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Whewell’s Gazette


Your weekly digest of all the best of

Internet history of science, technology and medicine

Editor in Chief: The Ghost of William Whewell

Volume #1                Monday 23 June 2014


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Luca, Leonardo, Albrecht and the search for the third dimension.

Many of my more recent readers will not be aware that I lost a good Internet friend last year with the unexpected demise of the history of art blogger, Hasan Niyazi. If you want to know more about my relationship with Hasan then read the elegy I wrote for him when I first heard the news. Hasan was passionate about Renaissance art and his true love was reserved for the painter Raffaello Sanzio da Urbino, better known as Raphael. Today, 6th April is Raphael’s birthday and Hasan’s partner Shazza (Sharon) Bishop has asked Hasan’s friends in the Internet blogging community to write and post something today to celebrate his life, this is my post for Hasan.


I’m not an art historian but there were a couple of themes that Hasan and I had in common, one of these was, for example, the problem of historical dating given differing calendars. Another shared interest was the history of linear perspective, which is of course absolutely central to the history of Renaissance art but was also at the same time an important theme in Renaissance mathematics and optics. I have decided therefore to write a post for Hasan about the Renaissance mathematicus Luca Pacioli who played an important role in the history of linear perspective.


Luca Pacioli artist unknown

Luca Pacioli
artist unknown

Luca Pacioli was born in Sansepolcro in the Duchy of Urbino in 1445.

Duchy of Urbino  Henricus Hondius 1635

Duchy of Urbino
Henricus Hondius 1635

Almost nothing is known of his background or upbringing but it can be assumed that he received at least part of his education in the studio of painter and mathematician Piero della Francesca (1415 – 1492), who like Pacioli was born in Sansepolcro.

Piero della Francesca Self Portrait

Piero della Francesca
Self Portrait

Pacioli and della Francesca were members of what is now known as the Urbino school of mathematics, as was Galileo’s patron Guidobaldo del Monte (1545 – 1607). These three Urbino mathematicians together with, Renaissance polymath, Leone Battista Alberti (1404 – 1472) all played an important role in the history of linear perspective.


Leon Battista Alberti  Artist unknown

Leon Battista Alberti
Artist unknown

Whilst still young Pacioli left Sansepolcro for Venice where he work as a mathematics tutor. Here he wrote his first book, an arithmetic textbook, around 1470. Around this time he left Venice for Rome where he lived for several months in the house of Alberti, from whom he not only learnt mathematics but also gained good connections within the Catholic hierarchy. Alberti was a Papal secretary.

In Rome Pacioli studied theology and became a Franciscan friar. From 1477 Pacioli became a peripatetic mathematics teacher moving around the courts and universities of Northern Italy, writing two more arithmetic textbooks, which like his first one were never published.

Ludovico Sforza became the most powerful man in Milan in 1476, at first as regent for his nephew Gian Galeazzo, and then, after his death in 1494, Duke of Milan.

Ludovico Sforza Zanetto Bugatto

Ludovico Sforza
Zanetto Bugatto

Ludovico was a great patron of the arts and he enticed Leonardo to come and serve him in Milan in 1482. In 1496 Pacioli became Ludivico’s court mathematicus. Leonardo and Pacioli became colleges and close friends stimulating each other over a wide range of topics.


Leonardo Francesco Melzi

Francesco Melzi

Before he went to Milan Pacioli wrote his most famous and influential book his Summa de arithmetica, geometria, proportioni et proportionalità, which he published in Venice in 1494. The Summa, as it is generally known, is a six hundred-page textbook that covers the whole range of practical mathematics, as it was known in the fifteenth-century. Pacioli was not an original mathematician and the Summa is a collection of other peoples work, however it became the most influential mathematics textbook in Europe and remained so for almost the whole of the sixteenth-century. As well as the basics of arithmetic and geometry the Summa contains the first printed accounts of double entry bookkeeping and probability, although Pacioli’s account of determining odds is wrong. From our point of view the most important aspect of the Summa is that it also contains the first extensive printed account of the mathematics of linear perspective.


