Last year on the five hundredth anniversary of his birth I duly recycled my old Conrad Gesner post and discovered to my delight that I had a small but distinguished Gesner fan club on my Twitter stream. We spent a happy 24 plus hours tweeting and retweeting each other’s tributes to and admirations of the Swiss polymath. At some point in a flippant mood I suggested that we should celebrate an annual Conrad Gesner Day on, 26 March his birthday. The suggestion was taken up with enthusiasm by the others and so we parted.

A couple of months ago Gesner’s name came up again and I said I was serious about celebrating Conrad Gesner Day and all the others immediately responded that they were very much still up for it so it’s on. At the moment Biodiversity Heritage Library (BHL @BioDivLIbrary), Michelle Marshall (Historical SciArt (@HistSciArt), New York Academy of Medicine Center for History (@NYAMHistory), the rare book librarian at Smithsonian Libraries and I are committed to celebrating Conrad Gesner Day. What about you?

What is going to happen? That’s up to all those involved. You can post blog posts, post illustrations from Gesner’s works on Twitter, Facebook, Instagram, whatever, where ever. Post links to sites about Gesner. If you want to write something on Gesner but don’t have your own blog, contact me and I’ll post it here at the Renaissance Mathematicus. I will collect all the contributions and post a Whewell’s Gazette style links list here at RM on the Monday.

The aim is not to glorify Conrad Gesner but to raise peoples’ awareness of a fascinating and important figure in the history of Renaissance science. Join us! Make a contribution! We already have a hash tag #**GesnerDay**.

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Today is Copernicus’ birthday (19 February 1473) and all over the Internet British and American posters are being, what they see as, scrupulously, politically correct and announcing today as the birthday of the Polish astronomer… All very well but it isn’t factually right.

Nicolas Copernicus was born in the city of Toruń, which is today in Poland but wasn’t at the time of his birth. The whole area in which Copernicus was born and in which he lived for all of his life, except when he was away studying at university, was highly dispute territory over which several wars were fought. Between 1454 and 1466 the Thirteen Years’ War was fought between the Prussian Confederation allied with the Crown of the Kingdom of Poland and the State of the Teutonic Knights. This war ended with the Second Peace of Toruń under which Toruń remained a free city now under the patronage of the Polish King.

As I pointed out in an earlier post Copernicus spent all of his adult life, after graduating from university, as a citizen of Ermland (Warmia), which was then an autonomous Prince Bishopric ruled by the Bishop of Frombork and the canons of the cathedral chapter, of which Copernicus was one.

All of this means that Copernicus was neither German nor Polish but was born a citizen of Toruń and died a citizen of Ermland. I realise that this doesn’t fit our neat modern concept of national states but that is the historical reality that people should learn to live with and to accept.

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Jones’ first foray into the world of #histSTM on 28 January with a piece entitled, *The charisma droids: today’s robots and the artists who foresaw them*, which is a review of the new major robot exhibition at the Science Museum. What he has to say about the exhibition doesn’t really interest me here but in the middle of his article we stumble across the following paragraph:

*So it is oddly inevitable that one of the first recorded inventors of robots was Leonardo da Vinci, consummate artist and pioneering engineer* [my emphasis]

Now I have no doubts that amongst his many other accomplishments Leonardo turned his amazingly fertile thoughts to the subject of automata, after all he, like his fellow Renaissance engineers, was a fan of Hero of Alexandria who wrote extensively about automata and also constructed them. Here we have the crux of the problem. Leonardo was not “one of the first recorded inventors of robots”. In fact by the time Leonardo came on the scene automata as a topic of discussion, speculation, legend and myth had already enjoyed a couple of thousand years of history. If Jones had taken the trouble to read Ellie Truitt’s (@MedievalRobots) excellent *Medieval Robots: Mechanism, Magic, Nature and Art* (University of Pennsylvania Press, 2015) he would have known just how wrong his claim was. However Jones is one of those who wish to perpetuate the myth that Leonardo is the source of everything. Actually one doesn’t even need to read Ms. Truitt’s wonderful tome, you can listen to her sketching the early history of automata on the first episode of Adam Rutherford’s documentary *The Rise of the Robots* on BBC Radio 4, also inspired by the Science Museums exhibition. The whole series is well worth a listen.

