Category Archives: History of Astronomy

Finding your way on the Seven Seas in the Early Modern Period

I spend a lot of my time trying to unravel and understand the complex bundle that is Renaissance or Early Modern mathematics and the people who practiced it. Regular readers of this blog should by now be well aware that the Renaissance mathematici, or mathematical practitioners as they are generally known in English, did not work on mathematics as we would understand it today but on practical mathematics that we might be inclined, somewhat mistakenly, to label applied mathematics. One group of disciplines that we often find treated together by one and the same practitioner consists of astronomy, cartography, navigation and the design and construction of tables and instruments to aid the study of these. This being the case I was delighted to receive a review copy of Margaret E. Schotte’s Sailing School: Navigating Science and Skill, 1550–1800[1], which deals with exactly this group of practical mathematical skills as applied to the real world of deep-sea sailing.

Sailing School001.jpg

Schotte’s book takes the reader on a journey both through time and around the major sea going nations of Europe, explaining, as she goes, how each of these nations dealt with the problem of educating, or maybe that should rather be training, seamen to become navigators for their navel and merchant fleets, as the Europeans began to span the world in their sailing ships both for exploration and trade.

Having set the course for the reader in a detailed introduction, Schotte sets sail from the Iberian peninsular in the sixteenth century. It was from there that the first Europeans set out on deep-sea voyages and it was here that it was first realised that navigators for such voyages could and probably should be trained. Next we travel up the coast of the Atlantic to Holland in the seventeenth century, where the Dutch set out to conquer the oceans and establish themselves as the world’s leading maritime nation with a wide range of training possibilities for deep-sea navigators, extending the foundations laid by the Spanish and Portuguese. Towards the end of the century we seek harbour in France to see how the French are training their navigators. Next port of call is England, a land that would famously go on, in their own estimation, to rule the seven seas. In the eighteenth century we cross the Channel back to Holland and the advances made over the last hundred years. The final chapter takes us to the end of the eighteenth century and the extraordinary story of the English seaman Lieutenant Riou, whose ship the HMS Guardian hit an iceberg in the Southern Atlantic. Lacking enough boats to evacuate all of his crew and passengers, Riou made temporary repairs to his vessel and motivating his men to continuously pump out the waters leaking into the rump of his ship, he then by a process of masterful navigation, on a level with his contemporaries Cook and Bligh, brought the badly damaged frigate to safety in South Africa.

Sailing School004

In each of our ports of call Schotte outlines and explains the training conceived by the authorities for training navigators and examines how it was or was not put into practice. Methods of determining latitude and longitude, sailing speeds and distances covered are described and explained. The differences in approach to this training developed in each of the sea going European nations are carefully presented and contrasted. Of special interest is the breach in understanding of what is necessary for a trainee navigator between the mathematical practitioners, who were appointed to teach those trainees, and the seamen, who were being trained, a large yawning gap between theory and practice. When discussing the Dutch approach to training Schotte clearly describes why experienced coastal navigators do not, without retraining, make good deep-sea navigators. The methodologies of these two areas of the art of navigation are substantially different.

The reader gets introduced to the methodologies used by deep-sea navigators, the mathematics developed, the tables considered necessary and the instruments and charts that were put to use. Of particular interest are the rules of thumb utilised to make course corrections before accurate methods of determining longitude were developed. There are also detailed discussions about how one or other aspect of the art of navigation was emphasised in the training in one country but considered less important in another. One conclusion the Schotte draws is that there is not really a discernable gradient of progress in the methods taught and the methods of teaching them over the two hundred and fifty years covered by the book.

Sailing School003.jpg

As well as everything you wanted to know about navigating sailing ships but were too afraid to ask, Schotte also delivers interesting knowledge of other areas. Theories of education come to the fore but an aspect that I found particularly fascinating were her comments on the book trade. Throughout the period covered, the teachers of navigation wrote and marketed books on the art of navigation. These books were fairly diverse and written for differing readers. Some were conceived as textbooks for the apprentice navigators whilst others were obviously written for interested, educated laymen, who would never navigate a ship. Later, as written exams began to play a greater role in the education of the aspirant navigators, authors and publishers began to market books of specimen exam questions as preparation for the exams. These books also went through an interesting evolution. Schotte deals with this topic in quite a lot of detail discussing the authors, publishers and booksellers, who were engaged in this market of navigational literature. This is detailed enough to be of interest to book historians, who might not really be interested in the history of navigation per se.

Schotte is excellent writer and the book is truly a pleasure to read. On a physical level the book is beautifully presented with lots of fascinating and highly informative illustrations. The apparatus starts with a very useful glossary of technical terms. There is a very extensive bibliography and an equally extensive and useful index. My only complaint concerns the notes, which are endnotes and not footnotes. These are in fact very extensive and highly informative containing lots of additional information not contained in the main text. I found myself continually leafing back and forth between main text and endnotes, making continuous reading almost impossible. In the end I developed a method of reading so many pages of main text followed by reading the endnotes for that section of the main text, mentally noting the number of particular endnotes that I wished to especially consult. Not ideal by any means.

This book is an essential read for anybody directly or indirectly interested in the history of navigation and also the history of practical mathematics. If however you are generally interested in good, well researched, well written history then you will almost certainly get a great deal of pleasure from reading this book.

[1] Margaret E. Schotte, Sailing School: Navigating Science and Skill, 1550–1800, Johns Hopkins University Press, Baltimore, 2019.


Filed under Book Reviews, History of Astronomy, History of Cartography, History of Mathematics, History of Navigation, Renaissance Science, Uncategorized

The emergence of modern astronomy – a complex mosaic: Part XXIII

The first period of telescopic, astronomical discoveries came to an end in 1613, which was seventy years after the publication of Copernicus’ De revolutionibus. This makes it a good point to stop and take stock of the developments that had taken place since the appearance of that epoch defining magnum opus. First we need to remind ourselves of the situation that had existed before Copernicus heliocentric hypothesis entered the world and triggered a whole new cosmology and astronomy debate. The mainstream standpoint was an uneasy combination of Aristotelian cosmology and Ptolemaic astronomy. Uneasy because, as some saw it, the Ptolemaic deferent and epicycle model of planetary motion contradicted Aristotle’s homocentric principle, which led to a revival of homocentric astronomy. Others saw the principle of uniform circular motion contradicted by Ptolemaeus’ use of the equant point. In fact, we know that the removal of the equant point, for exactly this reason, was the starting point of Copernicus’ own reform efforts. Another minority view that was extensively discussed was a geocentric system with diurnal rotation, as originated in antiquity by Heraclides of Pontus, regarded by some as more rational or acceptable than that the sphere of the fixed stars rotated once in twenty-four hours. Also still up for debate was the Capellan system with Mercury and Venus orbiting the Sun in a geocentric system. Then came Copernicus and added a new radical alternative to the debate.