Pacioli Summa Title Page

Pacioli Summa
Title Page

According to legend linear perspective in painting was first demonstrated by Fillipo Brunelleschi (1377 – 1446) in Florence early in the fifteenth-century. Brunelleschi never published an account of his discovery and this task was taken up by Alberti, who first described the construction of linear perspective in his book De pictura in 1435. Piero della Francesca wrote three mathematical treatises one on arithmetic, one on linear perspective and one on the five regular Euclidian solids. However della Francesca never published his books, which seem to have been written as textbooks for the Court of Urbino where they existed in the court library only in manuscript. Della Francesca treatment of perspective was much more comprehensive than Alberti’s.

During his time in Milan, Pacioli wrote his second major work his Divina proportione, which contains an extensive study of the regular geometrical solids with the illustrations famously drawn by his friend Leonardo.


Leonardo Polyhedra


These two books earned Pacioli a certain amount of notoriety as the Summa contains della Francesca’s book on linear perspective and the Divina proportione his book on the five regular solids both without proper attribution. In his Lives of the Most Excellent Italian Painters, Sculptors, and Architects, from Cimabue to Our Timesthe Italianartist and art historian, Giorgio Vasari (1511 – 1574)


Giorgio Vasari Self Portrait

Giorgio Vasari
Self Portrait

accused Pacioli of having plagiarised della Francesca, a not entirely fair accusation, as Pacioli does acknowledge that the entire contents of his works are taken from other authors. However whether he should have given della Francesca more credit or not Pacioli’s two works laid the foundations for all future mathematical works on linear perspective, which remained an important topic in practical mathematics throughout the sixteenth and seventeenth centuries and even into the eighteenth with many of the leading European mathematicians contributing to the genre.

With the fall of Ludovico in 1499 Pacioli fled Milan together with Leonardo travelling to Florence, by way of Mantua and Venice, where they shared a house. Although both undertook journeys to work in other cities they remained together in Florence until 1506. From 1506 until his death in his hometown in 1517 Pacioli went back to his peripatetic life as a teacher of mathematics. At his death he left behind the unfinished manuscript of a book on recreational mathematics, De viribus quantitatis, which he had compiled together with Leonardo.

Before his death Pacioli possibly played a last bit part in the history of linear perspective. This mathematical technique for providing a third dimensional to two dimensional paintings was discovered and developed by the Renaissance painters of Northern Italy in the fifteenth century, one of the artists who played a very central role in bringing this revolution in fine art to Northern art was Albrecht Dürer, who coincidentally died 6 April 1528, and who undertook two journeys to Northern Italy explicitly to learn the new methods of his Italian colleagues.

Albrecht Dürer Self Portrait

Albrecht Dürer
Self Portrait

On the second of these journey’s in 1506-7, legend has it, that Dürer met a man in Bologna who taught him the secrets of linear perspective.  It has been much speculated as to who this mysterious teacher might have been and one of the favoured candidates is Luca Pacioli but this is highly unlikely. Dürer was however well acquainted with the work of his Italian colleagues including Leonardo and he became friends with and exchanged gifts with Hasan’s favourite painter Raphael.


Filed under History of Mathematics, History of Optics, Renaissance Science, Uncategorized


The title is supposed to make you think of a typical article in the Daily Fail, Britain’s most obnoxious representative of the gutter press. It represents one of the dominant reactions by members of the Gnu Model ArmyTM to the Cosmos Bruno AffairTM. According to people such as Jason Rosenhouse and P Z Myer the persecution of such notable scientists as Giordano Bruno and Galileo Galilei by the Catholic Church has definitely hindered the progress of science and for good measure they or their supporters quote the words of wisdom of Über-Guru Neil deGasse Tyson that without religion science would be a thousand years more advanced. What an outrage, truly horrific the Church it seems has a lot to answer for, although I find it rather strange that they can’t dish up more examples than poor old Giordano and that universal symbol of Church oppression Galileo. I’m sure if they re-read their Draper-White they could manage to find some new names to beat the ignorant historians around the head with. I say ignorant historians because it was the historians complaining about the Bruno cartoon on the first episode of Cosmos that has brought out this charge by these stalwart defenders of scientific integrity.

Let us assume for a moment that Rosenhouse-Myer are correct and that the Catholic Church did in fact persecute Bruno and Galileo to block scientific progress does this necessarily mean that they were successful in their dastardly deeds? Did they truly manage to interrupt, slow down, or hinder the adoption, acceptance or acknowledgement of the heliocentric hypothesis or the belief in an infinite universe or the perception that the sun is a star or vice versa? No doubt about it, this is a serious charge and one that should definitely be explicated.