On 6 February Jones took his Leonardo fantasies to new heights in a piece, entitled *Did the Mona Lisa have syphilis*? Yes, seriously that is the title of his article. Retro-diagnosis in historical studies is a best a dodgy business and should, I think, be avoided. We have whole libraries of literature diagnosing Joan of Arc’s voices, Van Gough’s mental disorders and the causes of death of numerous historical figures. There are whole lists of figures from the history of science, including such notables as Newton and Einstein, who are considered by some, usually self declared, experts to have suffered from Asperger’s syndrome. All of these theories are at best half way founded speculations and all too oft wild ones. So why does Jonathan Jones think that the Mona Lisa had syphilis? He reveals his evidence already in the sub-title to his piece:

*Lisa del Giocondo, the model for Leonardo’s painting, was recorded buying snail water – then considered a cur for the STD: It could be the secret to a painting haunted by the spectre of death*.

That’s it folks don’t buy any snail water or Jonathan Jones will think that you have syphilis.

Let’s look at the detail of Jones’ amazingly revelatory discovery:

*Yet, as it happens, a handful of documents have survived that give glimpses of Del Giocondo’s life. For instance, she is recorded in the ledger of a Florentine convent as buying snail water (**acqua di chiocciole**) from its apothecary.*

*Snail water? I remember finding it comical when I first read this. Beyond that, I accepted a bland suggestion that it was used as a cosmetic or for indigestion. In fact, this is nonsense. The main use of snail water in pre-modern medicine was, I have recently discovered, to combat sexually transmitted diseases, including syphilis.*

So she bought some snail water from an apothecary, she was the female head of the household and there is absolutely no evidence that she acquired the snail water for herself. This is something that Jones admits but then casually brushes aside. Can’t let ugly doubts get in the way of such a wonderful theory. More importantly is the claim that “the main use of snail water snail water in pre-modern medicine was […] to combat sexually transmitted diseases, including syphilis” actually correct? Those in the know disagree. I reproduce for your entertainment the following exchange concerning the subject from Twitter.

**Greg Jenner** (**@greg_jenner)**

*Hello, you may have read that the Mona Lisa had syphilis. This thread points out that is probably bollocks*

* **Dubious theory – the key evidence is her buying “snail water”, but this was used as a remedy for rashes, earaches, wounds, bad eyes, etc…*

**Greg Jenner added**,

*Seen this @DrAlun** @DrJaninaRamirez** ? What say you? I’ve seen snail water used in so many different Early Modern remedies*

**Alun Withey (@DrAlun)**

*I think it’s an ENORMOUS leap to that conclusion. Most commonly I’ve seen it for eye complaints.*

**Greg Jenner**

*@DrAlun** @DrJaninaRamirez** yeah, as I thought – and syphilis expert @monaob1** agrees*

* ***Alun Withey**

*@greg_jenner** @DrJaninaRamirez** @monaob1** So, the burning question then, did the real Mona Lisa have sore eyes? It’s a game-changer!*

**Mona O’Brian (@monaob1)**

*@DrAlun** @greg_jenner** @DrJaninaRamirez** interested to hear the art historical interpretation on the ‘unhealthy’ eyes comment!*

**Alun Withey**

*@monaob1** @greg_jenner** @DrJaninaRamirez** doesn’t JJ say in the article there’s a shadow around her eyes? Mystery solved. *mic drop**

**Greg Jenner**

*@DrAlun** @monaob1** @DrJaninaRamirez** speaking as a man who recently had to buy eye moisturiser, eyes get tired with age? No disease needed*

* ***Mona O’Brian**

*@greg_jenner** Agreed! Also against the pinning of the disease on the New World, considering debates about the disease’s origin are ongoing*

**Jen Roberts (@jshermanroberts)**

*@greg_jenner** I just wrote a blog post about snail water for @historecipes** –common household cure for phlegmy complaints like consumption.*

**Tim Kimber (@Tim_Kimber)**

*@greg_jenner** Doesn’t the definite article imply the painting, rather than the person? So they’re saying the painting had syphilis… right?*

**Minister for Moths (@GrahamMoonieD)**

*@greg_jenner** but useless against enigmatic smiles*

Interestingly around the same time an advert was doing the rounds on the Internet concerning the use of snail slime as a skin beauty treatment. You can read Jen Roberts highly informative blog post on the history of snail water on *The Recipes Project*, which includes a closing paragraph on modern snail facials!