By 1613 most of the Aristotelian cosmology had been disposed of bit for bit. Aristotle’s sublunar meteorological comets had definitely become supralunar astronomical objects, although what exactly they were was still largely a mystery. As we shall see Galileo later embarrassed himself by maintaining a position on comets very close to that of Aristotle. The comets becoming supralunar had also disposed of Aristotle’s crystalline spheres, although Copernicus seems to have still believed in them. The telescopic discovery of the geographical features on the Moon and the spots on the Sun had put an end to Aristotle’s perfection of the celestial spheres. They together with the comets and the supernovas of 1573 and 1604, both of which had clearly been shown to be supralunar, also contradicted his immutability of the heavens. The discovery of the four largest moons of Jupiter ended the homocentric concept and the discovery of the phases of Venus, originating in a solar orbit, ruled a pure geocentric system but not a geo-heliocentric one. As a result of all these changes cosmology was up for grabs.

In astronomy the biggest single change was that nearly all astronomers, following Copernicus, now believed in the reality of their models and no longer viewed them as purely mathematical constructions designed to save the phenomena. This was a major shift as previously the discussion of the reality of the heavens was regarded as a discussion for philosophers and definitely not astronomers. So which models were up for discussion? Had in the intervening seventy years the debate simplified, reduced to a choice between two competing models, Ptolemaic geocentrism and Copernican heliocentrism, as Galileo would have us believe twenty years later? Actually no, if anything the situation had got considerably more confused with a whole raft full of astronomical models jostling for a place at the table. What were these competing models?

Given the telescopic observations of the phases of Venus and the assumption of similar phases for Mercury, a pure Ptolemaic geocentric model should have been abandoned but there was still a hard core that refused to simply give up this ancient model. Christoph Clavius (1538–1612) in the last edition of his Sphaera, the standard Jesuit textbook on astronomy, acknowledged problems with the geocentric model but urged his readers to find solutions to the problems within the model. As late as 1651 Giovanni Battista Riccioli (1598–1671), in the famous frontispiece to his Almagestum novum, shows Ptolemaeus lying defeated on the ground, whilst the heliocentric and geo-heliocentric systems are weighed against each other, but he is saying, I will rise again.


Frontispiece of Riccioli’s 1651 New Almagest. Source: Wikimedia Commons

Due to William Gilbert’s revival of the Heraclidian diurnal rotation, we now have two geocentric models, with and without diurnal rotation. The Copernican heliocentric system is, of course, still very much in the running but with much less support than one might expect after all the developments of the intervening seventy years.

Despite the phases of Venus all the various geo-heliocentric models are still in contention and because of the lack of empirical evidence for movement of the Earth these are actually more popular at this point in time than heliocentric ones. However, despite the lack of empirical evidence diurnal rotation enjoys a surprising level of popularity. We have a Capellan system, Venus and Mercury orbit the Sun, which orbits the Earth, both with and without diurnal rotation. Very much in consideration is the full Tychonic system; the five planets orbit the Sun, which together with the Moon orbits the Earth. Once again both with and without diurnal rotation. Riccioli favoured another variation with Venus, Mercury and Mars orbiting the Sun but with Jupiter and Saturn orbiting the Earth along with the Sun and Moon.

Perhaps the most interesting development was Kepler’s heliocentric system. Whilst Kepler regarded his system as Copernican, others regarded his elliptical system as a rival to not only to the geocentric and geo-heliocentric system but also to the Copernican heliocentric system with its deferent and epicycle orbital models. The most prominent example of this being Galileo, who promoted the Copernican system, whilst deliberately ignoring Kepler’s more advanced developments.

We can find solid evidence for this multiplicity of systems in various sources. The earliest in a card game devised by Johann Praetorius (1573–1616), professor for astronomy at the University of Altdorf near Nürnberg, which only exists in manuscript.


Source: Wikimedia Commons











Source: All playing card images Wikimedia Commons

Another much read source is the extraordinary Anatomy of Melancholy by the Oxford scholar Robert Burton (1577–1640). First published in 1621, it was republished five times over the next seventeen years, each edition being massively modified and expanded.


The Anatomy of Melancholy frontispiece 1638 ed. Source: Wikimedia Commons

In a section entitled Melancholy of the Air Burton discusses the various astronomical models, favouring the system of David Origanus (1558–1629), professor for Geek Greek and mathematics at the University of Frankfurt an der Oder, a Tychonic system with diurnal rotation.


Source: Wikimedia Commons

Burton, as well as being one of the most erudite scholars of the seventeenth century, was also a practicing astrologer, who is said to have hung himself in his Oxford chambers to fulfil his own prediction of his death.

Already mentioned above is Giovanni Battista Riccioli, whose Almagestum novum (1551) contains descriptions of a wide range of different systems.


Riccioli as portrayed in the 1742 Atlas Coelestis (plate 3) of Johann Gabriel Doppelmayer. Source: Wikimedia Commons

The book also contains a list of 126 arguments pro and contra heliocentricity, 49 for and 77 against, in which religios arguments play only a very minor role.

Another Jesuit was Athanasius Kircher (1602–1680), who sat at the centre of a world spanning astronomy correspondence network, receiving astronomical data from Jesuits all of the world, collating it and re-distributing it to astronomers throughout Europe.


Source: Wikimedia Commons

He described six different systems as late as 1656 in his Itinerarium extaticum, with a revised edition from 1671.


Diagrams of the different world systems, Ptolemaic, Platonic, Egyptian, Copernican, Tychonic and semi-Tychonic from Iter Exstaticum (1671 ed.) p. 37 Source:

Contrary to a widespread view the question of the correct astronomical system was still very much an open question throughout most of the seventeenth century, largely because there existed no conclusive empirical evidence available to settle the question.





Filed under History of Astronomy, History of science, Renaissance Science

The Royal Society really needs to work on its history of the telescope

One would think that the Royal Society being one of the eldest, but not the eldest as they like to claim, scientific societies in Europe when presenting themselves as purveyors of the history of science, would take the trouble to get their facts right. If, however, one thought this, one would be wrong. Last week on the Internet the Royal Society was pushing a slide show, under their own name, on Google Arts and Culture on the history of the telescope in astronomy that in terms of historical accuracy is less than one, as a historian of science, nay of the telescope, might hope or indeed wish for.

