In episode XIV of this series, we surveyed the final intellectual efforts within Europe to hold the knowledge accrued during antiquity upright for future generations in the work of such figures as Boethius (c. 480–524), Cassiodorus (c. 485–c. 585) and Isidore of Seville (c. 560–636). Efforts that were at least partially successful as that knowledge did not die out completely but took, so to speak, a rest for several centuries. Important to note, I wrote there in opposition to a widespread popular myth, propagated by many militant atheists, Christianity and Christians were not responsible for the decline and loss of classical learning in late antiquity. In fact, the opposite is true, what survived in Europe did so because it was conserved and copied in monastery libraries, which is where much of it was found by the manuscript hunters during the Renaissance.
As we have seen in the following six episode, following the decline of knowledge production within Europe, which reached a deep point in the seventh century, beginning in the eighth century the newly emerging Islamic culture originating in Western Asia took up the baton of knowledge production, first collecting, then translating, and finally analysing, commenting on, and expanding, not just the knowledge from European antiquity but also that from Persia, India, and even China.
We now turn back to Europe and the gradual reawakening of the acquisition of knowledge beginning in the eight and ninth centuries, which slowly gained momentum down to the twelfth century and the so-called Scientific Renaissance during which much of the knowledge acquired, analysed, expanded, and improved by the scholars of the Islamic period was translated back into Latin and became available again, or in some cases for the first time, to European scholars. I shall here only offer an outline sketch, as I have already dealt in detail with this process in my Renaissance Science series to which I will here supply links at the appropriate points.
Before moving on I will briefly mention three authors from the Early Middle Ages, that I didn’t mention earlier, whose books, whilst on a fairly low academic level kept the knowledge of and interest in the mathematic sciences throughout the medieval period.
The first is Martianus Capella, a Roman citizen of Madaura in North Africa, who was active in the early fifth century and who wrote De nuptiis Philologiae et Mercurii (On the Marriage of Philology and Mercury) a Neoplatonic, allegorical tale describing the seven liberal arts, trivium and quadrivium, who appear as the bridesmaids at the title’s wedding.
Grammar teaching, from a 10th-century manuscript of De nuptiis Philologiae et Mercurii Source: Wikimedia Commons
The seven liberal arts provided the backbone of the curriculum in the medieval cathedral schools and for the undergraduate degrees at the newly emerging universities in the High Middle Ages. This book was highly popular and very widely read, as can be attested by the, at least, two hundred and forty-one surviving manuscripts. It was first printed in Vincenza in 1499 and there was an edition published in in 1539 just four years before the publication of Copernicus’ Derevolutionibus.
There were numerous commentaries on the text by leading medieval scholars. Perhaps the most intriguing aspect of the book is that Capella introduces a geo-heliocentric system, in the astronomy section, in which Mercury and Venus orbit the Sun which in turn with the remaining four planets orbits the Earth. This is the earliest known presentation of a geo-heliocentric system although Capella introduces in a way that seems to suggest that it was already known. He and his system get an honorary mention in De revolutionibus.
Capella’s cosmological model Manuscript Florence, Biblioteca Medicea Laurenziana, San Marco 190, fol. 102r (11. Jahrhundert) Source:: Wikimedia Commons
Our second is a near-contemporary of Capella’s, the Roman citizen, whose origins are unknown, Macrobius Ambrosius Theodosius, usually referred to as Macrobius, whose Commentarii in Somnium Scipionis (Commentary on Cicero’s Dream of Scipio) expounds a series of theories on the dream from a Neoplatonic background, on the mystic properties of the numbers, on the nature of the soul, on astronomy and on music. His commentary was essentially an encyclopaedic rendering of the Platonic interpretation of terrestrial and celestial science. Like Capella’s De nuptiis this work was widely read and commented on by medieval scholars.
Image from Macrobius Commentarii in Somnium Scipionis: The Universe, the Earth in the centre, surrounded by the classical planets, including the sun and the moon, within the zodiacal signs. Source: Wikimedia Commons
We leave the fifth-century Roman Empire and travel to Britain in the seventh and eighth centuries, where we find the monk Bede (672/3–735) in the monastery of Jarrow. Known as the Venerable Bede (Beda Venerabilis), he is best known for his Historia ecclesiastica gentis Anglorum (Ecclesiastical History of the English People) written about 731. However, he also wrote an important text on measuring time, his De temporum ratione (The Reckoning of Time). The book covers basic cosmological topics before going on to calendrics and its main theme computus, the calculation of the dates of Easter and the other movable Church feast days.
De temporum ratione: This manuscript was made around 1100, possibly in France.
The work of these three together with that of Boethius (c. 480–524), Cassiodorus (c. 485–c. 585), and Isidore of Seville (c. 560–636), who I introduced in an earlier episode, meant that an awareness of the mathematical sciences was kept alive in the Early Middle Ages, although at a very low level, following the decline of the Roman Empire. This meant that when a higher level of learning and knowledge began to emerge in Europe later in the Middle Ages, there was a foundation on which to build.
The next step in the reintroduction of learning into Europe came when Karl der Große (742–814) (known as Charlemagne in English) had completed the conquest and unification of a very large part of Europe by the Franks. Although Karl himself was illiterate, he and his heir Louis the Pious (778–840) introduced an education programme for priest and increased the spread of Latin on the continent.
The programme was basically not scientific, it had, however, an element of the mathematical sciences, some mathematics, computus (calendrical calculations to determine the date of Easter), astrology and simple astronomy due to the presence of Alcuin of York (c. 735–804) as the leading scholar at Karl’s court in Aachen. Through Alcuin the mathematical work of the Venerable Bede (c. 673–735), who was also the teacher of Alcuin’s teacher, Ecgbert, Archbishop of York, flowed onto the European continent and became widely disseminated.
Karl’s Court had trade and diplomatic relations with the Islamic Empire, in particular with Abu Ja’far Harun ibn Muhammad al-Mahdi (c. 764–809), better known as Harun al-Rashid, the fifth Abbasid caliph, and there was almost certainly some mathematical influence there in the astrology and astronomy practiced in the Carolingian Empire.
In the eleventh century the three Ottos, Otto I (912–973), Otto II (955–983), and Otto III (980–1002), increased the levels of learning on the Imperial court and in the monasteries through contact with Byzantium. This renaissance acquired a strong mathematical influence through Otto the Third’s patronage of Gerbert of Aurillac (c. 946–1003). A patronage that would eventually lead to Gerbert becoming Pope Sylvester II. From his time living in Spain Gerbert introduced some of the basics of Islamic astronomy and mathematics into the rest of Europe.
In the eleventh and twelfth centuries two developments furthered and accelerated to growth in knowledge within Europe. On the one hand groups of students seeking advanced instruction and groups of teachers seeking students to instruct set up the first European universities. The Latin term universitas “being a number of persons associated into one body, a society, company, community, guild, corporation, etc.” These bodies became sanctioned by the Church and by local rulers and adopted the seven liberal arts, as propagated by the scholars of the early Middle ages, such as Boethius and Capella as their undergraduate curriculum. They developed three post graduate faculties, theology, law, and medicine.
Bologna University is the oldest medieval European university. Interior view of the Porticum and Loggia of its oldest College, the Royal Spanish College. Source: Wikimedia Commons
The second development was that scholars began to travel to the areas dominated by Islamic culture to acquire and translate the knowledge of the ancient Greeks and their Islamic interpreters and commentators from Arabic into Latin, during what is know known as the Scientific Renaissance. Europe was now there where the Islamicate culture had been in the seventh century, with an education establishment and the material on which to build or better rebuild an academic and especially a scientific culture.
The beginning of Aristotle’s De anima in the Latin translation by William of Moerbek.. Manuscript Rome, Biblioteca Apostolica Vaticana, Vaticanus Palatinus lat. 1033, fol. 113r (Anfang des 14. Jahrhunderts) Source: Wikimedia Commons
I have already written an extensive blog post on the Scientific Renaissance in my series Renaissance Science, and also one on the emergence of the medieval university, so I won’t repeat them here. Next time I shall be looking at medieval contributions to the development of some areas of physics.