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**Let’s remember we use Arabic numerals – 1, 2, 3 etc. Try dividing MCMLXVI by XXXIX – Sir Richard Evans (@Richard Evans36)**

There was no context to the tweet, a reply or whatever, so I can only assume that he was offering a defence of Islamic or Muslim culture against the widespread current attacks by drawing attention to the fact that we appropriated our number system along with much else from that culture. I would point out, as I have already done in my nineteenth-century style over long title, that one should call them Hindu-Arabic numerals, as although we appropriated them from the Islamic Empire, they in turn had appropriated them from the Indians, who created them.

As the title suggests, in his tweet Evans is actually guilty of perpetuating a widespread and very persistent myth concerning the comparative utility of the Hindu-Arabic number system and the Roman one when carrying out basic arithmetical calculations. Although I have taken Professor Evans’ tweet as incentive to write this post, I have thought about doing so on many occasions in the past when reading numerous similar comments. Before proving Professor Evans wrong I will make some general comments about the various types of number system that have been used historically.

Our Hindu-Arabic number system is a place-value decimal number system, which means that the numerals used take on different values depending on their position within a given number if I write the Number of the Beast, 666, the three sixes each represents a different value. The six on the far right stands for six times one, i.e. six, its immediate neighbour on the left stands for six time ten, i.e. sixty, and the six on the left stands for six times one hundred, i.e. six hundred, so our whole number is six hundred and sixty six. It is a decimal (i.e. ten) system going from right to left the first numeral is a multiple of 10^{0} (for those who maths is a little rusty, anything to the power of zero is one), the second numeral is a multiple of 10^{1}, the third is a multiple of 10^{2, }the forth is a multiple of 10^{3}, the fifth is a multiple of 10^{4}, and so on and so fourth. If we have a decimal point the first numeral to the right of it is 10^{-1} (i.e. one tenth), the second 10^{-2 }(i.e. one hundredth), the third 10^{-3 }(i.e. one thousandth), and so on and so forth. This is a very powerful system of writing numbers because it comes out with just ten numerals, one to nine and zero making it very economical to write.

The Hindu-Arabic number system developed sometime in the early centuries CE and our first written account of it is from the Indian mathematician, Brahmagupta, in his Brāhmasphuṭasiddhānta (“Correctly Established Doctrine of Brahma“) written c. 628 CE. It came into Europe via Al-Khwārizmī’s treatise, *On the Calculation with Hindu Numerals* from 825 CE, which only survives in the 12th-century Latin translation, *Algoritmi de numero Indorum**.* After its initial introduction into Europe in the high Middle Ages the Hindu-Arabic system was only really used on the universities to carry out computos, that is the calculation of the dates on which Easter falls. Various medieval scholars such as ~~Robert Grosseteste~~ John of Sacrobosco wrote elementary textbooks explaining the Hindu-Arabic system and how to use it. The system was reintroduced for trading purposes by Leonard of Pisa, who had learnt it trading with Arabs in Spain, in his book the *Liber Abbaci* in the thirteenth century but didn’t really take off until the introduction of double-entry bookkeeping in the fourteenth century.

The Hindu-Arabic system was not the earliest place-value number system. That honour goes to the Babylonians, who developed a place-value system about ~~1700~~ 2100* BCE but was not a decimal system but a sexagesimal system, that is base sixty, so the first numeral is a multiple of 60^{0}, the second a multiple of 60^{1}, the third a multiple of 60^{2}, and so on and so fourth. Fractions work the same, sixtieths, three thousand six-hundredths (!), and so on and so fourth. Mathematically a base sixty system is in some senses superior to a base ten one. The Babylonian system suffered from the problem that it did not have distinct numerals but a stroke list system with two symbols, one for individual stroke and a second one for ten stokes:

The Babylonian system also initially suffered from the fact that it possessed no zero. This meant that to take the simple case, apart from context there was no way of knowing if a single stroke stood for one, sixty, three thousand six hundred or whatever. The problem gets even more difficult for more complex numbers. Later the Babylonians developed a symbol for zero. However the Babylonian zero was just a placeholder and not a number as in the Hindu-Arabic system.

The Babylonian sexagesimal system is the reason why we have sixty minutes in an hour, sixty seconds in a minute, sixty minutes in a degree and so forth. It is not however, contrary to a widespread belief the reason for the three hundred and sixty degrees in a circle; this comes from the Egyptian solar years of twelve thirty day months projected on to the ecliptic, a division that the Babylonian then took over from the Egyptians.