Now Myer and Tyson are both practicing scientists whilst Rosenhouse is a mathematician, all of them work in disciplines that require one, if one makes a substantial claim, to provide the appropriate evidence or proof to support that claim. What is with their claim that religion has blocked the advance of science in general or in the case of Bruno and Galileo the acceptance of modern astronomy and cosmology in particular? Have our scientific practitioners provided the necessary evidence to back up their claims? Do they provide a tightly argued historical thesis based on solid documentary evidence to prove their assertions? Can they demonstrate that if the Church had not intervened modern astronomy would have become accepted much earlier than it was? Given their outspoken support of the ‘scientific method’, whatever that might be, you would expect them to do so, wouldn’t you? Do they hell! They don’t waste one single word on the topic. No evidence, no proofs, no academic arguments just plain straightforward unsubstantiated claims in the style of the gutter press. A pretty poor showing for the defenders of scientific faith.

But could they still be right? Even if they don’t take the trouble to provide the historical discourse necessary to substantiate their claims, could it be true that the Church’s actions against Bruno and Galileo did in fact have a negative influence on the acceptance of heliocentricity and other aspects of modern astronomy and cosmology? Let us examine the historical facts and answer the questions that Rosenhouse-Myer and Tyson are apparently above answering, the truth being apparently so obviously clear that they don’t require answering.

To start with the poor Giordano, Bruno was one of those who advocated Copernicus’ heliocentric astronomy already in the sixteenth-century. He however went beyond Copernicus in a series of cosmological speculations and it is these that Cosmos thought to be so important that they devoted eleven minutes of a forty-five minute broadcast to them. I shall deal with the acceptance of heliocentricity separately later and only address Bruno’s cosmology now. Copernicus himself expressly left the question as to whether the cosmos is finite or infinite, as he said, to the philosophers, with good reason. This question was purely speculative and could not, with the evidence and possibilities available to the Renaissance astronomer, be addressed in anything approaching a scientific manner. To all intents and purposes the cosmos appeared finite and Renaissance scholars had no means available to prove otherwise. Bruno’s speculation was of course not new.

In his own times Nicolas Cusanus had already considered the question and earlier, in the first-century BCE, the Epicurean philosopher poet Lucretius, Bruno’s inspiration, had included it in his scientific poem De rerum natura. Lucretius of course did not invent the concept but was merely repeating the beliefs of the fifth-century BCE Greek atomists. All of this demonstrates that the idea of an infinite cosmos was fairly common at the beginning of the seventeenth century and nothing the Church said or did was likely to stop anybody speculating about it. The thing that prevented anybody from going further than speculation was the lack of the necessary scientific apparatus to investigate the question, a similar situation to that of the string-theorists and multiverse advocates of today.

This does not mean that astronomers did not address the problem of the size of the cosmos and the distance to the stars. Amongst others Galileo, Jeremiah Horrocks, Christiaan Huygens and Isaac Newton all tried to estimate/calculate the distances within the solar system and outward towards the stars. First in the middle of the eighteenth century with the transit of Venus measurements were these efforts rewarded with a minimum of success. It wasn’t until the early nineteenth century that the first stellar distance measurements, through stellar parallax, were achieved. All of these delays were not caused by anything the Church had done but by the necessity of first developing the required scientific theories and apparatus.

Bruno’s next cosmological speculation was that the sun and the stars were one and the same. Once again there was nothing new in this. Anaxagoras had already had the same idea in the fifth-century BCE and John Philoponus in the fifth-century CE. Once again the problem with this speculation was not any form of religious objection but a lack of scientific theory and expertise to test it. This first became available in the nineteenth century with development of spectroscopy. This of course first required the development of the new matter theory throughout the seventeenth and eighteenth centuries, a process that involved an awful lot of science.

Bruno’s last speculation and the one that bothered the Church was the existence of inhabited planets other than the Earth. Again this was nothing new and whatever the Church might have thought about it that speculation generated a lively debate in the seventeenth century that is still going on. We still don’t actually know whether we are alone or not.