In the years following the publication of De Magnete in 1600 and the death of William Gilbert in 1603 a dispute developed between two leading English magnetists, William Barlow (1544 – 1625) and Dr Mark Ridley (1560–c. 1624), as to which of them was Gilbert’s true disciple.
We have already met William Barlow, son of a bishop, who was a successful career Church of England cleric, who never went to sea but became an expert on magnetism and navigation and was especially known for his mariner’s compass and variation compass designs. In 1605, he was appointed tutor and chaplain to Henry Frederick, Prince of Wales (1594–1612). Later, 1608 or 1609, the mathematician Edward Wright (1561–1615) was also appointed a tutor of Henry Frederick. Both Barlow and Wright were closely involved in the genesis of William Gilbert’s De Magnete. Barlow had also published a demonstration of Wright’s Mercator projection “obtained of a friend of mone of like professioin unto myself,” in his The Navigator’s Supply (1597). Both men lost their positions as tutor, when Henry Frederick died.
Prince Henry Frederick Portrait by Robert Peake the Elder, c. 1610 Source: Wikimedia Commons
We now leave Barlow for the moment and turn our attention the Mark Ridley, who we first met as one of the residents of Gilbert’s Wingfield house in London. In many ways Ridley’s career paralleled that of his erstwhile landlord. Ridley was born the second son of the six children of the Lancelot Ridley rector of Stretham in Cambridgeshire. Lancelot Ridley was an early prominent Protestant, promoted under Thomas Cranmer and favoured during the reign of Edward VI. He was subsequently deprived under Mary but rose again to prominence under Elizabeth I. Mark matriculated as a pensioner at Claire College Cambridge in 1577, graduating BA in 1581 and MA in 1584. He was licenced to practice medicine by the College of Physicians in 1590 and graduated MD in 1592.
On 27 May 1594 he was appointed by Elizabeth, on the recommendation of William Cecil, to serve Feodor Ivanovich, the tsar of Russia as physician.
Tzar Feodar I Source: Wikimedia Commons
He worked for five years in Moscow and on the death of Tsar Feodor in 1599, he was appointed physician to of his successor, Boris Godunov. Elizabeth requested that he be allowed to return to London in that year and Boris Godunov wrote to her commending him for his faithful service and releasing him.
Ridley became an active member of the College of Physicians and like Gilbert before him rose in their ranks, being elected censor in 1607. Over the years he was regularly elected to various offices in the organisation. Interestingly, Ridley is perhaps more significant as the author of the two Russian-English dictionaries than for his writings on magnetism.
While living in Russia between 1594 and 1599, he compiled two manuscript dictionaries of Russian: a Russian-English dictionary of 7,203 entries entitled A dictionarie of the vulgar Russe tongue and an English-Russian dictionary of 8,113 entries entitled A dictionarie of the Englishe before the vulger Russe tonnge. The former includes a short grammar of Russian on the first eight folios. Both dictionaries are now held at theBodleian Library at the University of Oxford (MSS Laud misc. 47a and 47b). (Wikipedia)
Gilbert’s De Magnete was, of course, not without its critics. But in the early phase things remained fairly quiet, especially in England, where the book and its author were much admired. However, between 1603 and 1604 the splendidly named and titled Guillaume de Nautonier, sieur de Castel-Franc au haut Languedoc, Géographe du roi Henri IV (1560– 1620)
Guillaume de Nautonier
published the equally splendidly titled:
Mecometrie de leymant cest a dire La maniere de mesurer les longitudes par le moyen de l’eymant. Par laquelle est enseigné, un tres certain moyen, au paravant inconnu, de trouver les longitudes geographiques de tous lieux,–aussi facilement comme la latitude. Davantage, y est monstree la declinaison de la guideymant, pour tous lieux. Œuvre nécessaire aux admiraux, cosmographes, astrologues, geographes, pilotes, geometriens, ingenieux, mestres des mines, architectes, et quadraniers. (The mecometry of the loadstone or the way to determining the longitude by means of the loadstone…)
In this work Le Nautonier accepts Gilbert’s claim that the Earth is a magnet but claims that he discovered this independently, although, unlike Gilbert, he offers no experiments or other proofs to back up his claim. He was the first to state that the Earth is a tilted dipole, giving 67°N and 67°S for their latitudes and by modern reckoning approximately 30°E and 150°W as their longitudes. He stated that the Earth was a perfect sphere, and, as the book title states, resurrected the already debunked theory that magnetic variation was regular and using it one could determine longitude. He devoted a lot of space to refuting Gilbert’s explanations of the irregularities in variation. Initially there was no reaction to this book in England, although it would be thoroughly debunked in France by Didier Dounot (1574–1640), professor for mathematics on the Académies du roi, in his Confutation de l’invention des longitudes ou De la mecometrie de l’eymant. Cy devant mise en lumiere souz le nom de Guillaume le Nautonnier, sieur de Castel-Franc au haut Languedoc (1611)
The first reactions in England were triggered in 1608 by the publication by Anthony Linton, chaplain to Charles, Lord Howard of Effingham, who served as High Admiral from 1585–1618, of his Newes of the Complement of the Art of Navigation. And of the Mightie Empire of Cataia Together with the Straits of Anian.
In this rather strange volume, Linton, “after citing the criticisms of the art of navigation of Humphrey Gilbert, Thomas Digges, William Borough, Richard Polter, and Edward Wright, whose chart he praised, he pointed out that in navigation position-finding was still imperfect.”[1] Rather stating the obvious. He then claimed that any navigator could ‘make his conclusions of Latitude, Longitude, and Variation,’ as accurately ‘as is possible to be done in any other Mathematicall practice in use amongst us’ by ‘continued observation’, and by exploiting the existence of the two magnetic poles. By the use of certain globes and charts of his devising, obtainable at a price, and ‘in six other ways’, the navigator, knowing , ‘the vaiation of the Compasse and the Latitude of the place’ would find out by Aritmeticall calculation the true longitude of the same place’. However, for the satisfactory working of this admirable but obscurely worded system there appeared to be one serious drawback only, namely, that it required ‘professors of greater skill and practice in the Mathematics, then now commonly found’.[2] This very jumbled account obviously preaches the same gospel as Le Nautonier’s early work and raises the question, whether Linton had plagiarised it, to which we don’t know the answer.
Both of Henry Frederick’s navigation tutors now responded to Linton and Le Nautonier’s arguments. De Magnete was written in Latin and first got translated into English in the nineteenth century. This meant that his theories were not accessible to the mariners who couldn’t read Latin. Barlow wrote a manuscript presenting and explaining Gilbert’s ideas on magnetism and the compass in English. In this work he argued against and debunked the theory propagated by Linton and Le Nautonier. Barlow gave a copy of the manuscript to Sir Thomas Chaloner (1559–1615), a courtier and Governor of the Courtly College for the household of Prince Henry Frederick, so basically Barlow’s employer as chaplain and tutor to the prince. Chaloner manage to lose this manuscript as well as a second copy that he had agreed to have published. This was the situation in 1615, when Chaloner died.
Monument of Sir Thomas Chaloner St Nicolas’ Church Chiswick
Edward Wright simply refuted the argument in an appendix to the expanded second edition of his Certaine Errors in Navigation, arising either of the Ordinarie Erroneous Making or Vsing of the Sea Chart, Compasse, Crosse Staffe, and Tables of Declination of the Sunne, and Fixed Starres Detected and Corrected published in 1610, in which he listed the observed variation in many places. The volume was dedicated to “THE HIGH AND MIGHTIE PRINCE HENRY; eldest Son to our soueraigne Lord King Iames: Prince of Wales, Duke of Cornwell, Earle of Chester, &c.”
Ridley entered the fray in 1613 with the publication of his first book on magnetism:
A SHORT TREATISE of Magneticall Bodies and Motions. By Marke Ridley Dr in phisicke and Philosophie Latly Physition to the Emperour of Russia, and one of ye eight principals or Elects of the Colledge of Physitions in London. London Printed by Nicholas Okes. 1613.