The Greeks used letters for numbers. For this purpose the Greek alphabet was extended to twenty-seven letters. The first nine letters represented the numbers one to nine, the next nine the multiples of ten from ten to ninety and the last nine the hundreds from one hundred to nine hundred. For the thousands they started again with alpha, beta etc. but with a ~~superscript~~ subscript prime mark. So twice through the alphabet takes you to nine hundred thousand nine hundred and ninety-nine. If you need to go further you start at the beginning again with two subscript primes. Interestingly the Greek astronomers continued to use the Babylonian sexagesimal system, a tradition in the astronomy that continued in Europe down to the Renaissance.

We now turn to the Romans, who also have a simple stroke number system with a cancelled stroke forming an X as a bundle of ten strokes. The X halved horizontally through the middle gives a V for a bundle of five. As should be well known L stands for a bundle of fifty, C for a bundle of one hundred and M for a bundle of one thousand given us the well known Roman numerals. A lower symbol placed before a higher one reduces it by one, so LX is sixty but XL is forty. Of interest is the well-known IV instead of IIII for four was first introduced in the Middle Ages. The year of my birth 1951 becomes in Roman numerals MCMLI.

When compared with the Hindu-Arabic number system the Greek and Roman systems seem to be cumbersome and the implied sneer in Professor Evans’ tweet seems justified. However there are two important points that have to be taken into consideration before forming a judgement about the relative merits of the systems. Firstly up till the Early Modern period almost all arithmetic was carried out using a counting-board or abacus, which with its columns for the counters is basically a physical representation of a place value number system.

The oldest surviving counting board dates back to about 300 BCE and they were still in use in the seventeenth century.

A skilful counting-board operator can not only add and subtract but can also multiply and divide and even extract square roots using his board so he has no need to do written calculation. He just needed to record the final results. The Romans even had a small hand abacus or as we would say a pocket calculator. The words to calculate, calculus and calculator all come from the Latin *calculi*, which were the small pebbles used as counters on the counting board. In antiquity it was also common practice to create a counting-board in a sand tray by simply making parallel groves in the sand with ones fingers.

Moving away from the counting-board to written calculations it would at first appear that Professor Evans is correct and that multiplication and division are both much simpler with our Hindu-Arabic number system than with the Roman one but this is because we are guilty of presentism. In order to do long multiplication or long division we use algorithms that most of us spent a long time learning, often rather painfully, in primary school and we assume that one would use the same algorithms to carry out the same tasks with Roman numerals, one wouldn’t. The algorithms that we use are by no means the only ones for use with the Hindu-Arabic number system and I wrote a blog post long ago explaining one that was in use in the early modern period. The post also contains links to the original post at Ptak Science books that provoked my post and to a blog with lots of different arithmetical algorithms. My friend Pat Belew also has an old blog post on the topic.

I’m now going to give a couple of simple examples of long multiplication and long division both in the Hindu-Arabic number system using algorithms I learnt I school and them the same examples using the correct algorithms for Roman numerals. You might be surprised at which is actually easier.

My example is 125×37

125

37

875 Here we have multiplied the top row by 7

__3750__ Here we have multiplied the top row by 3 and 10

__4625 __We now add our two partial results together to obtain our final result.

To carry out this multiplication we need to know our times table up to nine times nine.

Now we divide 4625 : 125

4625 : 125 = 37

__375__

875

875

000

First we guestimate how often 125 goes into 462 and guess three times and write down our three. We then multiply 125 by three and subtract the result from 462 giving us 87. We then “bring down” the 5 giving us 875 and once again guestimate how oft 125 goes into this, we guess seven times, write down our seven, multiply 125 by 7 and subtract the result from our 875 leaving zero. Thus our answer is, as we already knew 37. Not exactly the simplest process in the world.

How do we do the same with CXXV times XXXVII? The algorithm we use comes from the Papyrus Rhind an ancient Egyptian maths textbook dating from around 1650 BCE and is now known as halving and doubling because that is literally all one does. The Egyptian number system is basically the same as the Roman one, strokes and bundles, with different symbols. We set up our numbers in two columns. The left hand number is continually halved down to one, simple ignoring remainders of one and the right hand is continually doubled.