The slide show in question is titled, Silent Harmony: astronomy at the Royal Society: Discover how innovation in telescopes and other optical instruments changed the way we see the universe. Following the title slide we have another general blurb slide but things then get serious on the history level, we get told under the heading, The new astronomy:


Galileo Portrait by Ottavio Leoni Source: Wikimedia Commons

Galileo Galilei (1564-1642) was the first to explore the solar system using a telescope. His work directly built on famous predecessors such as Nicolaus Copernicus (1473-1543) and Johannes Kepler (1571-1630), who set out to model a heliocentric universe – one in which the sun is at the centre of the universe – and theorise the motion of planets. 

Sometimes I tire slightly of repeating myself but once more into the breach dear friends, once more. Galileo was not the first to explore the solar system using a telescope. That honour goes to a man in London, you know London home of the Royal Society, Thomas Harriot (1560–1621).


Portrait often claimed to be Thomas Harriot (1602), which hangs in Oriel College, Oxford. Source: Wikimedia Commons

Also at the same time as Galileo was aiming his telescope at the heavens in Padua, Simon Marius (1573–1625) was doing the same in Ansbach in Franconia


Simon Marius Source: Wikimedia Commons

and Giovanni Paolo Lembo (1570–1618) and Odo van Maelcote (1572–1615) in Rome. Whilst Galileo was more than prepared to call himself a Copernican, he very strongly rejected or ignored the work of Johannes Kepler, so saying that his work directly built on that of Kepler is more than a simple distortion of history. To say that these three theorised the motion of planets is to say the least bizarre, all astronomical models whether heliocentric, geocentric or geo-heliocentric theorise the motion of planets that is a large part of what astronomy is. We are not finished with Signor Galileo:

Galileo’s Starry Messenger was the first published work to incorporate scientific observations made using a telescope.

The treatise contains descriptions of lunar landscapes, new stars in well-known constellations and the major satellites of Jupiter.

This is all correct, however because he was the first to publish people make the mistake of thinking he was the first or even the only one to make telescopic observations in 1609. Moving on, the next slide caption isn’t correct:

Galileo designed and built the most powerful telescope of his generation.

His own instrument, a thirty-power magnifier preserved at the Museo Galileo in Florence, served as model to other instrument-makers for many years.

I’m beginning to think that the Royal Society has got something against Thomas Harriot. Whilst Galileo did indeed build a thirty-power telescope it was not the most powerful telescope of his generation, Harriot built a fifty-power one. However, as in a Dutch telescope (convex objective/concave eyepiece) the field of vision diminishes with magnification the fifty-power telescope proved next to useless. Galileo’s own instrument did not serve as a model to other instrument-makers for many years that, is to put it mildly, total bullshit. Lots of people knew how to construct a simple Dutch telescope and did so without any reference to Galileo.

We skip a few slides and arrive at the most famous President of the Royal Society, Isaac Newton;


Portrait of Newton by Godfrey Kneller, 1689 Source: Wikimedia Commons

we get a picture of Newton’s reflecting telescope with the following caption:


Replica of Newton’s second reflecting telescope, which he presented to the Royal Society in 1672 Source: Wikimedia Commons

The Royal Society also owns a reflecting telescope made by Newton as a direct application of his theories on light and colour.

This statement is a best misleading and at worst simply wrong depending on how you interpret it. Newton’s theories on light and colour led him to the awareness that the coloured fringes visible on the images of the then normal refracting telescope were the result of chromatic aberration, i.e. the visible light being split up into the colour spectrum when passing through a spherical lenses. This discovery led him to developing a reflecting telescope because he believed falsely that creating an achromatic lens was impossible. It would be more than half a century before Chester Moore Hall invented the first achromatic lens. The principle of the reflecting telescope, which with a suitable mirror, does not suffer from chromatic aberration, had been known since antiquity and Newton was by no means the first to try and construct one. He was, however, the first to succeed in producing a functioning reflecting telescope. You can read an outline of the full history of the reflecting telescope here. Interestingly nobody succeeded in copying Newton’s achievements for the best part of fifty years, when John Hadley (1682–1784), another fellow of the Royal Society, who gets no mention in this slide show, finally succeeded in producing large scale functioning reflecting telescopes; Newton’s instrument was little more than a toy.

The instrument allowed him to make various observations conclusive with his theories on gravity.

This caption is just high-grade rubbish. Newton did not make any observations with this instrument that were in anyway connected with his theory of gravity, let alone conclusive with it.

There are, in the mean time, quite a few good books on the history of the telescope, I have most of them sitting on my book shelf and I’m sure some of them are in the Royal Society’s library, so why didn’t who ever put this slide show together consult them or simply ask an expert?









Filed under History of Astronomy, History of Optics, History of science, Myths of Science

The emergence of modern astronomy – a complex mosaic: Part XXII

The publication of Galileo’s Sidereus Nuncius was by no means the end of the spectacular and game changing telescopic astronomical discoveries during that first hot phase, which spanned 1610 to 1613. There were to be three further major discoveries, one of which led to a bitter priority dispute that would in the end play a role in Galileo’s downfall and another of which would sink Ptolemaeus’ geocentric model of the cosmos for ever.

The first new discovery post Sidereus Nuncius was the rather strange fact that Saturn appeared to have ears or as Galileo put it, it was three bodies “accompanied by two attendants who never leave his side.”


Galileo’s drawings of Saturn

What Galileo had in fact observed were the rings of Saturn, which however because of the relative positions of Saturn and the Earth were not discernable as rings but as strange semi-circular projections on either side of the planet. What exactly the strange protrusions visible on Saturn were would remain a mystery until Christiaan Huygens solved the problem much later in the century. The astronomers of the Collegio Romano claimed priority on the Saturn discovery. Whether they or Galileo saw the phenomenon first cannot really be determined but it demonstrates once again that Galileo was by no means the only one making these new telescopic discoveries. Saturn’s two “attendants” didn’t really play a role in the ongoing astronomy/cosmology debate but the next discovery did in a very major way.

Probably stimulated by a letter from his one time student Benedetto Castelli (1578–1643) Galileo turned his attention to Venus and its potential phases.


Benedetto Castelli Source: Wikimedia Commons

If Venus was indeed lit by the sun then in both Ptolemaeus’ geocentric system and in a heliocentric system it would, like the moon, display phases but these phases would differ according to whether Venus orbited the Earth in a geocentric system or the sun in either a heliocentric or a geo-heliocentric one. Galileo’s observations clearly showed that the phases of Venus were consistent with a solar orbit and not a terrestrial one.