Given my knowledge of the history of science I can’t see anywhere, where the Church hindered or even slowed down scientific progress on those things that Bruno speculated about in his cosmological fantasy. But what about heliocentricity, here surely the Church’s persecution of both Bruno and Galileo hindered science bay the hounds of anti-religious rationalism.

What follows is a brief sketch of the acceptance of the heliocentric astronomy hypothesis in the sixteenth and seventeenth centuries. This is a subject I’ve dealt with before in various posts but it doesn’t hurt to repeat the process as there are several important lessons to be learnt here. To begin with there is a common myth that acceptance of ‘correct’ new scientific theories is almost instantaneous. To exaggerate slightly, Einstein published his General Theory of Relativity in 1915 and the world changed overnight or at the latest when Eddington confirmed the bending of light rays conform with general relativity in 1919. In reality the acceptance of the general theory of relativity was still a topic of discussion when I was being educated fifty years later and that despite numerous confirmatory tests. Before it is accepted a major new scientific theory must be examined, questioned, tested, reformed, modified and shown to be superior to all serious alternatives. In the Early Modern Period with communication considerably slower this process was even slower.

Copernicus published his De revolutionibus in 1543 and there were only ten people in the entire world, including Bruno but much more importantly both Kepler and Galileo, who accepted it lock, stock and barrel by 1600. This system had only one real scientific advantage over the geocentric one; it could explain the retrograde movement of the planets. However this was not considered to be very important at the time. There were some relatively low-key religious objection but these did not play any significant role in the very slow initial acceptance of the theory. The problematic objections were observationally empirical and had already been discussed by Ptolemaeus in his Syntaxis Mathematiké in the second-century CE. Put very simple if the world is spinning very fast and hurtling through space at an alarming speed why don’t we get blown away? Copernicus had the correct answer to this problem when he suggested that the atmosphere was carried round with the earth in the form of a bubble so to speak. Unfortunately he lacked the physics to explain and justify such a claim. It would take most of the seventeenth century and the combined scientific efforts of Kepler, Galileo, Stevin, Borelli, Descartes, Pascal, Huygens, Newton and a whole boatload of lesser lights to create the necessary physics to explain how gravity holds the atmosphere in place whilst the earth is moving.  This process was not hindered by the Church in anyway whatsoever.

There was a second level of acceptance of Copernicus theory, an instrumental one, as a mathematical model to deliver astronomical data for various applications, astrology, cartography, navigations etc. Here the system based on the same inaccurate data as the Ptolemaic one did not fair particularly well. Disgusted by the inaccuracy of both systems Tycho Brahe started a new long-term observational programme to obtain new accurate data. Whilst doing so he developed a third model, the so-called geo-heliocentric model, in which the planets orbited the sun, which in turn orbited the stationary earth. This model had the advantage of explaining retrograde motion without setting the earth in motions, a win-win situation.

The first major development came with the invention of the telescope in 1608 and its application to astronomical observation from 1609 onwards. The first telescopic discoveries did not provide any proofs for either the Copernican or the Tychonic models but did refute both the Aristotelian homocentric model and the Ptolemaic model. Around the same time a new candidate, the Keplerian elliptical astronomy, entered the ring with the publications of Kepler’s Astronomia nova in 1609. For a full list of the plethora of possible astronomical models at the beginning of the seventeenth century see this earlier post.

By 1620 the leading candidate was a Tychonic model with diurnal rotation. It should be pointed out that due to the attempts of Galileo and Foscarini to reinterpret Holy Scripture in favour of heliocentricity the Catholic Church had entered the action in 1615 and forbidden the heliocentric theory but not the heliocentric hypothesis. The distinction is important. The theory says heliocentricity is a scientific fact the hypothesis says it’s a possibility. At this time heliocentricity was in fact an unproved hypothesis and not a theory. This is the point where Rosenhouse-Myers step in and claim that the Church hindered scientific progress but did they. The straightforward answer is no. The astronomers and physicist carried on looking for answers to the open questions and solutions to the existing problems. There is no evidence whatsoever of a slowing down or interruption in their research efforts.