1 | XXXVII | CXXV |

2 | XVIII | CCXXXXVV=CCL |

3 | VIIII | CCCCLL=CCCCC=D |

4 | IIII | DD=M |

5 | II | MM |

6 | I | MMMM |

You now add the results from the right hand column leaving out those where the number on the left is even i.e. rows 2, 4 and 5. So we have CXXV + D + MMMM = MMMMDCXXV. All we need to carry out the multiplication is the ability to multiply and divide by two! Somewhat simpler than the same operation in the Hindu-Arabic number system!

Division works by an analogous algorithm. So now to divide 4625 by 125 or MMMMDCXXV by CXXV

1 | I | CXXV |

2 | II | CCXXXXVV=CCL |

3 | IIII | CCCCLL=CCCCC=D |

4 | IIIIIIII=VIII | DD=M |

5 | VVIIIIII=XVI | MM |

6 | XXVVII=XXXII | MMMM |

We start with 1 on the left and 125 on the right and keep doubling both until we reach a number on the right that when doubled would be greater than MMMMDCXXV. We then add up those numbers on the left whose sum on the right equal MMMMDCXXV, i.e. rows 1, 3 and 6, giving us I+IIII+XXXII = XXXIIIIIII = XXXVII or 37.

Having explained the method we will now approach Professor Evan’s challenge

1 | I | XXXIX=XXXVIIII |

2 | II | XXXXXXVVIIIIIIII=LXXVIII |

3 | IIII | LLXXXXVVIIIIII=CLVI |

4 | IIIIIIII=VIII | CCLLVVII=CCCXII |

5 | VVIIIIII=XVI | CCCCCCXXII=DCXXIIII |

6 | XXVVII=XXXII | DDCCXXXXIIIIIIII=MCCXLVIII |

~~Adding rows 6, 3 and 2 on the right we get MCCXLVIII+CLVI+LXXVIII=MCML i.e. MCMLXVI less XVI so our result is XXXII+XVI+II = L remainder XVI~~

6 + 5 + 2 = MCCXLVIII+DCXXIIII+LXXVIII = 1950 + 16(reminder) is the correct value for the given example (MCMLXVI) Thanks to Lucas (see Comments!)

Now that wasn’t that hard was it?

Interestingly the ancient Egyptian halving and doubling algorithms for multiplication and division are, in somewhat modified form, how modern computers carry out these arithmetical operations.

* Added 13 February 2017: I have been criticised on Twitter, certainly correctly, by Eleanor Robson, a leading expert on Cuneiform mathematics, for what she calls a sloppy and outdated account of the sexagesimal number system. For those who would like a more up to date and anything but sloppy account then I suggest they read Eleanor Robson’s (not cheap) *Mathematics in Ancient Iraq*: *A Social History*, Princeton University Press, 2008

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The earth did not come into existence about four and a half billion years ago with the borders of the national states stamped into its surface. In fact even within the one hundred to two hundred thousand years that Homo sapiens have occupied the earth the concept of a nation state is, in historical terms, a very recent one. Also within the time since nation states have existed their borders have not been static but have ebbed and flowed like the tide; states coming into and going out of existence down the centuries.

Brabant and Savoy, two important European states that existed in the High Middle Ages and Early Modern Period have long since disappeared into the mists of history. Looking at the modern map of Europe, The Netherlands only came into existence in the late sixteenth century, whilst its neighbour Belgium was created in 1815. Germany only really became a nation state following the fall of Hitler and the Nazis in 1945 and was for several decades two nation states, East and West, which only became finally united on 3 October 1990.

The early years of Wikipedia saw several epic battles over the nationality of scientific heroes, the most notorious being over Nicolaus Copernicus, which became so vitriolic that it was a news item on BBC Radio 4’s flagship news magazine, *The Today Programme*. The Poles and Germans carrying on a dispute that dates back to the late eighteenth century; a dispute that is totally barmy, as he was actually neither Polish nor German, as I explained in an earlier post. The nationality of the Islamic mathematician Muḥammad ibn Mūsā al-Khwārizmī, who gave algebra and the algorithm their names, is also disputed between Persia and Uzbekistan. The astronomer Johannes Hevelius, a native of Danzig, or should that be Gdańsk, is like Copernicus claimed by both Germany and Poland. The Jesuit mathematician, astronomer and physicist Ruđer Josip Bošković (English: Roger Joseph Boscovich) is claimed by Croatia, Serbia and Italy, although it should be noted he became a naturalised French citizen and the end of his life. Anther astronomer with dual nationality is the Italian Giovanni Domenico Cassini who ended his life as the Frenchman Jean-Dominique Cassini. Although it is debateable whether it is correct to call Cassini an Italian, as Italy only became a united national state in 1861, about one hundred and fifty years after his death