Like Barlow he presented his theories in English for those who couldn’t read Latin. He debunked the various myths about the healing power of magnets etc and propagated the theories of Gilbert as presented in De Magnete. He then goes on to debunk the theories of Linton and Le Nautonier. After which he presents his own incorrect theory:
‘when travelling or sailing … it will be very necessary for thee to be stored with the Marriners Compasse for the sea … to know the way … and also to have the Inclinatory-needle truly placed in his ring, and the Directory needle, or a little flie Magneticall in the boxe, fastened at the bottome … for to know under what latitude thou art every day of thy voyage …’ Now one of the chief purposes of his book was to describe the benefits that would arise from the use of ‘the Directory-Magneticall-needle … for the description of Ports, Havens, Forelands, Capes, Bayes, and Rivers, for the more perfect making of Sea-cardes … and all Mathematicall instruments for measuring and surveying …’ and to explain the manner of using it. Yet the instrument was fundamentally unsound, for the mutual attraction and repulsion of the magnetical needles in close juxtaposition, such as he envisaged, foredoomed it to failure because of the resultant errors.[3]
MAGNETICALL Aduertisements : or DIVERS PERTINENT obserruations, and approued experiments concerning the nature and properties of the Load-stone: Very pleasant for knowledge, and most needful for practice, or trauelling, or framing of Instruments fir for trauellers both by Sea and Land.
Act. 17.26 He hath made of one bloud all nations of men for to dwell on the face of the earth, and hath determined the times before appointed, and the bounds of theior habitation, that they should seeke the Lord, &c.
LONDON; Printed by Edward Griffin for Timothy Barlow, and are to be sold at his shop in Pauls Church-yard at the signe of the Bull-head. 1616.
He didn’t name Ridley directly but referred to his “propositions set abroad in another man’s name and yet some of them not rightly understood by the partie usurping them.”[4] He wrote:
I was the first that made the inclinatory instrument transparent to be used pendant, with a glass on both sides, and a ring at the top … and moreover I hanged him in a compass box, wjere with two onces weight he will be fit for use at sea. I first found out and showed the difference between iron and steel, and their tempers for magnetical uses … I was also the first that showed the right way of touching needles …[5]
To demonstrate that he, not Ridley, was Gilbert’s heir he stated that he had been researching magnetism since 1576 and that Gilbert had appreciated his contributions. To prove this, he included a letter that Gilbert had sent to him in 1602. This is in fact the only letter of Gilbert’s that has survived:
To the Worshipfull my good friend, Mr. William Barlowe at Easton by Winchester.
Recommendations with many thanks for your paines and courtesies, for your diligence and enquiring, and finding diuers good secrets, I pray proceede with double capping your load-stone you speake of, I shall bee glad to see you, as you write, as any man, I will haue any leisure, if it were a moneth, to conferre with you, you have shewed mee more–and brought more light than any man hath done. Sir, I will commend you to my L. of Effingham, there is heere a wise learned man, a Secretary of Venice, he came sent by that State, and was honourably received by her Majesty, he brought me a lattin letter from a Gentle-man of Venice that is very well learned, whose name is Iohannes Franciscus Sagredus, he is a great Magneticall man, and writeth that hee hath conferred with diuers learned men in Venice and with Readers of Padua, and reporteth wonderfull liking of my booke, you shall have a copy of the letter: Sir, I propose to adioyne an appendix of six or eight sheets of paper to my booke after a while, I am in hand with it of some new inuentions and I would haue some of your experiments, in your name and inuention put into it, if you please, that you may be knowen for an augmener of that art. So for this time in haste I take my leaue the xiiyth of February.
One major bone of contention between the two disciples of Gilbert was his embrace of Copernicanism with his assumption of a magnetic diurnal rotation of the Earth. As a conservative official of the Church, Barlow totally rejected this aspect of Gilbert’s work, remaining a staunch geocentrist. Ridley, however, going further than Gilbert, adopted a full heliocentric cosmology, as can be seen from his inclusion of the newest results from Galileo and Kepler in his book.
Barlow’s veiled accusation of plagiarism did not escape Ridley and he responded with a pamphlet: Magneticall Animadversions. Made by Dr Mark Ridley, Doctor in Physicke. Upon certain Magneticall Advertisements, lately published, From Maister William Barlow. (1617) His criticism was scathing:
‘There is almost no proposition in this book which most Mariners, Instrument-Makers, Compasse -makers, Cocke-makers, and Cutlers of the better and more understanding sort around London and the Suburbs have not known, practized, and made long before.’ His so-called inventions were ‘most of them in the Doctor Gilbert’s Booke, as I said before, or else such ordinary things that any ingenious workman hath or may easily invent or make; unles you hold all men Dulberts like your rare workman of Winchester.’[7]
Barlow’s response came immediately in his, A Briefe Discovery of the Idle Animadversions of Marke Ridley (1618):
This time it was personal. He tried to discredit Ridley, suggesting that he had morally compromised himself in order to ‘in so short a time become [the Russian] Empoerors principall Physition.’ In a double entendre to Ridley’s observations or ‘looks’ with the new-fangled telescope, he insinuated that the youthful Ridley had seduced the Czar, ‘for his lookes … are his meanes.’[8]
Ridley delivered a parting shot with his, Appendix or an Addition … unto his Magneticall Treatise in answer to M. Barlow (1618).
Despite Ridley’s attacks, Barlow reprinted his Magneticall Advertisements unchanged, except for a new title page, in 1618.
And so, the verbal war between the two heirs of William Gilbert ground to a halt. In their major publications, in this unpleasant exchange, both had made important contributions to the ongoing debate on magnetism and the compass, most importantly making much of Gilbert’s work accessible in English, for those unable to read Latin. However, at the same time they had made a public spectacle of themselves in their bitter dispute, a behaviour that was, unfortunately all too common amongst scholars during the Renaissance.
[1] David W. Waters, The Art of Navigation in England in Elizabethan and Early Stuart Times, Yale University Press, New Haven, 1958, p. 274.
Although Islamic scholars made substantial contributions to mechanics, astronomy, and especially optics along the road from the Greek ta physika to modern physics, it was in the realm of mathematics that they made what was probably their greatest contribution to the development of that discipline.
Greek science was to a great extent dominated by geometry, first and foremost the work of Euclid but also that of Apollonius and Archimedes. This continued to be the case during the Middle Ages and Greek geometry also loomed large in Islamic scientific culture. However, one characteristic of the new science developed in the seventeenth century in Europe was the rejection of the synthetic mathematics of Euclidian geometry for the newly emerging analytical mathematics that would become known as calculus. The roots of this change are to be found in the new streams of mathematics inherited from Islamic sources.
Islamic mathematicians developed three new streams of mathematics, arithmetic, algebra, and trigonometry all three of which they had in turn acquired from their predecessors in India. Of course, all three streams existed in one form or another in Ancient Greece but what the Islamic scholars acquired from India was of an entirely different calibre to what had gone before in Ancient Greece.
The arithmetic that Islamic science acquired from India was, of course, the place value decimal number system of which the eighteenth-century French mathematician, physicist, astronomer Pierre-Simon Laplace once wrote:
It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.
The place value decimal number system evolved over a period of several centuries finally reaching a semi-complete form with the introduction of zero as a number in the Brāhmasphuṭasiddhānta of the mathematician and astronomer Brahmagupta (c. 598–c. 668 CE).
Brahmagupta?
In this work Brahmagupta presents the place value decimal number system including positive, negative numbers and zero, the rules of the four fundamental operations (addition, subtraction, multiplication, and division) in a form that would be at home in a modern elementary arithmetic textbook. The one exception being his attempt to define division by zero, which as we all know ids a no,no.
Verse from chapter XVIII of the Brāhmasphuṭasiddhānta describing the rules for zero as a number
Brahmagupta’s texts were translated into Arabic in about 750 by Abū ʿAbdallāh Muḥammad bin Ibrāhīm bin Ḥabīb al-Fazārī (died early ninth century) together with Yaʿqūb ibn Ṭāriq (died c. 796) as ‘Az-Zīj ‛alā Sinī al-‛Arab or the Sindhind.