The Phases of Venus in both systems

The pure Ptolemaic geocentric system was irredeemably sunk but not, and that must be strongly emphasised, a number of geo-heliocentric systems. As already mentioned earlier, because they never strayed far from the sun’s vicinity and in a geocentric system even shared the sun orbital period, Mercury and Venus had since antiquity been assumed, by some, to orbit the sun whereas the sun orbited the earth in what is known as the Capellan system; a system that was very popular in the Middle Ages and had been praised as such by Copernicus in his De revolutionibus. Phases of Venus indicating a solar orbit were, of course, also consistent with a full Tychonic system in which the planets, apart from the moon, orbited the sun, which in turn together with the moon orbited the earth, as well as several variant semi-Tychonic systems. It was assumed that Mercury also orbited the sun, although its phases were first observed by  Pierre Gassendi (1592–1655) in 1631. The heliocentric phases of Venus were also discovered independently by Thomas Harriot, who, as always, didn’t publish, by Simon Marius, whose discovery was published by Kepler, and by the Collegio Romano astronomers, who also didn’t published but announced their discovery in their correspondence.

The other major telescopic discovery was the presence of blemishes or spots on the surfaces of the sun, again something that contradicted Aristotle’s assumption of the perfection of the celestial bodies. This discovery led to one of Galileo’s biggest priority disputes. This whole sorry episode began with a communication from the Augsburger banker and science fan, Marcus Welser(1558–1614), who was also a close friend of the Jesuits.


Marcus Welser Source: Wikimedia Commons

This communication contained three letters on sunspots written by the Ingolstädter Jesuit Christoph Scheiner (1573 or 75–1650) under the pseudonym, Appeles.


Christoph Scheiner (artist unknown)

Welser wanted to hear Galileo’s opinion on Scheiner’s discovery. Galileo was deeply offended, the heavens were his territory and only he was allowed to make discoveries there! The dispute was carried on two levels, the first was the question of priority and the second was the question of how to interpret what had been observed. Although, during the whole dispute Galileo kept changing the date when he first observed sunspots, in order to establish his priority and to claim the discovery as his, viewed with hindsight the priority dispute was a bit of a joke. We now know that Thomas Harriot  had recorded observations of sunspot before either Galileo or Scheiner but because he never published his observations, they were blissfully unaware of his priority. Even stranger, Johannes Fabricius (1587–1616), the son of Kepler’s intellectual sparing partner David Fabricius, had brought home a telescope from university in Leiden, where Rudolph Snell (1546–1613) was already holding lectures on the telescope in 1610, and together with his father had not only been observing sunspots but had already published a pamphlet on his observation in Wittenberg in 1611, where he was now studying.


The second part of the dispute was by far and away the more important. Scheiner had initially interpreted the sunspots as shadows cast upon the surface of the sun by small satellites orbiting it. It is was possible that through this interpretation he wished to preserve the Aristotelian perfection of this celestial body. Galileo opposed this interpretation and was convinced, correctly as it turned out, that the sunspots were actually some sort of blemishes on the surface of the sun.

Galileo answered Scheiner’s letters with three of his own, in the process stepping up his observation of the sunspots, as well as gathering observational reports from other astronomers. He was able to show through the quality of his observations and through mathematical analysis that the sunspots must be on the surface of the sun and that the sun must be revolving about its axis. With time Scheiner came to accept Galileo’s conclusions. Scheiner published three more sunspot letters under the title Accuratior Disquisitio in 1612.


The Accademia dei Lincei, which had elected Galileo a member when he came to Rome to celebrate the Jesuit’s confirmation of his telescopic discoveries, published Scheiner’s original three letters together with Galileo’s three answering letters in a book titled, Istoria e Dimontrazioni, in 1613.


Having in his opinion won the priority dispute and proved that the sunspots were on the surface of the sun, Galileo basically gave up on his solar observations; Scheiner did not. Having built what was effectively the first Keplerian or astronomical telescope with two convex lenses, instead of one convex and one concave, as in the Dutch or Galilean telescope, giving a much wider field of vision and a much clearer and stronger image, Scheiner set out on a programme of solar astronomy.


Scheiner Observing the Sun

The astronomical telescope provided an inverted image but this was irrelevant as Scheiner was projecting the image onto paper in order to simplify the drawing on the sunspots and also to protect his eyes. A method also used by Fabricius and Galileo. He mounted his telescope on a special holder that allowed him to follow the sun in its journey across the heavens.


Scheiner’s Helioscope

The end of this programme was his Rosa Ursina sive Sol, published in 1626-30, which remained the most important book on solar astronomy until the nineteenth century.


Scheiner’s Sunspot Observations

Galileo’s and Scheiner’s priority dispute entails a strong sense of historical irony. Not only did Harriot begin observing sunspots earlier than both of them and Johannes Fabricius publish on the subject before either of them but Chinese and Korean astronomers had been recording naked-eye observations of sunspots since the first millennium BCE. There are also scattered observations of sunspots beginning with the ancient Greeks and down through the Middle Ages in Europe.


A drawing of a sunspot in the Chronicles of John of Worcester 1129 Source: Wikimedia Commons

Famously Kepler recorded observations of a large sunspot that he made in 1607 mistakenly believing that he was observing a transit of Mercury.

1613 marks the end of the first phase of astronomical telescopic discoveries, partially because the observers continued to use Dutch or Galilean telescopes instead of changing to the vastly superior Keplerian or astronomical telescopes, largely influenced by Galileo’s authority, he publicly rubbished astronomical telescopes, basically because he hadn’t started using them first; the transition to the better instruments would take a couple of decades to be completed.









Filed under History of Astronomy, History of science, Renaissance Science

The emergence of modern astronomy – a complex mosaic: Part XXI

A widespread myth in the popular history of astronomy is that Galileo Galilei (1564–1642) was the first or even the only astronomer to realise the potential of the newly invented telescope as an instrument for astronomy. This perception is very far from the truth. He was just one of a group of investigator, who realised the telescopes potential and all of the discoveries traditionally attributed to Galileo were actually made contemporaneously by several people, who full of curiosity pointed their primitive new instruments at the night skies. So why does Galileo usually get all of the credit? Quite simply, he was the first to publish.


Galileo’s “cannocchiali” telescopes at the Museo Galileo, Florence

Starting in the middle of 1609 various astronomers began pointing primitive Dutch telescopes at the night skies, Thomas Harriot (1560–1621) and his friend and student William Lower (1570–1615) in Britain, Simon Marius (1573–1625) in Ansbach, Johannes Fabricius (1587–1616) in Frisia, Odo van Maelcote (1572–1615) and Giovanni Paolo Lembo (1570–1618) in Rome, Christoph Scheiner (1573 or 1575–1650) in Ingolstadt and of course Galileo in Padua. As far as we can ascertain Thomas Harriot was the first and the order in which the others took up the chase is almost impossible to determine and also irrelevant, as it was who was first to publish that really matters and that was, as already stated, Galileo.