The latest case of, potentially, disputed nationality that caught my eye and generated this post occurred in an article on the BBC News website, *The Irish novel that seduced the USSR*, the story of the novel *The Gadfly* by Ethel Voynich. Don’t Panic! The Renaissance Mathematicus has not metamorphosed overnight into a blog for literature criticism, you might understand when I say that Ethel Voynich was born Ethel Lilian Boole the youngest of the five daughters of the mathematician and logician George Boole and his wife the proto-feminist and educationalist Mary Everest-Boole. What provoked this post was that the article describes Ethel Voynich as an Irish writer.

Ethel Lilian Boole was born 11 May 1864 in the city of Cork in the Irish province of Munster, so she is Irish, right? Well, maybe not. My eldest sister was born in Rangoon in Burma, so she is Burmese, right? Actually she isn’t, she was born British and has remained British all of her life. Likewise, my brother was born in Lahore, so he’s Pakistani, right. Once again no, he was born British and remained British up to his death two years ago. Both of them were born in what was then British India of British parents, although my mother like my sister was born in Rangoon, and so both of them were automatically British citizens. My bother’s potential nationality is made even more complex by the fact that when he was born Lahore was in India but is now in Pakistan.

Let’s take a closer look at Ethel Lilian. At the time of her birth Ireland was part of the United Kingdom of Britain and Ireland, a country ruled by a single government in Westminster, London. Her father, George Boole, was born in Lincoln and was thus English.

Her mother Mary Everest, the niece of Georg Everest for whom the mountain is named, was born in Wickwar in Gloucestershire and so was also English, although her family is Welsh. The family name, by the way, is pronounced Eve-rest and not Ever-est.

To complicate matters, George Boole died 8 December 1864 just seven months after Ethel Lilian’s birth and Mary immediately returned to England with her five daughters. Ethel Lilian grew up in England and never returned to Ireland and identified as English not Irish. Given her parentage it is doubtful whether she should be referred to as Irish at all, despite having been born in Cork.

It is even more of a stretch to call *The Gadfly* an Irish novel. Ethel Lilian travelled extensively throughout Europe, as an adult and the novel, which is set in Italy and features an English hero, was first published in New York and then London before being translated into Russian, whereupon it became a mega best seller in Russia. To call it an Irish novel purely because of Ethel Lilian’s birth and seven-month residency in Cork is in my opinion a bridge too far.

All five of Boole’s daughters led fascinating and historically significant lives. You can read a short account of *Those Amazing Boole Girls* on my friend Pat’s Blog or for a fuller account I heartily recommend Desmond MacHale’s excellent biography, *The Life and Work of George Boole: A Prelude to the Digital Age*. The family history is dealt with even more fully in Gerry Kennedy’s *The Booles and the Hintons: Two Dynasties That Helped Shape the Modern World*, which I haven’t read yet (it’s on the infinite reading list) but which has received excellent reviews.

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The more general question of the influence of the printed book on the evolution of modern science led quite naturally to a deepened interest in the early history of scientific book publication in which Nürnberg again played a role through Regiomontanus the first printer publisher of scientific books.

Curiously Nürnberg was also the site of the first paper mill north of the Alps, paper being an essentially ingredient in mass production of printed books and this fact led to a strong interest in the history of paper making and to the materials that preceded paper as a medium for transmitting the written word.

Another seminar that I took part in at the university, following my return to the history of science, concerned the history of illustrations in scientific texts, which awakened my interest in the various methods of illustration reproduction and their histories. Another Nürnberger, Albrecht Dürer, played a significant role in that history.

Over the years I acquired a deep interest, and a modicum of knowledge of the histories of all the various aspects of recording knowledge in word and picture, so it was not surprising that my interest was drawn almost magnetically to a fairly recent new publication with the title, *The Book: A Cover to Cover Exploration of the Most Powerful Object of Our Times*. An interest made even stronger by the fact that the author of this tome is Keith Houston, the author of both the book *Shady Characters: The Secret Life of Punctuation, Symbols & Other Typographical Marks*, a serious candidate for ultimate geek bedtime reading, and of the blog of the same name. Unable to resist temptation I acquired a copy of *The Book*.