The earliest Arabic text on the Hindu numerals was written by Muḥammad ibn Musá al-Khwārizmī (c. 780–c. 850) The kitab al-jam’ wa’l-tafriq al-ḥisāb al-hindī (Addition andsubtraction According to the Hindu Calculation) probably written about 800 CE. It didn’t survive in Arabic but there is a Latin translation made in the twelfth century.
First page of the Latin translation Source: Wikimedia Commons
Abū Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī (c. 801–873) wrote his kitāb fī isti’māl al-‘adād al-hindī (On the Use of the Hindu Numerals) around the same time, which also didn’t survive.
Al-Kindi on an Iraqi stamp from 1962 Source: Wilimedia Commons
The earliest surviving works are Kitāb al-uṣūl fī l-ḥisāb al-hindī (“Book of the Principles of Hindu reckoning”) by Abul-Hasan Kūshyār ibn Labbān (971–1029), and Kitāb al‑takmila fī l-ḥisāb (“The completion of arithmetic”) by Ibn Ṭāhir al-Baghdādī (d. 1037). The Kitāb al-fuṣūl fī l-ḥisāb al-hindī (“The book of chapters on Hindu arithmetic”) by Abū l‑Ḥasan al-Uqlīdisī (fl. c. 950) is the first text to describe decimal fractions, which the Indian mathematicians had not developed.
However, Islamic scholars used a variety of number systems. They used the place value decimal number system written with number symbols but also written with Arabic letters as in an alpha-numerical number system. Beyond that they used a pure sexagesimal system, inherited from the Babylonians. They also followed Ptolemaeus with a so-called astronomical number system that used a decimal system for the whole numbers combined with sexagesimal fractions for the fraction part. One area in which the place value decimal number system was widely used was in what we would now term commercial arithmetic. Special applications that drifted towards algebra were the determination of profit or loss shares in trade deals and in the determination of inheritance shares under the complex Islamic inheritance rules.
Algebra and arithmetic are closely linked and this was very much the case in the medieval Islamic adoption and development of algebra. In its origins algebra was restricted to what we would now term the theory of equations. We find aspects of this in virtually all pre-Islamic mathematical cultures, Egyptian, Babylonia, China, Indian and Greece. Whereas the first four all practiced a largely arithmetical approach to the solution of equations, the Greeks developed a geometrical algebra for such solutions. We still retain elements of this when we talk about quadratic and cubic equations; for the Ancient Greek mathematicians such equations describing geometrical figures.
The early Islamic mathematicians borrowed heavily from all of the earlier sources. Once again very influential was the Brāhmasphuṭasiddhānta of Brahmagupta. J. L. Berggren attributes the creation of algebra to al-Khwārizmī:
Out of this dual heritage of solutions to problems asking for the discovery of numerical and geometrical unknowns Islamic civilisation created and named a science–algebra.[1]
A Soviet postage stamp issued 6 September 1983, commemorating al-Khwārizmī’s (approximate) 1200th birthday Source: Wikimedia Commons
It is well-known that the term algebra is derived from the title of al- Khwārizmī’s book al-Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah (The Compendious Book on Calculation by Completion and Balancing), whereal-Jabr means “setting back in its place” or “restoration.” Al- Khwārizmī “uses the term to denote the operation of restoring a quantity subtracted from one side of the equation to the other side to make it positive.”[2] The Latinised version of his name also provided us with the term algorithm. Although, Algorisme was originally the term for calculating with the Hindu-Arabic numer system.
A page from al-Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah Source: Wikimedia Commons
Although al- Khwārizmī is the best known Islamic algebra author he is by no means the only one. The Mesopotamian polymath Thābit ibn Qurra (c. 830–901) gave a more general demonstration of the solution of quadratic equations than al- Khwārizmī.
The prominent Egyptian mathematician Abū Kāmil Shujāʿ ibn Aslam ibn Muḥammad Ibn Shujāʿ (c. 850–c. 930) was known as Al-ḥāsib al-miṣrī (The Egyptian Calculator). His most influential work was his Kitāb fī al-jabr wa al-muqābala (Book of Algebra), which superseded and expanded on al- Khwārizmī work.
He wrote about al_Khwārizmī:
I have studied with great attention the writings of the mathematicians, examined their assertions, and scrutinized what they explain in their works; I thus observed that the book by Muḥammad ibn Mūsā al-Khwārizmī known as Algebra is superior in the accuracy of its principle and the exactness of its argumentation. It thus behooves us, the community of mathematicians, to recognize his priority and to admit his knowledge and his superiority, as in writing his book on algebra he was an initiator and the discoverer of its principles, …(Wikipedia)
Kitāb fī al-jabr wa al-muqābala
The first chapter teaches algebra by solving problems of application to geometry, often involving an unknown variable and square roots. The second chapter deals with the six types of problems found in Al-Khwarizmi’s book, but some of which, especially those of x2, were now worked out directly instead of first solving for x and accompanied with geometrical illustrations and proofs. The third chapter contains examples of quadratic irrationals as solutions and coefficients. The fourth chapter shows how these irrationalities are used to solve problems involving polygons. The rest of the book contains solutions for sets of indeterminate equations, problems of application in realistic situations, and problems involving unrealistic situations intended forrecreational mathematics. (Wikipedia)
Like that of al- Khwārizmī, Abū Kāmil’s work would filter through to Europe in the later Middle Ages, as did the work of the Persian mathematician and engineer Abū Bakr Muḥammad ibn al Ḥasan al-Karajī (c. 935–c. 1029). His three principal surviving works are mathematical: Al-Badi’ fi’l-hisab (Wonderful on calculation), Al-Fakhri fi’l-jabr wa’l-muqabala (Glorious on algebra), and Al-Kafi fi’l-hisab (Sufficient on calculation). Whereas the work of al- Khwārizmī and , Abū Kāmil were still anchored in the algebraic geometry of the Greeks, al-Karajī went as long way to making it a numerical discipline.
Although Brahmagupta had dealt with negative numbers and the rules for calculating with negative quantities, they were largely ignored by the early Islamic algebraists. Al-Samawʾal ibn Yaḥyā al-Maghribī (c. 1130–c. 1180), who was born in Baghdad into a Jewish family of North African origin he converted to Islam, introduced the rule of signs in his al-Bahir fi’l-jabr, (The brilliant in algebra), written when he was nineteen years old. He also dealt with the law of exponents and polynomial division.
Binomial coefficients from Al-Samawal al-Maghribi al-Bahir fi’l-jabr,
Our final Islamic algebraist is Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm Nīsābūrī (1048–1131) better known in English as Omar Khayyam (‘Umar al-Khayyāmī) as a poet but he was polymath, who did important work in mathematics and astronomy. His most important development in algebra was a geometrical general theory of cubic equations.
‘Umar al-Khayyāmī) “Cubic equation and intersection of conic sections” the first page of a two-chaptered manuscript kept in Tehran University. Source: Wikimedua Commons
The third major innovative area of Islamic mathematics was trigonometry. Trigonometry had its origins in Greek astronomy, with Hipparchus (c. 190–c. 120 BCE) providing a table of chords of a circle to designate the size of angles.
Being astronomy, the application is, of course only to spherical triangles. His table did not survive but Ptolemaeus took it over in his Mathēmatikē Syntaxis know in Arabic as the Almagest.
When the Indians took over many aspects of Ancient Greek astronomy they also acquired the cord measure of angles, which they halved to create the sine, a table of sines is presented in the Surya Siddhanta from the 4thor fifth centuries.
English translation of the Surya Siddhanta by Rev. Ebenezer Burgess 1935 Source
This work also defines the cosine, versine and inverse sine. Early Islamic astronomers acquired their astronomy from both Ancient Greece and India but went on to use the Indian sine rather than the Greek cord measure for angles.
The tangent function was known to various ancient cultures, outside of astronomy, as a means for determining the hight of structures. Because the shadow of a tall object creates a right angle triangle from which the tangent and cotangent can be used to determine the height of the object, the tangent became known as the shadow function.