Harriot made a simple two-dimensional telescopic sketch of the moon in the middle of 1609.


Thomas Harriot’s initial telescopic sketch of the moon from 1609 Source: Wikimedia Commons

Both Galileo and Simon Marius started making telescopic astronomical observations sometime late in the same year. At the beginning Galileo wrote his observation logbook in his Tuscan dialect and then on 7 January 1610 he made the discovery that would make him famous, his first observation of three of the four so-called Galilean moons of Jupiter.


It was on this page that Galileo first noted an observation of the moons of Jupiter. This observation upset the notion that all celestial bodies must revolve around the Earth. Source: Wikimedia Commons

Galileo realised at once that he had hit the jackpot and immediately changed to writing his observations in Latin in preparation for a publication. Simon Marius, who made the same discovery just one day later, didn’t make any preparations for immediate publication. Galileo kept on making his observations and collecting material for his publication and then on 12 March 1610, just two months after he first saw the Jupiter moons, his Sidereus Nuncius (Starry Messenger of Starry Message, the original Latin is ambiguous) was published in Padua but dedicated to Cosimo II de Medici, Fourth Grand Duke of Tuscany. Galileo had already negotiated with the court in Florence about the naming of the moons; he named them the Medicean Stars thus taking his first step in turning his discovery into personal advancement.


Title page of Sidereus nuncius, 1610, by Galileo Galilei (1564-1642). *IC6.G1333.610s, Houghton Library, Harvard University Source: Wikimedia Commons

What exactly did Galileo discover with his telescope, who else made the same discoveries and what effect did they have on the ongoing astronomical/cosmological debate? We can start by stating quite categorically that the initial discoveries that Galileo published in his Sidereus Nuncius neither proved the heliocentric hypothesis nor did they refute the geocentric one,

The first discovery that the Sidereus Nuncius contains is that viewed through the telescope many more stars are visible than to the naked-eye. This was already known to those, who took part in Lipperhey’s first ever public demonstration of the telescope in Den Haag in September 1608 and to all, who subsequently pointed a telescope of any sort at the night sky. This played absolutely no role in the astronomical/cosmological debate but was worrying for the theologians. Christianity in general had accepted both astronomy and astrology, as long as the latter was not interpreted deterministically, because the Bible says  “And God said, Let there be lights in the firmament of the heaven to divide the day from night; and let them be for signs, and for seasons, and for days, and years:” (Gen 1:14). If the lights in the heavens are signs from God to be interpreted by humanity, what use are signs that can only be seen with a telescope?

Next up we have the fact that some of the nebulae, indistinct clouds of light in the heavens, when viewed with a telescope resolved into dense groups of stars. Nebulae had never played a major role in Western astronomy, so this discovery whilst interesting did not play a major role in the contemporary debate. Simon Marius made the first telescopic observations of the Andromeda nebula, which was unknown to Ptolemaeus, but which had already been described by the Persian astronomer, Abd al-Rahman al-Sufi (903–986), usually referred to simply as Al Sufi. It is historically interesting because the Andromeda nebula was the first galaxy to be recognised outside of the Milky Way.


Al Sufi’s drawing of the constellation Fish with the Andromeda nebula in fount of it mouth

Galileo’s next discovery was that the moon was not smooth and perfect, as required of all celestial bodies by Aristotelian cosmology, but had geological feature, mountains and valleys, just like the earth i.e. the surface was three-dimensional and not two-dimensional, as Harriot had sketched it. This perception of Galileo’s is attributed to the fact that he was a trained painter used to creating light and shadows in paintings and he thus recognised that what he was seeing on the moons surface was indeed shadows cast by mountains.

As soon as he read the Sidereus Nuncius, Harriot recognised that Galileo was correct and he went on to produce the first real telescopic map of the moon.


Thomas Harriot’s 1611 telescopic map of the moon Source: Wikimedia Commons

Galileo’s own washes of the moon, the most famous illustrations in the Sidereus Nuncius, are in fact studies to illustrate his arguments and not accurate illustrations of what he saw.


Galileo’s sketches of the Moon from Sidereus Nuncius. Source: Wikimedia Commons

That the moon was earth like and for some that the well-known markings on the moon, the man in the moon etc., are in fact a mountainous landscape was a view held by various in antiquity, such as Thales, Orpheus, Anaxagoras, Democritus, Pythagoras, Philolaus, Plutarch and Lucian. In particular Plutarch (c. 46–c. 120 CE) in his On the Face of the Moon in his Moralia, having dismissed other theories including Aristotle’s wrote:

Just as our earth contains gulfs that are deep and extensive, one here pouring in towards us through the Pillars of Herakles and outside the Caspian and the Red Sea with its gulfs, so those features are depths and hollows of the Moon. The largest of them is called “Hecate’s Recess,” where the souls suffer and extract penalties for whatever they have endured or committed after having already become spirits; and the two long ones are called “the Gates,” for through them pass the souls now to the side of the Moon that faces heaven and now back to the side that faces Earth. The side of the Moon towards heaven is named “Elysian plain,” the hither side, “House of counter-terrestrial Persephone.”

So Galileo’s discovery was not so sensational, as it is often presented. However, the earth-like, and not smooth and perfect, appearance of the moon was yet another hole torn in the fabric of Aristotelian cosmology.

Of course the major sensation in the Sidereus Nuncius was the discovery of the four largest moons of Jupiter.


Galileo’s drawings of Jupiter and its Medicean Stars from Sidereus Nuncius. Image courtesy of the History of Science Collections, University of Oklahoma Libraries. Source: Wikimedia Commons

This contradicted the major premise of Aristotelian cosmology that all of the celestial bodies revolved around a common centre, his homo-centricity.  It also added a small modicum of support to a heliocentric cosmology, which had suffered from the criticism, if all the celestial bodies revolve around the sun, why does the moon continue to revolve around the earth. Now Jupiter had not just one but four moons, or satellites as Johannes Kepler called them, so the earth was no longer alone in having a moon. As already stated above Simon Marius discovered the moons of Jupiter just one day later than Galileo but he didn’t publish his discovery until 1614. A delay that would later bring him a charge of plagiarism from Galileo and ruin his reputation, which was first restored at the end of the nineteenth century when an investigation of the respective observation data showed that Marius’ observations were independent of those of Galileo.