Having delved deeply into the subject over a number of years I expected to be entertained, Houston is a witty writer, but not really to learn much that was new. I was mistaken, even though I consider myself well informed on the topic I took away much that was new from Houston’s excellent study of the topic.

The Book is divided into four sections, *The Page*, *The Text*, *Illustrations* and *Form*. The first deals with the history of writing material from papyrus over parchment to paper and the progress from hand-made paper to modern industrial paper production. The second deals with methods of bringing writing onto that material starting with Babylonian cuneiform symbols impressed into clay tablets, outlining the history of ink and moving on to the history of moveable type printing. Once again covering the arc from the cradle of civilisation to the twentieth century. Part three does the same for pictures on the page. The final part deals with the forms that books have taken over the centuries from the papyrus roles to the codex and the various sizes and forms that the codex has adopted down the years. We also get a detailed history of the evolution of bookbinding.

Houston has researched his topic exceedingly well and delivers his cornucopia of information in a well-digested and easily accessible form for the reader, with a healthy portion of humour. One aspect of the book that appealed to me as a history of science myth buster is Houston’s use of multiple layers of historical story telling. For example, he takes a topic and tells his readers how its history was understood and presented in the nineteenth century. Then he explains how modern research showed this to be wrong and represents the history from this standpoint. Having gone into great detail he then explodes this version by showing why it can’t be true. I’m not going to go here into any great detail, as it would spoil the fun for future readers, and it really is fun, but Houston gives his readers a useful lesson in the evolution of the historiography of his subject.

One thing that has to be said is that *The Book* is beautifully produced with much obvious loving care for detail. It is printed with a very attractive typeface on lovely paper both of which make it a real pleasure to hold and to read. It comes bound in heavy light-grey carton boards joined together by dark read spinal binding tape. Its gatherings are, as befits a book about the history of the book, stitched and not glued. Throughout the book, starting with the cover, all of the bits and pieces that a book consists of are bracketed and labelled with their corrected technical terms. The book is beautifully illustrated, each illustration possessing an extensive explanatory text of its own. There are a helpful further reading list, extensive endnotes (as always I would have preferred footnotes) and an equally extensive index. Despite being just over 400 pages long, and being a high quality, beautifully produced, bound book it retails at a ridiculously low price. The publishers offer it at $29.95 but it can be had for less than twenty pounds, euro or dollar depending on your location.

If you have any interest in the history of the book as an object or the history of moveable type printing then I can only recommend acquiring a copy of Keith Houston’s wonderful book on the book.

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“Mathematicus, it’s the Latin root of the word mathematician.”

“Then why can’t you just write The Renaissance Mathematician instead of showing off and confusing people?”

“Because a mathematicus is not the same as a mathematician.”

“But you just said…”

“Words evolve over time and change their meanings, what we now understand as the occupational profile of a mathematician has some things in common with the occupational profile of a Renaissance mathematicus but an awful lot more that isn’t. I will attempt to explain.”

The word mathematician actually has its origins in the Greek word mathema, which literally meant ‘that which is learnt’, and came to mean knowledge in general or more specifically scientific knowledge or mathematical knowledge. In the Hellenistic period, when Latin became the lingua franca, so to speak, the knowledge most associated with the word mathematica was astrological knowledge. In fact the terms for the professors[1] of such knowledge, mathematicus and astrologus, were synonymous. This led to the famous historical error that St. Augustine rejected mathematics, whereas his notorious attack on the mathematici[2] was launched not against mathematicians, as we understand the term, but against astrologers.

However St. Augustine lived in North Africa in the fourth century CE and we are concerned with the European Renaissance, which, for the purposes of this post we will define as being from roughly 1400 to 1650 CE.

The Renaissance was a period of strong revival for Greek astrology and the two hundred and fifty years that I have bracketed have been called the golden age of astrology and the principle occupation of our mathematicus is still very much the casting and interpretation of horoscopes. Mathematics had played a very minor role at the medieval universities but the Renaissance humanist universities of Northern Italy and Krakow in Poland introduced dedicated chairs for mathematics in the early fifteenth century, which were in fact chairs for astrology, whose occupants were expected to teach astrology to the medical students for their astro-medicine or as it was known iatro-mathematics. All Renaissance professors of mathematics down to and including Galileo were expected to and did teach astrology.