Once again the Persian mathematician al- Khwārizmī was a pioneer in this branch of mathematics producing sine, cosine, and tangent tables. Another Persian astronomer, mathematician and geographer, Habash al-Hasib al-Marwazi (766 – d. after 869) described and produced tables of the tangent and cotangent.
The Syrian astronomer Abū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī aṣ-Ṣābiʾ al-Battānī (before 858–929) defined and produced tables for the secant and cosecant. He was also the first to apply the trigonometric functions to plane triangles. In general, Islamic mathematicians introduced the use of trigonometrical functions into surveying and cartography.
al-Battānī Source: Wikimedia Commons
Abū al-Wafāʾ Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī (940–998), born in Khorasan (in today’s Iran), was the first to present all six of the trigonometrical functions in his Kitabal‐Majisṭī .
Page of the manuscript of Kitab al-majisti by Abu al-Wafa. (Source)
Abū ʿAbd Allāh Muḥammad ibn Muʿādh al-Jayyānī (989–1079), an Arabic mathematician from al-Andalus produced his Kitab madschhulat qisiyy al-kura (The book of unknown arcs of the sphere) a treatise on spherical trigonometry. Al-Jayyānī’s work on spherical trigonometry contains formulae for right-handed triangles, the general law of sines, and the solution of a spherical triangle by means of the polar triangle.
A page from Al-Jayyānī’s work on spherical trigonometry
The Persian polymath, Nasīr al-Dīn al-Tusī (1201–1274), in his work asch-Schakl al-Qattāʿ (Treatise on the Quadrilateral) was the first to handle trigonometry as a mathematical disciple independent of astronomy. He dealt both with the cordal trigonometry of the Greeks as well as the six modern functions, introducing the law of tangents for spherical triangles and providing proofs of it and the law of sines.
Throughout the medieval Islamic period from al- Khwārizmī in the eighth century to Ulugh Beg in the fifteenth, Islamic astronomers and mathematicians continually worked on developing new mathematical methods to calculate ever more accurate tables of trigonometrical functions. In general, they took the simple method developed by Hipparchus to determine the size of angles in astronomy and over many generations developed an entire branch of mathematics, which would continue to increase in importance after re-entering Europe.
It is difficult to overemphasise to contributions that Islamic mathematicians made in various areas of mathematics that they had inherited from their predecessors, developments that would play a significant role in the general development of science and physics in particular in later centuries.
[1] J. L. Berggren, Episodes in the Mathematics of Medieval Islam, Springer, New York, 2003, p. 102
It is quite common that people get asked what they think is the most import development in technology or the most significant technological invention in human history. Apart from the ubiquitous wheel, which is almost certainly the most common answer, unless they are historians, they will almost always name something comparatively modern and usually big and impressive–the steam engine, the automobile, the airplane, the computer or whatever. However, having been at one time in my life, for a number of years, an archaeologist, I am very much aware of the massive impact that seemingly everyday things had on the development of human society–the most obvious is cooking with fire, but also making, ceramics, bricks, glass, simple tools, and many other things many of them seemingly small and insignificant. In response to a fascinating blog post by Rachel Laudan on the uses to which gourds were put in the history of cooking, I once wrote a blog post on the significance of the invention of the sewing needle.
This being the case, I couldn’t resist when I came across reviews of Roma Agrawal’s book Nuts & Bolts and bought a copy, which I read with growing enthusiasm and delight. I couldn’t resist because the full title is Nuts & Bolts: Seven Small Inventions That Changed the World (in a Big Way).[1]
Roma Agrawal is not a historian but a structural engineer, a graduate of Oxford University, BA physics, and Imperial college, MA Structural engineering, who has worked on major engineering project, including the Shard in London. In her book she brings an engineer’s eyes to a popular historical view of the nail, the wheel, the spring, the magnet, the lens, string, and the pump. Outlining not only their origins, their evolution, the multiple forms they have taken and the multiple uses to which they have been put but also giving a soft scientific and engineering explanation of how they work in terms of forces and resistance.
From the outset this book is wonderfully written and a delight to read. The world’s textbook writers could learn a lesson or two from Agrawal on how to hold a reader’s interest and entertain them whilst at the same time educating them. She makes it seem very easy.
She starts with the nail, a very simple, small, seemingly insignificant everyday object that most people wouldn’t even think of when asked to list important historical invention. However, the nail is and has been a very important element in building projects of all sizes throughout the world for millennia. She traces its origins, its developments, and its very important transition from being hand forged to machine made. She explains how the force of friction enables nails to hold things together. However, she doesn’t just deal with nails in this chapter but with screws, rivets, and nuts and bolts, which as she explains are all basically evolved forms of the humble nail. In this direction the mental leap that most surprised me is that the piles–wood, metal, concrete–driven into the ground to support building are in reality just very big nails.
After the nail, Agrawal turns to that perennial favourite greatest invention, the wheel. We of course get the wheel enabling transport but more significantly she takes her readers on a whirlwind tour of many of the other places where wheel can be found fulfilling an important function. We have the potter’s wheel, cog wheels and gear wheels, the invention of the bicycle and the invention of the gyroscope. She includes a fascinating section on Josephine Cochran’s invention of the dishwasher. One facet of Agrawal’s narratives is that where possible she draws attention to the contributions made by women to the history of technology. She takes us through the evolution of better wheels from the simple solid plank wheel down to the sophisticated spoked wheels of modern bicycles and closes by stating, “Human progress and the reincarnations of the wheel and axel are intricately intertwined. And that’s why we should absolutely continue to reinvent the wheel.”
Our next small invention is the humble spring, which doesn’t immediately spring to mind when asked about the greatest inventions. (I’ll let myself out!) One revelation that totally blew my mind when I first read it, is that the bow, as in bow and arrow, is a spring! If you want to know why the elaborately curved Mongolian bow is superior to the European longbow this is the place to go. Moving on via springs in guns Agrawal land at a device that lives from its springs the mechanical clock. Here we meet another aspect of Agrawal’s approach, hands on. The opening paragraphs of the nail section found her hand forging nails in a smithy, we now find in the workshop of Dr Rebecca Struthers, independent watchmaker and horologist. Struthers put out her own book Hands ofTime: A Watchmaker’s History of Time (Hodder & Stoughton) in 2023. The lady engineer and the lady watchmaker take the reader through the history of the clock and the central role that springs came to play in their construction. John Harrison, of course, gets a nod on route. Fascinatingly the structural engineer introduces her readers to building, suspended on springs to protect them from earthquakes or to shield them from external vibrations.
Our interest is now directed to the magnet, where it is not long before we get briefly introduced Dr William Gilbert and his De Magnete but we don’t linger, quickly progressing to the development in magnets and their materials now that magnetism had been established as a science. Having sketched the developed the modern magnet we get introduced to the electric telegraph, a massive communications revolution, that depended on magnets. The electric telegraph was superceded by the telephone another communications device dependent on the magnet. This capital argues for the magnet as the driver of modernity with the television following on the heels of the telegraph and telephone. Here Agrawal pulls another rabbit out of her hat, ignoring the western developers in favour of the story Takayanagi Kenjiro the independent Japanese inventor of the television. The section closes with the story of LEDs.
Up till now, whilst reading, I was really enjoying Agrawal’s fascinating and stimulating book and then I ran into her section on the lens, and soon wished I hadn’t. Readers of this blog will know that the history of optics is one of my special areas of study and I’m sorry but Agrawal’s story of the lens is a trainwreck! I’ll move on for now but return to the lens later.
As opposed to the chapter on the lens, the chapter on string is a delight. Agrawal opens with the steel cables that hold up suspension bridges, which is not what one normally thinks about when somebody uses the word string. However, as she points out the cables on smaller suspensions bridges, such as the one that was one of he first engineering projects, are twisted together out of steel fibres in exactly the same way as string is made by twisting together plant fibres. The heavier ones are made with a slightly different process but are also basically string. She then moves on to sewing and the sawing needle, sewing thread being, of course another form of string. Moving on we have cloth which is usually woven or knitted string. String has truly played a major roll in human history. The chapter closes with a discourse on music made with string instruments and instead of the violins or guitars, one might expect we get a fascinating detailed description on the tanpura, the drone instrument in Indian music, and how the strings are manipulated to produce the vibrating, droning sound.