Between 1618 and 1621 Kepler published his Epitome astronomiae Copernicanae explaining his elliptical astronomy and his three laws of planetary motion in simple terms and in 1627 the Tabulae Rudolphinae the astronomical tables based on his system and Tycho’s new accurate data. It was these two publications that would lead to the general acceptance of heliocentricity by those able to judge by around 1660. Kepler’s publications delivered the desired accurate prognoses of planetary positions, eclipses etc. required by astrologers, cartographers, navigators etc.

At no point in the 120 years between the initial publication of Copernicus’ De revolutionibus and the general acceptance of heliocentricity in the form of Kepler’s elliptical astronomy is there any evidence of the Church having slowed or hindered progress in this historical process. To close it should be pointed out that it would be another seventy years before any solid scientific evidence for the heliocentric hypothesis was found by Bradley, in the form of stellar aberration.






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

A double heliocentrism anniversary?

Georg Joachim Rheticus was born 500 years ago today in Feldkirch, now in Austria, on 16th February 1514, as Dennis Danielson put it in the title of his excellent Rheticus biography, he was the first Copernican. [1] It was Rheticus who travelled to Frauenburg in 1539 and over many months persuaded Copernicus to publish his De revolutionibus, publishing his own Narratio prima, to test the water for the heliocentric hypothesis in 1540.

Rheticus' Horoscope taken from Danielson The First Copernican p. 16

Rheticus’ Horoscope taken from Danielson The First Copernican p. 16

Rheticus’ name will always be associated with that of Copernicus and heliocentrism.  Another who is inseparably bound up with Copernicus and heliocentrism is Galileo Galilei who celebrated his 450th birthday yesterday, or did he? All over the Internet people were celebrating Galileo’s 450th birthday yesterday, the 15th February, Both the MacTutor History of Mathematics article and the English Wikipedia give his birthdate as 15th February 1564, the latter citing Galileo at Work by Stillman Drake, the Grand Seignior of Galileo studies, but was it? Already on Thursday last week as people were gearing up for the great day Lorenzo Smerillo of Montclair State University pointed out on the History of Astronomy Mailing List that Galileo was actually born on the 16th February and not the 15th.  Somewhat confused, I turned to the two most recent   scholarly biographies of Galileo, David Wootton’s Galileo Watcher of the Skies[2] and John Heilbron’s Galileo[3]; the former says the 15th, the latter the 16th. Interestingly both refer to Galileo’s horoscope, which he cast himself. Another Galileo expert William Shea gives the birthdate in his Galileo Selected Writings, as the 16th and in a footnote explains the reason for the confusion, the same one that Smerillo had already given and which I will now explain.

Galileo's Horoscope

Galileo’s Horoscope

As you can see Galileo’s horoscope gives the date and time of birth twice:

1564. 15. febr. h. 22.30. lat. 42. 30

16. febr. h. 4. pm


The first set of figures are given in Italian hours, which follow the Islamic and Jewish custom of numbering the hours of the day from sunset. Sunset on the 15th February in Northern Italy was at 5:30 pm so the 22.30 hour on the 15th would be 4 pm on the 16th. This is of course the second set of figures giving the date and time of birth in French hours. This shows clearly that Galileo was born on the 16th not the 15th.  The 3.30 is probably an error estimate based on uncertainty as to the time of sunset.

Confusingly Wootton argues against this interpretation insisting on the 15th in a complex discussion of the subject.[4]

Our double anniversary is however somewhat confused by another piece of calendrical confusion. Both of our heliocentric astronomers were born before the calendar reform so their birthdates are given according to the Julian Calendar, this of course means that our double anniversary is not actually today but first on the 26th February.

Just to throw another spanner into the works, both of the birthdates are taken from Renaissance horoscopes making them instantly suspect, why? It was a common practice in the Renaissance for astrologers to rectify horoscopes. This was the practice of adjusting times of birth by hours and even sometimes a whole day to make the resulting horoscope more harmonious with the real life of the horoscope’s subject. Rheticus for example was known to be an adherent of this practice.