The publication of the Sidereus Nuncius was an absolute sensation and the book quickly sold out. Galileo went, almost literally overnight, from being a virtually unknown, middle aged, Northern Italian, professor of mathematics to the most celebrated astronomer in the whole of Europe. However, not everybody celebrated or accepted the truth of his discoveries and that not without reason. Firstly, any new scientific discovery needs to be confirmed independently by other. If Simon Marius had also published early in 1610 things might have been different but he, for whatever reasons, didn’t publish his Mundus Jovialis (The World of Jupiter) until 1614. Secondly there was no scientific explanation available that explained how a telescope functioned, so how did anyone know that what Galileo and others were observing was real? Thirdly, and this is a very important point that often gets ignored, the early telescopes were very, very poor quality suffering from all sorts of imperfections and distortions and it is almost a miracle that Galileo et al discovered anything with these extremely primitive instruments.

As I stated in the last episode, the second problem was solved by Johannes Kepler in 1611 with the publication of his Dioptrice.


A book that Galileo, always rather arrogant, dismissed as unreadable. This was his triumph and nobody else was going to muscle in on his glory. The third problem was one that only time and improvements in both glass making and the grinding and polishing of lenses would solve. In the intervening years there were numerous cases of new astronomical discoveries that turned out to be artefacts produced by poor quality instruments.

The first problem was the major hurdle that Galileo had to take if he wanted his discoveries to be taken seriously. Upon hearing of Galileo discoveries, Johannes Kepler in Prague immediately put pen to paper and fired off a pamphlet, Dissertatio cum Nuncio Sidereo (Conversation with the Starry Messenger) congratulating Galileo, welcoming his discoveries and stating his belief in their correctness, which he sent off to Italy. Galileo immediately printed and distributed a pirate copy of Kepler’s work, without even bothering to ask permission, it was after all a confirmation from the Imperial Mathematicus and Kepler’s reputation at this time was considerably bigger than Galileo’s.

Johannes Kepler, Dissertatio cum Nuncio sidereo… (Frankfurt am Main, 1611)

A reprint of Kepler’s letter to Galileo, originally issued in Prague in 1610

However, Kepler’s confirmations were based on faith and not personal confirmatory observations, so they didn’t really solve Galileo’s central problem. Help came in the end from the Jesuit astronomers of the Collegio Romano.

Odo van Maelcote and Giovanni Paolo Lembo had already been making telescopic astronomical observations before the publication of Galileo’s Sidereus Nuncius. Galileo also enjoyed good relations with Christoph Clavius (1538–1612), the founder and head of the school of mathematics at the Collegio Romano, who had been instrumental in helping Galileo to obtain the professorship in Padua. Under the direction of Christoph Grienberger (1561–1636), soon to be Clavius’ successor as professor for mathematics at the Collegio, the Jesuit astronomers set about trying to confirm all of Galileo’s discoveries. This proved more than somewhat difficult, as they were unable, even with Galileo’s assistance via correspondence, to produce an instrument of sufficient quality to observe the moons of Jupiter. In the end Antonio Santini (1577–1662), a mathematician from Venice, succeeded in producing a telescope of sufficient quality for the task, confirmed for himself the existence of the Jupiter moons and then sent a telescope to the Collegio Romano, where the Jesuit astronomers were now also able to confirm all of Galileo’s discovery. Galileo could not have wished for a better confirmation of his efforts, nobody was going to doubt the word of the Jesuits.

In March 1611 Galileo travelled to Rome, where the Jesuits staged a banquet in his honour at which Odo van Maelcote held an oration to the Tuscan astronomer. Galileo’s strategy of dedicating the Sidereus Nuncius to Cosimo de Medici and naming the four moons the Medicean Stars paid off and he was appointed court mathematicus and philosophicus in Florence and professor of mathematics at the university without any teaching obligations; Galileo had arrived at the top of the greasy pole but what goes up must, as we will see, come down.





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Mathematical aids for Early Modern astronomers.

Since its very beginnings in the Fertile Crescent, European astronomy has always involved a lot of complicated and tedious mathematical calculations. Those early astronomers described the orbits of planets, lunar eclipses and other astronomical phenomena using arithmetical or algebraic algorithms. In order to simplify the complex calculations needed for their algorithms the astronomers used pre-calculated tables of reciprocals, squares, cubes, square roots and cube roots.


Cuniform reciprocal table Source

The ancient Greeks, who inherited their astronomy from the Babylonians, based their astronomical models on geometry rather than algebra and so needed other calculation aids. They developed trigonometry for this work based on chords of a circle. The first chord tables are attributed to Hipparkhos (c. 190–c. 120 BCE) but they did not survive. The oldest surviving chord tables are in Ptolemaeus’ Mathēmatikē Syntaxis written in about 150 CE, which also contains a detailed explanation of how to calculate such a table in Chapter 10 of Book I.


Ptolemaeus’ Chord Table taken from Toomer’s Almagest translation. The 3rd and 6th columns are the interpolations necessary for angles between the given ones

Greek astronomy travelled to India, where the astronomers replaced Ptolemaeus’ chords with half chords, that is our sines. Islamic astronomers inherited their astronomy from the Indians with their sines and cosines and the Persian astronomer Abū al-Wafāʾ (940–998 CE) was using all six of the trigonometrical relations that we learnt at school (didn’t we!) in the tenth century.


Abū al-Wafāʾ Source: Wikimedia Commons

Astronomical trigonometry trickled slowly into medieval Europe and Regiomontanus (1536–1576)  (1436–1476) was the first European to produce a comprehensive work on trigonometry for astronomers, his De triangulis omnimodis, which was only edited by Johannes Schöner and published by Johannes Petreius in 1533.

Whilst trigonometry was a great aid to astronomers calculating trigonometrical tables was time consuming, tedious and difficult work.

A new calculating aid for astronomers emerged during the sixteenth century, prosthaphaeresis, by which, multiplications could be converted into additions using a series of trigonometrical identities:

Prosthaphaeresis appears to have first been used by Johannes Werner (1468–1522), who used the first two formulas with both sides multiplied by two.

However Werner never published his discovery and it first became known through the work of the itinerant mathematician Paul Wittich (c. 1546–1586), who taught it to both Tycho Brahe (1546–1601) on his island of Hven and to Jost Bürgi (1552–1632) in Kassel, who both developed it further. It is not known if Wittich learnt the method from Werner’s papers on one of his visits to Nürnberg or rediscovered it for himself. Bürgi in turn taught it to Nicolaus Reimers Baer (1551–1600) in in exchange translated Copernicus’ De revolutionibus into German for Bürgi, who couldn’t read Latin. This was the first German translation of De revolutionibus. As can be seen the method of prosthaphaeresis spread throughout Europe in the latter half of the sixteenth century but was soon to be superceded by a superior method of simplifying astronomical calculations by turning multiplications into additions, logarithms.