The final chapter is devoted to the pump, which Agrawal defines as a way of raising water to a higher level. After a brief sketch of the history of the water lifting devices, she turns to a description of the most fascinating of all pumps, the human heart. The heart is a small pump with an incredible performance. However, Agrawal is not deviating from engineering to biology but the description of the heart is used as an introduction to the story of the development of the heart-lung machine, a truly fascinating story of a piece of medical engineering history. After this excurse into the medical discipline we follow Agrawal into the equally fascinating story of the development of the breast milk pump, which Agrawal was led to through her own problems with breast feeding.
We return to the lens. This starts, as much of the book, with a personal anecdote about the conception of Agrawal’s daughter, which was by artificial insemination and a description of the microscope developed to study the insemination of ova. This is one of several personal stories in the book that illustrates Agrawal’s interest in the topic under discussion. Having introduced the lens through the microscope, we now move back to the origins and history of the lens, here she goes off the rails. She accepts that the so-called Nimrud lenses (7thcentury BCE) are lenses and not simply ground and polished pieces of lens shaped crystal, for which there is simply no proof whatsoever. I think they are more probably decorative stones.
She now moves on to the Greeks and writes the following:
The Greeks laid down some basic rules of how light reflects off mirrors and even bends through lenses.
The Greeks did indeed study the basics of refraction but those studies had almost nothing to do with lenses. The most extensive study of refraction was by Ptolemaeus, who was concerned with atmospheric refraction in astronomy and most important failed to determine the sine law of refraction.
Having quickly rubbished Greek theories of optics without going into detail we arrive at Ibn al-Haytham (b. 965 BCE). After a biographical sketch she makes the claim that “he finally explained correctly how sight works.” Although Ibn al-Haytham made great progress towards a correct explanation of how sight works, it is by no means completely correct and above all most of the elements he uses in his model are taken from the Greek sources that she doesn’t present. She then presents one of al-Haytham’s experiments claiming that it proves his theories, which it doesn’t. We then get the extraordinary statement:
Ibn al-Haytham’s work related to optics was groundbreaking for many reasons. For the first time, someone suggested correctly, that light exists independently of vision.
Sorry, but this is pure and utter garbage!
He also said that light travels in rays along straight lines, and these rays are not modified by other rays that cross their path.
This was already known to the Greeks.
For the first time, he conducted a scientific study of images formed by lenses.
Ibn al-Haytham did not conduct a scientific study of images formed by lenses. He made some minor comments on the images formed by spherical lenses.
We then get the classic:
In another interesting link, physicist Jim Al-Khalili writes that Ibn al-Haytham’s discussion on perspective-which was translated into Italian in the fourteenth century-enabled Renaissance artists to create the illusion of three-dimensional depth in their work.
This illustrates a major problem in her work on al-Haytham, she uses the highly hagiographic and historically inaccurate work of Al-Khalili as her source, rather than the historically accurate, in depth studies of David C. Lindberg, A. Mark Smith, and A. I. Sabre.
As far as the development of linear perspective during the Renaissance is concerned, the geometry of linear perspective is the optical geometry of Euclid, which is in no way dependent on anything al-Haytham wrote. Of the early developers of linear perspective Lorenzo Ghiberti (1378–1455) indeed quotes al-Haytham. However, we know nothing about the sources which inspired Filippo Brunelleschi (1377–1446) to carry out his famous demonstration of linear perspective. Finally, Mark Smith thinks that Leon Battista Alberti (1404–1472), who wrote and published the first explanation of linear perspective in his Della Pittura (1435)/De Pictura (1436) did not reference optical literature to write his book but that it was based on his work recording the architectural ruins in Rome using a plane table. More importantly, Alberti states clearly in his book that for linear perspective it is irrelevant whether one holds an extramission theory of optics, Euclid, or an intromission one, al-Haytham.
We then get the claim that that Ibn al-Haytham “laid the foundation of what we now describe as scientific method.” As al-Haytham’s experimental programme is an extended copy of that of Ptolemaeus’ programme this claim is simply refuted.
Following an explanation of how lenses work, we get a horrible piece of ahistorical garbage:
The science of optics advanced significantly in the Islamic empires, but the practical applications of lenses remained largely limited to burning glasses and simple magnification. Centuries later, when the Islamic Golden Age of science [my emphasis] began to dim in the Middle East, and as light began to break through the Dark Ages in the West, [my emphasis] Europe’s Renaissance thinkers built on the work of their medieval counterparts to truly harness the superpower of lenses.
The concept of the Islamic Golden Age of science is, today, increasingly viewed with scepticism by historians as it is particularly difficult to define just when it was supposed to have ended. The term Dark Ages, however, is not just viewed with scepticism but has been totally banned from the vocabulary of serious historical discussion.
Having written this paragraph, Agrawal then dives straight into the invention of the microscope, strangely making here no mention of either the invention of eyeglasses (spectacles) or the telescope. This is particularly bizarre as a couple of pages earlier she had written, “ He [Ibn al-Haytham] laid the foundations for scientists after him – including Newton, who published his work 700 years later – to not only study and explain light even further, but also to engineer spectacles, microscopes, telescopes, cameras, and more.” Note Newton gets a name check but a whole list of other significant contributors to the history of optics, Kepler for example, don’t. Without the invention of spectacles, no industry of lens making would have developed, and without spectacles no telescope, and without the telescope no microscope!
Interestingly, the earliest date for the end of the so-called Islamic Golden Age of science is the fall of Baghdad at the hand of the Mongols in 1258, which almost coincides with the invention of spectacles in Northern Italy, which by the way, was in no way connected to the optical theories of Ibn al-Haytham.
We get a few lines on Robert Hooke and his Micrographia before she writes the following:
No doubt inspired by Hooke’s work, a Dutch shopkeeper with little formal education decided to look closer, leading him to seeing many things that humans had never seen before.
The Dutch shopkeeper is, of course Antony Leeuwenhoek, who was actually quite a bit more than just a shop keeper. There is actually no evidence that Leeuwenhoek was inspired by Hooke. This is a purely speculative theory proposed by Brian J. Ford, who is the source that Agrawal uses for he comments on Leeuwenhoek.
There follows an account of Leeuwenhoek’s single lens microscopes which ends with the following:
Holding the microscope up to his eye, he could peer through his handmade lenses, some of which could magnify objects by an astonishing 266 times. To put this in perspective, the microscopes with two lenses invented in the late sixteenth century by the Dutch father and son team, Hans and Zacharias Janssen[my emphasis], could only magnify up to a maximum of ten times, because of the limited quality of the lenses and blurring effects first studied by Ibn al-Haytham.
The claim that Hans and Zacharias Janssen invented the microscope in the sixteenth century was very dubious at the best when it was first presented, apart from anything else Zacharias Janssen would have been only four-years-old at the time given in the story. However, modern research by Huib Zuidervaaart, has shown that Zacharias Janssen, who is also credited with the invention of the telescope, had nothing whatsoever to do with optics before 1616.
We don’t actually know who invented the microscope but it is assumed that several early telescope makers and user, such as Galileo, looked through their Dutch or Galilean telescopes the wrong way round and realised that it functioned as a microscope. Several people in Galileo’s circle in the Accademia dei Lincei used such Galilean microscopes and it was Giovanni Faber of the Lincei, who gave the instrument its name. The first use of a Keplerian telescope, with two convex lenses, is credited to Cornelis Drebbel in 1619.
We then get an account of Leeuwenhoek’s discoveries culminating in his discovery of sperm. Agrawal writes:
Combined with the theory that all female animals have eggs, which also made its appearance in the mid-1670s…
This theory originated with William Harvey in his De Generatione, Ex ovo omnia – All things come from an egg, in 1651.
The rest of the chapter deals with the development of the microscope and its use in artificial insemination followed by a long section on the history of the history of the camera, both more or less acceptable.