[1] Dennis Danielson, The First Copernican, Georg Joachim Rheticus and the Rise of the Copernican Revolution, Walker and co., New York, 2006

[2] David Wootton, Galileo Watcher of the Skies, Yale University Press, New Haven and London, 2010

[3] J. L. Heilbron, Galileo, Oxford University Press, Oxford, 2010

[4] David Wootton, Accuracy and Galileo: A Case Study in Quantification and the Scientific Revolution, The Journal of the Historical Society, Vol.10, 2010 pp. 43-55


Filed under History of Astronomy, Uncategorized

Alas, poor Wallace


I have never reblogged somebody else’s post from another blog but this superb post on the current public misrepresentation of Alfred Russel Wallace by his fan club, posted by John van Wyhe on Rebekah “Becky” Higgitt’s teleskopos blog, is so in tune with the ethos of the Renaissance Mathematicus that I have decided to reblog it here. Read and enjoy!

Originally posted on teleskopos:

This guest post by John van Wyhe is the result of my asking him to expand on a point raised on Facebook…

This year is the centenary of the death of Victorian naturalist Alfred Russel Wallace. This has sparked an unprecedented amount of media attention. (Compare with the 2009 Darwin bicentenary) The Wallace “experts” most often interviewed, however, are usually not historians of science, but scientists or enthusiasts. This would be unacceptable for physics, economics or even sports. So why is it so routinely the case for history of science? It is a small field, but there are many departments and scholars in our universities who conduct sophisticated research on science past. If we want to tell the public about Victorian science, surely historians of science should be in the conversation?

In the hands of admiring amateurs, Wallace has evolved into a heroic but forgotten genius – wrongfully obscured…

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Getting the measure of the earth.

It is generally accepted that the Pythagoreans in the sixth century BCE were the first to recognise and accept that the earth is a sphere. It is also a historical fact that since Aristotle in the fourth century BCE nobody of any significance in the western world has doubted this fact. Of course recognising and accepting that the earth is a sphere immediately prompts other questions, one of the first being just how big a sphere is it? Now if I want to find the circumference of a cricket ball (American readers please read that as a baseball ball) I whip out my handy tape measure loop it around the ball and read of the resulting answer, between 224mm and 229mm (circa 230mm for American readers). In theory I could take an extremely long tape measure and following a meridian (that is a great circle around the globe through the north and south poles) loop it around the globe reading off the answer as before, 40,007.86 km (radius) 6356.8km according to Wikipedia. However it doesn’t require much imagination to realise the impracticality of this suggestion; another method needs to be found.

Famously, the earliest known scientific measurement of the polar circumference was carried out by Eratosthenes in the third century BCE. Eratosthenes measured the elevation of the sun at midday on the summer solstice in one of two cities that he thought to be on the same meridian knowing that the sun was directly overhead at the other.  Knowing the distance between the cities it is a relative simple trigonometrical calculation to determine the polar circumference. Don’t you love it when mathematicians say that a calculation is simple!  He achieved an answer of 250 000 stadia but as there were various stadia in use in the ancient world at this time and we don’t know to which stadia he was referring we don’t actually know how accurate his measure was.

Other astronomers in antiquity used the more common method of measuring a given distance on a meridian, determining the latitude of the ends and again using a fairly simple trigonometrical calculation determining the polar circumference. This method proved to be highly inaccurate because of the difficulties of accurately measuring a suitably long, straight north south section of a meridian. The errors incurred leading to large variations in the final circumference determined.

In the eleventh century CE the Persian scholar al-Biruni developed a new method of determining the earth’s circumference. He first measured the height of a suitable mountain, using another of those simple trigonometrical calculations, then climbing the mountain measuring the angle of dip of the horizon. These measurements were followed by, you’ve guessed it, yet another simple trigonometrical calculation to determine the circumference. Various sources credit al-Biruni with an incredibly accurate result from his measurements, which is to be seriously doubted. For various reasons it is almost impossible to accurately determine the angle of dip and the method whilst theoretically interesting is in practice next to useless.

In the Renaissance Gemma Frisius’ invention of triangulation in 1533 provided a new method of accurately measuring a suitably long north south section of a meridian. The first to apply this method to determine the length of one degree of meridian arc was the Dutch mathematician Willibrord Snel, as described in his Eratosthenes Batavus (The Dutch Eratosthenes) published in 1617. He measured a chain of triangles between Alkmaar and Bergen op Zoom and determined one degree of meridian arc to be 107.395km about 4km shorter than the actual value. Snel’s measurement initially had little impact but it inspired one that was to become highly significant.