As is often the case in the histories of science and mathematics logarithms were not discovered by one person but almost simultaneously, independently by two, Jost Bürgi and John Napier (1550–1617) and both of them seem to have developed the idea through their acquaintance with prosthaphaeresis. I have already blogged about Jost Bürgi, so I will devote the rest of this post to John Napier.


John Napier, artist unknown Source: Wikimedia Commons

John Napier was the 8th Laird of Merchiston, an independently owned estate in the southwest of Edinburgh.


Merchiston Castle from an 1834 woodcut Source: Wikimedia Commons

His exact date of birth is not known and also very little is known about his childhood or education. It is assumed that he was home educated and he was enrolled at the University of St. Andrews at the age of thirteen. He appears not to have graduated at St. Andrews but is believed to have continued his education in Europe but where is not known. He returned to Scotland in 1571 fluent in Greek but where he had acquired it is not known. As a laird he was very active in the local politics. His intellectual reputation was established as a theologian rather than a mathematician.

It is not known how and when he became interested in mathematics but there is evidence that this interest was already established in the early 1570s, so he may have developed it during his foreign travels. It is thought that he learnt of prosthaphaeresis through John Craig (d. 1620) a Scottish mathematician and physician, who had studied and later taught at Frankfurt an der Oder, a pupil of Paul Wittich, who knew Tycho Brahe. Craig returned to Edinburgh in 1583 and is known to have had contact with Napier. The historian Anthony à Wood (1632–1695) wrote:

one Dr. Craig … coming out of Denmark into his own country called upon John Neper, baron of Murcheston, near Edinburgh, and told him, among other discourses, of a new invention in Denmark (by Longomontanus as ’tis said) to save the tedious multiplication and division in astronomical calculations. Neper being solicitous to know farther of him concerning this matter, he could give no other account of it than that it was by proportionable numbers. [Neper is the Latin version of his family name]

Napier is thought to have begum work on the invention of logarithms about 1590. Logarithms exploit the relation ship between arithmetical and geometrical series. In modern terminology, as we all learnt at school, didn’t we:

Am x An = Am+n

Am/An = Am-n

These relationships were discussed by various mathematicians in the sixteenth century, without the modern notation, in particularly by Michael Stefil (1487–1567) in his Arithmetica integra (1544).


Michael Stifel Source: Wikimedia Commons


Michael Stifel’s Arithmetica Integra (1544) Source: Wikimedia Commons

What the rules for exponents show is that if one had tables to convert all numbers into powers of a given base then one could turn all multiplications and divisions into simple additions and subtractions of the exponents then using the tables to covert the result back into a number. This is what Napier did calling the result logarithms. The methodology Napier used to calculate his tables is too complex to deal with here but the work took him over twenty years and were published in his Mirifici logarithmorum canonis descriptio… (1614).


Napier coined the term logarithm from the Greek logos (ratio) and arithmos (number), meaning ratio-number. As well as the logarithm tables, the book contains seven pages of explanation on the nature of logarithms and their use. A secondary feature of Napier’s work is that he uses full decimal notation including the decimal point. He was not the first to do so but his doing so played an important role in the acceptance of this form of arithmetical notation. The book also contains important developments in spherical trigonometry.

Edward Wright  (baptised 1561–1615) produced an English translation of Napier’s Descriptio, which was approved by Napier, A Description of the Admirable Table of Logarithmes, which was published posthumously in 1616 by his son Samuel.


Gresham College was quick to take up Napier’s new invention and this resulted in Henry Briggs (1561–1630), the Gresham professor of geometry, travelling to Edinburgh from London to meet with Napier. As a result of this meeting Briggs, with Napier’s active support, developed tables of base ten logarithms, Logarithmorum chilias prima, which were publish in London sometime before Napier’s death in 1617.


He published a second extended set of base ten tables, Arithmetica logarithmica, in 1624.


Napier’s own tables are often said to be Natural Logarithms, that is with Euler’s number ‘e’ as base but this is not true. The base of Napierian logarithms is given by:

NapLog(x) = –107ln (x/107)

Natural logarithms have many fathers all of whom developed them before ‘e’ itself was discovered and defined; these include the Jesuit mathematicians Gregoire de Saint-Vincent (1584–1667) and Alphonse Antonio de Sarasa (1618–1667) around 1649, and Nicholas Mercator (c. 1620–1687) in his Logarithmotechnia (1688) but John Speidell (fl. 1600–1634), had already produced a table of not quite natural logarithms in 1619.


Napier’s son, Robert, published a second work by his father on logarithms, Mirifici logarithmorum canonis constructio; et eorum ad naturales ipsorum numeros habitudines, posthumously in 1619.


This was actually written earlier than the Descriptio, and describes the principle behind the logarithms and how they were calculated.

The English mathematician Edmund Gunter (1581–1626) developed a scale or rule containing trigonometrical and logarithmic scales, which could be used with a pair of compasses to solve navigational problems.


Table of Trigonometry, from the 1728 Cyclopaedia, Volume 2 featuring a Gunter’s scale Source: Wikimedia Commons

Out of two Gunter scales laid next to each other William Oughtred (1574–1660) developed the slide rule, basically a set of portable logarithm tables for carry out calculations.

Napier developed other aids to calculation, which he published in his Rabdologiae, seu numerationis per virgulas libri duo in 1617; the most interesting of which was his so called Napier’s Bones.


These are a set of multiplication tables embedded in rods. They can be used for multiplication, division and square root extraction.


An 18th century set of Napier’s bones Source: Wikimedia Commons

Wilhelm Schickard’s calculating machine incorporated a set of cylindrical Napier’s Bones to facilitate multiplication.

The Swiss mathematician Jost Bürgi (1552–1632) produced a set of logarithm tables independently of Napier at almost the same time, which were however first published at Kepler’s urging as, Arithmetische und Geometrische Progress Tabulen…, in 1620. However, unlike Napier, Bürgi delivered no explanation of the how his table were calculated.


Tables of logarithms became the standard calculation aid for all those making mathematical calculations down to the twentieth century. These were some of the mathematical tables that Babbage wanted to produce and print mechanically with his Difference Engine. When I was at secondary school in the 1960s I still carried out all my calculations with my trusty set of log tables, pocket calculators just beginning to appear as I transitioned from school to university but still too expensive for most people.