Of course, the series of historical errors in this chapters leads on to speculate if the history in the other chapters is accurate. Unlike this chapter the others are not my speciality but as far as I could ascertain they are historically acceptable.
The book has neither foot nor endnotes. There are lists of the experts consulted for each chapter and also a separate extensive bibliography of sources for each. There is also a useful index. The book has occasional black and white illustrations many of which are had drawn, one assumes by the author. Despite my complaints about the chapter on the lens, I recommend Roma Agrawal’s book, which is despite the flaws mentioned above an excellent read.
[1] Roma Agrawal, Nuts & Bolts: Seven Small Inventions That Changed the World (in a Big Way), Hodder & Stoughton, London, 2023.
In a recent excellent video on Hypatia – Myths and History, Tim O’Neill correctly pointed out that the claim that Hypatia created the astrolabe was rubbish, going on to claim that it had existed for at least five centuries before she lived. Tim’s second claim is in fact wrong but is just one of many commons claims about the ancient origins of the astrolabe. I have decided to give a brief sketch of what we actually know about the origins of this multipurpose astronomical instrument.
NATIONAL MARITIME MUSEUM, GREENWICH In 694 ah (1294–95 ce), Mahmud ibn Shawka al-Baghdadi produced this astrolabe.
It would surprise most people to discover that the earliest known treatise on the astrolabe was written by Theon of Alexandria (c. 335–c. 405 CE), Hypatia’s father. This work is no longer extant but the Suda, the tenth-century Byzantine encyclopaedia, mentions it. Both the treatise on the astrolabe by the Greek, Christian scholar John Philoponus (c.490–c. 570) and that of the Syriac scholar Severus Sebokht (575–667) draw heavily on the treatise of Theon. It is not known and cannot be ascertained whether Theon invented the plane astrolabe or was merely writing about an already existing instrument.
The earliest surviving reference to the plane astrolabe is in a letter from Synesius of Cyrene (c. 373–c. 414), the Greek bishop of Ptolemais describing how Hypatia taught him how to construct a silver plane astrolabe as a gift for an official. This is the origin of the myth that she invented the astrolabe.
The invention of the astrolabe has been variously attributed to Ptolemaeus (c. 100–c. 170), Hipparchus (c. 190–c. 120 BCE) and Apollonius of Perga (c. 240–c. 190 BCE) but there is absolutely no evidence to support any of these attributions. Hipparchus and Apollonius both probably used a dioptra attached to a protractor to measure angles, which can be regarded as a precursor to the astrolabe.
A dioptra (Greek: διόπτρα) is a classical astronomical and surveying instrument, dating from the 3rd century BC. The dioptra was a sighting tube or, alternatively, a rod with a sight at both ends, attached to a stand. If fitted with protractors, it could be used to measure angles. (Wikipedia)
The reverse face of a plane astrolabe is basically a dioptra mounted on a protractor
Reverse face of an astrolabe with alidade (dioptra) North African, 9th century AD, Planispheric Astrolabe Khalili Collection Source: Wikimedia Commons
but it is the front of the instrument that is the key element of the instrument.
This is a stereographic projection of the celestial hemisphere known as a planisphere.
The planisphere face of an astrolabe
The earliest known reference to the planisphere is a text by Ptolemaeus:
The Planisphaeium (Greek: Ἅπλωσις ἐπιφανείας σφαίρας, lit. ’Flattening of the sphere’) contains 16 propositions dealing with the projection of the celestial circles onto a plane. The text is lost in Greek (except for a fragment) and survives in Arabic and Latin only. (Wikipedia)
Once again people try to attribute the origin of the planisphere to Hipparchus but as with the astrolabe, there is absolutely no evidence to support this attribution.
Based on his authorship of the Planisphaeium, some try to attribute the invention of the astrolabe to Ptolemaeus but in his Mathēmatikē Syntaxis (Greek: Μαθηματικὴ Σύνταξις, lit. ’Mathematical Systematic Treatise’), better known as the Almagest, he describes the instrument that he used for his observations and it was an armillary sphere, not an astrolabe.
On Thursday 15 November 2023, I checked into a clinic in Bad Kissingen, Lower Franconia to start twenty-one days of orthopaedic rehabilitation for my fucked back. On the following Monday, the fifth day, I was feeling totally shitty and on the Tuesday morning I tested positive for Covid. I broke off my rehabilitation and on the Wednesday I was sent home.
Having waited for the Christmas’ and New Years’ holiday period to pass I reapplied to my health insurance and was granted a new rehabilitation.
On Monday 25 March 2024, I checked into a clinic in Bad Kissingen, Lower Franconia to start twenty-one days of orthopaedic rehabilitation for my fucked back. On Monday 8 march, the fifteenth day, I was feeling totally shitty and on the Tuesday morning I tested positive for Covid. I broke off my rehabilitation and on the Wednesday I was sent home.
Normal service will be resumed as soon as I stop coughing my soul out!
Some of you will remember that back in November I announced that I would be taking a break from writing my blog in order to get some medical rehabilitation for my fucked spine (official medical terminology). You might also remember that this turned into a farce when on entering the clinic I almost immediately acquired a dose of the dreaded Covid. Having successfully jumped over all the bureaucratic hurdles, I’m now due to restart my medical rehabilitation on next Monday, 25 March, meaning there will be no new blog posts during the next three weeks.
Here’s hoping that I don’t develop typhoid or something this time. As Phillip Helbig suggested I should have signed off my hiatus post last time:
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 ofDifferences 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 theEye, 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 theEye 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 toLight: 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. 72Ibn 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.
[1] David C. Lindberg, Theories of Vision: From Al-Kindi to Kepler, University of Chicago Press, 1976, p. 19
William Gilbert’s De Magnete is a book that covers a wide range of information on all aspects of magnetism, loadstones, magnets, and the magnetic compasses. He was a high ranking physician living in London and doesn’t appear to have travelled anywhere else let along sailed anywhere on a ship. This raises the justified question; how did he acquire much of the knowledge that he presents to his readers? Did he write the book alone, or were there others involved in its production?
We know that he borrowed liberally from the works of Petrus Peregrinus de Maricourt (fl. 1269), Robert Norman (dates unknown), and William Barlow (1544–1625) without really acknowledging those borrowings. We would say he plagiarised them, but what he did was common practice amongst scientific authors during the Renaissance. There were, however, other parts of the book that relied on mariner’s knowledge to which Gilbert almost certainly did not have access. He boasts of having acquired knowledge of the behaviour of the mariner’s compass over all on the globe from conversations with the circumnavigators, Francis Drake (c. 1540–1596) and Thomas Cavendish (1560–1592) but were there others?
We know according to the reports that at least one and possibly two others actually contributed text to De Magnete. Following Gilberts death, two other magnetists claimed the right to be considered his true disciple, William Barlow (1544–1625), who I dealt with in an earlier episode, and Mark Ridley (1560–c. 1624), who as I noted in an earlier episode lived in Wingfield House with Gilbert and whom I will deal with in the next post. Their rivalry developed into a mudslinging match in various publications, which I will also deal with in the next post. In one of his ripostes to Barlow, Mark Ridley wrote:
[Edward Wright] was a verie skilful and painefull man in the Mathematickes, a worthy reader of that Lecture of Navigation for the East-India Company … [T]his man took great paines in the correcting the printing of Doctor Gilberts booke, and was very conversant with him, and considering of that sixt booke [of De Magnete] which you [Barlow] no way beleeve, I asked him whether it was any way of his making or assistance, for that I knew him to be most perfect in Copernicus from his youth, and he denied that he gave any aide thereunto, I replied that the 12 chapter of the 4 Booke must needs be his, because of the table of the fixed Starres, so he confessed that he was the author of that chapter, and inquiring further whether he observed the Author [Gilbert] skillfull in Copernicus, he answered that he did not, then it was found that one Doctor Gissope [Joseph Jessop] was much esteemed by him, and lodged in his house whom he knew alwaies to be a great Scholler in the Mathematick, who was a long time entertained by Sir Charles Chandish, he was a great assistance in that matter as we judged, and I have seen whole sheetes of this mans own hand writing of Demonstrations to this purpose out of Copernicus, in a book of Philosophie copied out in another hand[.]