The meridian arc measurement inspired by Snel was carried out by the French astronomer Jean-Félix Picard who was born the son of a bookseller, also called Jean, in La Flèche on 21st July 1620.  As is unfortunately all too often the case for mathematicians in the Early Modern Period we know very little about Picard’s background or childhood but we do know that he went to school at the Jesuit College in La Flèche where he benefited from the Clavius mathematical programme as did other La Flèche students such as Descartes, Mersenne and Gassendi. Picard left La Flèche around 1644 and moved to Paris where he became a student of Gassendi then professor for mathematics at the Collège Royal. Whether he was ever formally Gassendi’s student is not known but he certainly assisted in his astronomical observations in the 1640s. In 1648 Picard left Paris for health reasons but in 1655 he returned as Gassendi’s successor at the Collège Royal; an appointment based purely on his reputation, as he had published nothing at this point in his life.

Jean Picard (artist unknown)

Jean Picard (artist unknown)

In 1665 Jean-Baptist Colbert became finance minister of France and began to pursue an aggressive science policy.

Colbert 1666 Philippe de Champaigne

Colbert 1666 Philippe de Champaigne

He established the Académie des sciences in 1666 modelled on its English counterpart the Royal Society but unlike Charles who gave his scientists no financial support Colbert supplied his academicians, of whom Picard was one, with generous salaries. It was also Colbert who motivated his academicians to produce a new, modern, accurate map of France and this was when Picard became a geodesist and cartographer.

Following the methods laid down by Snel Picard made the first measurement of what is now the legendary Paris meridian, which would a hundred years later in extended form become the basis of the metre and thus the metric system. He first measured an eleven-kilometre base line south of Paris between Villejuif and Juvisy across what is now Orly airport using standardised wooden measuring rods.

Southern end of Picard's baseline

Southern end of Picard’s baseline


Northern end of Picard's baseline

Northern end of Picard’s baseline

The straight path that he created became the Avenue de Paris in Villejuif and later the Route National 7 through Orly to Juvisy. From this baseline Picard triangulated northwards through Paris and a little further south. For his triangulation Picard used a theodolite whose sighting telescope was fitted with cross hair. The first ever use of such an instrument. Picard determined one degree of meridian arc to be 110.46 km making the polar radius 6328.9 km.

Picard's triangulation and his instruments

Picard’s triangulation and his instruments

Whilst Picard was out in the field measuring triangles Colbert was hiring Giovanni Domenico Cassini away from Bologna to work in the newly constructed Paris Observatory in what was probably to most expensive scientific transfer deal in the seventeenth century.

Giovanni Cassini (artist unknown)

Giovanni Cassini (artist unknown)

Following the success of Picard’s meridian triangulation he set about using the skills he had developed to map the coastline of France together with Cassini and Philippe de La Hire. The results of their endeavours greatly reduced the presumed size of France provoking Louise XIV’s famous quip that he had lost more territory to the cartographers than he had ever lost to his enemies.

Map showing both old and new French coastlines

Map showing both old and new French coastlines

Picard now began preparations for the accurate mapping of France but died before the project could begin. Cassini took up the reins and the mapping of France became a Cassini family project stretching over four generations.

Picard’s determination of the size of the earth would go on to play a significant role in the history of physics. In 1666 when the young Isaac Newton first got an inkling of the concept of a universal gravity he asked himself if the force that causes an object to fall to the ground (that infamous apple) is the same force that prevents the moon from shooting off at a tangent to its orbit, which it should do according to the law of inertia. Young Newton did a quick calculation on the back of an envelope and determined that it wasn’t.  As we now know they are of course the same force so what went wrong with the young Isaac’s calculations? The size of the earth that he had used in his calculation had been wrong. In the 1680s when Newton returned to the subject and redid his calculation he now took Picard’s value and discovered that his original assumption had indeed been correct. In his Principia Newton uses Picard’s value with acknowledgement.

The difference between Picard’s value for one degree of meridian arc and that determined by Snel led Cassini and his son to hypothesise that the earth is a prolate spheroid (lemon shaped) whereas Newton and Huygens had hypothesised that it is an oblate spheroid (orange shaped) a dispute that I’ve blogged about in the past.


Picard made other important contributions to astronomy and physics and it’s a little bit sad that that today when people hear or read the name Jean Picard they think of a character in a TV science fiction series and not a seventeenth century French astronomer.

