introduction to formal logic. How do I argue correctly, so that I transport truth from my premises to my conclusions. Our understanding of logic and the logic that we use have evolved since Aristotle, but logic still lies at the heart of all formal scientific proofs. Stealing from Wikipedia the six Aristotelian works on logic are:

1. The Categories (Latin: Categoriae) introduces Aristotle’s 10-fold classification of that which exists:  substance, quantity, quality, relation, place, time, situation, condition, action, and passion.
2. On Interpretation (Latin: De Interpretatione) introduces Aristotle’s conception of proposition and judgement, and the various relations between affirmative, negative, universal, and particular propositions. 
3. The Prior Analytics (Latin: Analytica Priora) introduces his syllogistic method argues for its correctness, and discusses inductive inference.
4. The Posterior Analytics (Latin: Analytica Posteriora) deals with definition, demonstration, inductive reasoning, and scientific knowledge.
5. The Topics (Latin: Topica) treats issues in constructing valid arguments, and inference that is probable, rather than certain. It is in this treatise that Aristotle mentions the Predicables, later discussed by Porphy and the scholastic logicians.
6. The On Sophistical Refutations (Latin: De Sophisticis Elenchis) gives a treatment of logical fallacies, and provides a key link to Aristotle’s tractate on rhetoric.

Added 17 August

Although not really clearly spelt out, Aristotle propagated an axiomatic deductive system for securing knowledge. Starting from self-evident premises that require no proof one uses a chain of deductive logic until one arrives at empirically observed facts. Although we would regard his premise that the Earth is a sphere because all falling objects fall to the centre of the universe as self-evident, this is the form of argument, sketched above, he uses to demonstrate that the Earth is really a sphere. 

It is important to note, for the evolution of scientific thought in Europe throughout the centuries after Aristotle, that when applied to nature he didn’t regard mathematical proofs as valid. He argued that the objects of mathematics were not natural and so could not be applied to nature. He did however allow mathematics in what were termed the mixed sciences, astronomy, statics, and optics. For Aristotle mathematical astronomy merely delivered empirical information on the position of the celestial bodies. Their true nature was, however, delivered by non-mathematical cosmology. I shall deal with statics and optics separately. 

In recent times, various voices have claimed that the adherence to Aristotle’s vision of science hindered the evolution of the discipline. It is a similar claim to that of the gnu atheists that Christianity blocked the evolution of science. In the case of Aristotle, I think we should bear in mind that in antiquity his popularity waned fairly quickly after his death, and he was superceded by the Stoics and then the Epicureans as the flavour of the century in philosophy and although this included the period of the greatest Greek mathematicians Archimedes (c. 287–c.212 BCE) Apollonius of Perga (c. 240–c. 190 BCE), who both made significant advances in both pure and applied mathematics, it cannot be said that the world advanced significantly towards modern science.

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^[1] James Hannam, The Globe: How the Earth Became Round, Reaktion Books, London, 2023 p. 93

^[2] Hannam p. 95