Not my copy but this is the set of log tables that accompanied me through my school years

Later in the late 1980s at university in Germany I had, in a lecture on the history of calculating, to explain to the listening students what log tables were, as they had never seen, let alone used, them. However for more than 350 years Napier’s invention served all those, who needed to make mathematical calculations well.














Filed under History of Astronomy, History of Mathematics, History of Technology, Renaissance Science

The emergence of modern astronomy – a complex mosaic: Part XX

It is not an exaggeration to say that the invention of telescope was a very major turning point in the general history of science and in particular the history of astronomy. Basic science is fundamentally empirical; people investigating the world make observations with their senses–taste, sight, touch, smell, hearing–then try to develop theories to describe and explain what has been observed and recorded. The telescope was the first ever instrument that was capable of expanding or strengthening one of those senses that of sight. The telescope made it possible to see things that had never been seen before.

The road to the telescope was a long one and one of the questions is why it wasn’t invented earlier. There are various legends or myths about devices to enable people to see things at a distance throughout antiquity and various lens shaped objects also from the distant past that might or might not have been lenses. Lenses in scientific literature in antiquity and the early middle ages were burning lenses used to focus sunlight to ignite fires. The first definite use of lenses to improve eyesight were the so-called reading stones, which emerged around 1000 CE, approximately hemispherical lenses, placed on documents to help those suffering from presbyopia, weakening of the ability of the eye to focus due to aging.


Source: Zeiss

Reading glasses utilising plano-convex lenses first appeared around 1290.


The earliest pictorial evidence for the use of eyeglasses is Tommaso da Modena’s 1352 portrait of the cardinal Hugh de Provence reading in a scriptorium Source: Wikimedia Commons

The current accepted theory of the discovery of simple lenses is that in the Middle Ages monks cutting gems to decorate reliquary discovered the simple magnifying properties of the gemstones they were grinding and polishing.


Reliquary Cross, French, c. 1180 Source: Wikimedia Commons

By the middle of the fifteenth century eye glasses utilising both convex and concave lenses were being manufactured and traded, so why did it take until 1608 before somebody successfully combined a concave lens and convex lens to create a simple so-called Dutch telescope?

There are in fact earlier in the sixteenth century in the writings of Girolamo Fracastoro (ca. 1476–1553) and Giambattista della Porta (1532–1615) descriptions of the magnifying properties of such lens combinations but these are now thought to refer to special eyeglasses rather than telescopes.

Della Porta Telescope Sketch

The early lenses were spherical lenses, which were hand ground and polished and as a result were fairly inaccurate in their form tending to deviate from their ideal spherical form the further out one goes from the centre.  These deformations caused distortions in the images formed and combining lenses increased the level of distortion making such combinations next to useless. It is now thought that the breakthrough came through the use of a mask to stop down the diameter of the eyepiece lens cutting out the light rays from the periphery, restricting the image to the centre of the lens and thus massively reducing the distortion. So who made this discovery? Who first successfully developed a working telescope?

This question has been hotly discussed and various claims just as hotly disputed since at least the middle of the seventeenth century. However, there now exists a general consensus amongst historian of optics.

[To see the current stand on the subject read the bog post that I wrote at this time last year, which I don’t intend to repeat here]

Popular accounts of the early use of the telescope in astronomy almost always credit Galileo Galilei, at the time a relatively unknown professor for mathematics in Padua, with first recognising the potential of the telescope for astronomy; this is a myth.

As can be seen from the quote from the French newsletter AMBASSADES DV ROY DE SIAM ENVOYE’ A L’ECELence du Prince Maurice, arriué à la Haye le 10. Septemb.1608., recording the visit of the ambassador of the King of Siam (Thailand), who was also present at the first demonstration of the telescope the potential of this new instrument, as a tool for astronomy was recognised from the very beginning:

even the stars which normally are not visible for us, because of the scanty proportion and feeble sight of our eyes, can be seen with this instrument.

In fact the English polymath Thomas Harriot (1560–1621) made the earliest known telescopic, astronomical observations but, as with everything else he did, he didn’t publish, so outside of a small group of friends and acquaintances his work remained largely unknown. Also definitely contemporaneous with, if not earlier than, Galileo the Franconian court mathematicus, Simon Marius (1573–1625), began making telescopic observations in late 1609. However, unlike Galileo, who as we will see published his observations and discoveries as soon as possible, Marius didn’t publish until 1614, which would eventually bring the accusation of having plagiarised Galileo.  At the Collegio Romano, the Jesuit University in Rome, Odo van Maelcote (1572–1615) and Giovanni Paolo Lembo (1570–1618) were also making telescopic observations within the same time frame. There were almost certainly others, who didn’t make their observations public.

Before we turn to the observations and discoveries that these early telescopic observers made, we need to look at a serious technical problem that tends to get ignored by popular accounts of those discovery, how does a telescope work? In 1608 when the telescope first saw the light of day there existed absolutely no scientific explanation of how it worked. The group of early inventors almost certainly discovered its magnifying effect by accident and the first people to improve it and turn it into a viable scientific instrument, again almost certainly, did so by trial and error. At this point the problem is not to find the optical theory needed to develop better telescopes systematically but to find the optical theory necessary to justify the result the telescope produced. Using any sort of instrument in science requires a scientific explanation of how those results are achieved and as already stated at the beginning no such theory existed. The man, who came to the rescue, was Johannes Kepler in the second of his major contributions to the story of heliocentric astronomy.

Already in 1604 in his Ad Vitellionem Paralipomena Astronomiae pars optica, Kepler had published the first explanation of how lenses focus light rays and how eyeglasses work to compensate for short and long sightedness so he already had a head start on explaining how the telescope functions.



Francesco Maurolico (1494–1575) had covered much of the same ground in his Theoremata de lumine et umbra earlier than Kepler but this work was only published posthumously in 1611, so the priority goes to Kepler.


In 1611 Kepler published his very quickly written Dioptrice, in which he covered the path of light rays through single lenses and then through lens combinations. In this extraordinary work he covers the Dutch or Galilean telescope, convex objective–concave eyepiece, the astronomical or Keplerian telescope, convex objective–convex eyepiece, the terrestrial telescope, convex objective–convex eyepiece–convex–field–lens to invert image, and finally for good measure the telephoto lens! Galileo’s response to this masterpiece in the history of geometrical optics was that it was unreadable!


Source: Wikimedia Commons

In the next section we will turn to the discoveries that the various early telescopic astronomical observers made and the roles that those various discoveries played in the debates on, which was the correct astronomical model of the cosmos. A much more complicated affair than it is often presented.







Filed under History of Astronomy, History of Optics, History of science, Renaissance Science