[The photos showing the monuments marking the ends of Picard's baseline are taken from Paul Murdin, Full Meridian of Glory: Perilous Adventures in the Competition to Measure the Earth, Copernicus Books, 2009]


Filed under History of Astronomy, History of Cartography, History of Physics, History of science, Uncategorized

How to insult an entire profession.

I’ve never heard of SALON, which is apparently some sort of pseudo-intellectual event agency. This organisation is presenting one of their events in the Banqueting House in London on 24th June with the title 1649. Alone the opening sentence of the description made me cringe an a historian:

1649 was a pivotal year. The English public – having tired of a King who had raised taxes for wars and spent it on art – upped and executed him.

I leave it to my educated and knowledge thirsty readers to read up on the real causes of the English Revolution and the resulting regicide, as this is not the purpose of this brief post. My interest concerns rather more the speaker chosen to present the history of science of the period, the good Dr Stuart Clark, who should be well known to the readers of this blog for his displays of history of science ignorance here and here. Salon presents him thus:

Stuart Clark, described by The Independent as a UK star of astrophysics teaching (alongside Stephen Hawking) will be on hand to explain the scientific world of 1649.  Having undertaken extensive research for his acclaimed historical fiction series based in this period, no one is better qualified to explain where science was at in the mid 17th century, and how new ideas were beginning to remodel the minds and hearts of the people of England. [my emphasis]

I personally regard the statement, “no one is better qualified to explain where science was at in the mid 17th century”, as a crass insult to all professional historians of science and not just the legion of very competent experts for the science of the seventeenth century whom it disqualifies.


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A bit on the side.

One of the joys of the world of blogging is the guest post. The Renaissance Mathematicus has provided cyberspace to a couple of excellent guest posts in the past and hopes to attract some more in the future.

As many readers will know, because I keep repeating it, I actually guest blogged at the excellent Evolving Thoughts blog of John Wilkins (@john_s_wilkins) the Albino Aussie AnthropoidTM as well as the equally excellent Ether Wave Propaganda of Will Thomas (@GWilliamThomas) before I started up this little endeavour. Later I did a series of guest posts on the guest blog of the Scientopia collective.

Now my wandering eye has struck again and I have indulged in a little tickle on the side with a guest post at the fascinating Recipes Project blog (@historecipes). If you are dying to know how to differentiate between Mucardinus avellanarius and Glis glis and how to stuff the latter the Roman way then wander on over and take a look.

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Out to Lunch!

Hurricane force winds allowing I shall be making a flying visit to England on the coming weekend. On Monday 19th December I shall be in London for the day on my way back to Germany and I will be lunching with Rebekah “Becky” Higgitt  and possibly her colleague Richard Dunn in Greenwich. Any readers of the Renaissance Mathematicus who are in London and who have time would be very welcome to join us; if you want to come leave a message in the comments or send me an email.


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Multiplying the Renaissance way

At the always excellent Ptak Science Books blog John Ptak has a nice post about Renaissance multiplication 9876 X 6789 = 67048164 in which he was unable to work out the algorithm used to carry out the multiplication. In the following I show the example from John’s blog as it was displayed followed by the correct form with working method.

Multiplication the Diamond











The Diamond done correctly:











From left to right lower row L1,L2,L3,L4

From left to right upper row U1,U2,U3,U4


Row 1: L1 X U4

Row 2: L1 X U3, L2 X U4

Row 3: L1 X U2, L2 X U3, L3 X U4

Row 4: L1 X U1, L2 X U2, L3 X U3, L4 X U4

Row 5: L2 X U1, L3 X U2, L4 X U3

Row 6: L3 X U1, L4 X U2

Row 7: L4 X U1

Then sum vertically from right to left

Write 4

8+5+3=16 write 6 carry 1

1+2+4+6+6+2=21 write 1 carry 2

2+6+4+9+5+4+7+1=38 write 8 carry 3

3+3+2+4+6+6+2+8=34 write 4 carry 3

3+4+8+5+3+7=30 write 0 carry 3

3+4+4+6=17 write 7 carry 1

1+5=6 write 6

Added 11/11: Also motivated by John Ptak, Ray Girvan at Journal of a Southern Book Reader has a really good poston the subject of these Renaissance multiplication algorithms, definitely recommended reading.


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