All that I can find about Joseph Jessop, who, according to Ridley, instructed Gilbert in Copernican cosmology is that he was apparently a fellow London physician and an erstwhile fellow of King’s.
In contrast to the elusive Dr Jessop, Edward Wright (1561–1615) is one of the most prominent figures in relevant circles in the last quarter of the sixteenth century and the first quarter of the seventeenth. A leading mathematical practitioner, not just in England but in the whole of Europe, particularly in the areas of cartography and navigation. He had solved the mathematical problem of how to construct the Mercator projection and published it in one of the most important English books on navigation, his Certaine Errors in Navigation in 1599. He had made Simon Stevin’s equally important De Havenvinding (1599) available to English mariners by translating it into English and publishing it as The Hauen-finding Art, or The VVay to Find any Hauen or Place at Sea, by the Latitude and Variation also in 1599. He was the designer of important mathematical instruments, an advisor on and teacher of navigation and cartography.
Cover of Wright’s Certaine Errors Source: Wikimedia CommonsSource
As well as this supposed anonymous contribution to Gilbert’s masterpiece he is also a named contributor as the author of a so-called laudatory address at the beginning of the book or to give it its full title:
To the most learned Mr. William Gilbert, the distinguished London physician and father of the magnetic philosophy : a laudatory address concerning these books on magnetism, by Edward Wright.
Wright lays it on thick in his opening paragraph:
Should there be any one, most worthy sir, who shall disparage these books and researchers of yours, and who shall deem these studies trifling and in no wise sufficiently worthy of a man consecrated to the graver study of medicine, of a surety he will be esteemed no common simpleton. For that the uses of the loadstone are very considerable, yea admirable, is too well known even among men of the lowest class to call for many words from me at this time or for any commendation. In truth in my opinion, there is no subject-matter of higher importance or of greater utility to the human race upon which you could have brought your philosophical talents to bear.
Having in a long passage of purple prose emphasised the importance of the invention of the compass for mariners, Wright initially concentrates on the topic of magnetic variation, seeming to believe in opposition to Gilbert that the use of variation to determine longitude is a real possibility. He then moves on to the topic of magnetic dip and the possibility that this seems to offer to determine latitude by inclement and overcast weather. Here his praise goes into overdrive:
Thus then, to bring our discourse back again to you, most worthy and learned Mr. Gilbert (whom I gladly acknowledge as my master in this magnetic philosophy[my emphasis]), if these books of yours on the Loadstone contained nought save this one method of finding latitude from the magnetic dip, now first published by you, even so our British mariners as well as the French, the Dutch, the Dames, whenever they have to enter the British sea or the strait of Gibraltar from the Atlantic Ocean, will justly hold them worth no small sum of gold.
With reference to the sentence in brackets that I have emphasised, it should be remembered that Wright is no humble mariner but a graduate of Cambridge University, who is a leading authority on all aspects of navigation and the magnetic compass, as well as a published author and translator, so high praise indeed. It should however be noted that the plan to determine latitude by magnetic dip propagated by Gilbert in his book and so highly praised here, by Wright, was never actually realised.
Wright goes on to address Gilbert’s theory of diurnal rotation and rehashes the standard physical argument in its favour, that it is more plausible to believe that the comparatively small sphere of the Earth rotates once every twenty-four hours than that the vastly larger sphere of the fixed stars does so. He considers the religious objection but finally comes down in favour of a geocentric model with diurnal rotation.
Towards the end of his laudatory address Wright references two other European experts:
Nor is there any doubt that those most learned men, Petrus Plantius (a most diligent student not so much of geography as of magnetic observations) and Simon Stevinius, a most eminent mathematician will be not a little rejoiced when first they set eyes on these your books and therein see their own 𝜆𝜄𝜇𝜈𝜀𝜐-𝜌𝜀𝜏𝜄𝜅ή𝜈 or method of finding ports so greatly and unexpectedly enlarged and developed; and of course they will, as far as the may be able, induce all navigators among their own countrymen to note the dip no less than the variation of the needle.
Petrus Plancius (1552–1622) was a Flemish astronomer, cartographer, and clergyman, who was an expert on safe maritime routes to India and the Spice Islands. He would go on to become one of the founders of the Dutch East India Company in 1602. He is famous for his celestial globes and in particular for training the navigator Pieter Dirkszoon Keyser (c. 1540–1596)to be one of the first to map the stars in the southern hemisphere. Simon Stevin is already known to us and Gilbert endorsed the scheme of Simon Stevin (1548–1620), put forward in his The Hauen-finding Artto provide tables of the correctly measured variation to compare with measured observations as an aid to navigation. It can be assumed that Wright as the translator of The Hauen-finding Art introduced Gilbert to Stevin’s work.
Of interest is the following allusion:
Let your magnetic Philosophy, most learned Mr. Gilbert, go forth then under the best auspices–that work held back not for nine years only, according to Horace’s Council, but for almost another nine…
Copernicus alludes to the same advice from Horace’s The Art of Poetry on the opening page of the preface to De Revolutionibus:
For he [Tiedemann Giese] repeatedly encouraged me and, sometimes adding reproaches, urgently requested me to publish this volume and finally permit it to appear after being buried among my papers and lying concealed not merely until the ninth year but by now the fourth period of nine years.
Turning now to Book 4 Chapter 12 of De Magnete, which Ridley relates was authored by Wright we find a detailed technical section on the best way to determine magnetic variation, which I described in my post in this series on De Magnete so, The twelfth chapter of book four provides the best and most detailed description of how to determine variation published up till that time.
The chapter describes in great technical details the various ways of determining magnetic variation at sea and on land. It includes detailed instruction for the design and construction of special instruments for this task and outlines the mathematics necessary to carry out the calculations. It includes Tycho Brahe’s value for the deviation of the Arctic pole-star from true north, 2 deg. 55 min. but gives 3 degrees as a good approximation. It also includes a list of the right ascension and declination of bright, brilliant stars not far from the equator for determining variation at night and the construction of an instrument to do so. It closes with instructions on how to construct an instrument for finding the ortive amplitude on the horizon. For those who don’t know, the ortive amplitude is defined thus:
The arc of the horizon between the true east or west point and the centre of the sun, or a star, at its rising or setting. At the rising, the amplitude is eastern or ortive. (Wiktionary)
Instrument for determining variation on landInstrument for determining variation at sea at nightan instrument for finding the ortive amplitude on the horizon.
All the above is very much in Wright’s area of expertise rather than Gilbert’s, so the claim that he wrote this chapter is very plausible. This of course raises the question as to whether Wright was the author, or co-author of, or advisor on other sections of the book of a similar technical nature. This question could probably only be answered if we could find Gilberts working notes, draft manuscript(s), or correspondence from when he was working on the book. Unfortunately, when he died he donated his library and one assumes his papers to the College of Physicians of which he was President. I say, unfortunately, because the College of Physicians and its entire library was lost in the Great Fire of London, so we will never know if Wright contributed more to De Magnete or not.
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 IdeasPage from The Book of Secrets in the Results of IdeasPage 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 automataAl-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.
The Brightest Stars for the Construction of Mechanical Clocks (al–Kawākib al–durriyya fī waḍҁal–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.
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 16th century between the observatory in Istanbul and Europe.
[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 InternationalSymposium for the History of Arabic Science, Aleppo, April 5–12 1976, Aleppo: Institute forb the History of Arabic Science, 1979.
If your philosophy of [scientific] history claims that the sequence should have been A→B→C, and it is C→A→B, then your philosophy of history is wrong. You have to take the data of history seriously.
John S. Wilkins 30th August 2009
Culture is part of the unholy trinity—culture, chaos, and cock-up—which roam through our versions of history, substituting for traditional theories of causation. – Filipe Fernández–Armesto “Pathfinders: A Global History of Exploration”
The Renaissance Mathematicus 