Of course, to teach astrology they also had to practice and teach astronomy, which in turn required the basics of mathematics – arithmetic, geometry and trigonometry – which is what our mathematicus has in common with the modern mathematician. Throughout this period the terms Astrologus, astronomus and mathematicus – astrologer, astronomer and mathematician – were synonymous.

A Renaissance mathematicus was not just required to be an astronomer but to quantify and describe the entire cosmos making him a cosmographer i.e. a geographer and cartographer as well as astronomer. A Renaissance geographer/cartographer also covered much that we would now consider to be history, rather than geography.

The Renaissance mathematicus was also in general expected to produce the tools of his trade meaning conceiving, designing and manufacturing or having manufactured the mathematical instruments needed for astronomer, surveying and cartography. Many were not just cartographers but also globe makers.

Many Renaissance mathematici earned their living outside of the universities. Most of these worked at courts both secular and clerical. Here once again their primary function was usually court astrologer but they were expected to fulfil any functions considered to fall within the scope of the mathematical science much of which we would see as assignments for architects and/or engineers rather than mathematicians. Like their university colleagues they were also instrument makers a principle function being horologist, i.e. clock maker, which mostly meant the design and construction of sundials.

If we pull all of this together our Renaissance mathematicus is an astrologer, astronomer, mathematician, geographer, cartographer, surveyor, architect, engineer, instrument designer and maker, and globe maker. This long list of functions with its strong emphasis on practical applications of knowledge means that it is common historical practice to refer to Renaissance mathematici as mathematical practitioners rather than mathematicians.

This very wide range of functions fulfilled by a Renaissance mathematicus leads to a common historiographical problem in the history of Renaissance mathematics, which I will explain with reference to one of my favourite Renaissance mathematici, Johannes Schöner.

Schöner who was a school professor of mathematics for twenty years was an astrologer, astronomer, geographer, cartographer, instrument maker, globe maker, textbook author, and mathematical editor and like many other mathematici such as Peter Apian, Gemma Frisius, Oronce Fine and Gerard Mercator, he regarded all of his activities as different aspects or facets of one single discipline, mathematica. From the modern standpoint almost all of activities represent a separate discipline each of which has its own discipline historians, this means that our historical picture of Schöner is a very fragmented one.

Because he produced no original mathematics historians of mathematics tend to ignore him and although they should really be looking at how the discipline evolved in this period, many just spring over it. Historians of astronomy treat him as a minor figure, whilst ignoring his astrology although it was this that played the major role in his relationship to Rheticus and thus to the publication of Copernicus’ *De revolutionibus*. For historians of astrology, Schöner is a major figure in Renaissance astrology although a major study of his role and influence in the discipline still has to be written. Historians of geography tend to leave him to the historians of cartography, these whilst using the maps on his globes for their studies ignore his role in the history of globe making whilst doing so. For the historians of globe making, and yes it really is a separate discipline, Schöner is a central and highly significant figure as the founder of the long tradition of printed globe pairs but they don’t tend to look outside of their own discipline to see how his globe making fits together with his other activities. I’m still looking for a serious study of his activities as an instrument maker. There is also, as far as I know no real comprehensive study of his role as textbook author and editor, areas that tend to be the neglected stepchildren of the histories of science and technology. What is glaringly missing is a historiographical approach that treats the work of Schöner or of the Renaissance mathematici as an integrated coherent whole.

The world of this blog is at its core the world of the Renaissance mathematici and thus we are the Renaissance Mathematicus and not the Renaissance Mathematician.

[1] That is professor in its original meaning donated somebody who claims to possessing a particular area of knowledge.

[2] Augustinus De Genesi ad Litteram,

*Quapropter bono christiano, sive mathematici, sive quilibet impie divinantium, maxime dicentes vera, cavendi sunt, ne consortio daemoniorum animam deceptam, pacto quodam societatis irretiant. II, xvii, 37*

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Regular readers of this blog will know that I champion the claims of Johannes Kepler to being the most significant natural philosopher of the Early Modern Period against the rival claims of Copernicus, Galileo, Descartes, Newton et al. So I am naturally interested in any new books that appear with Kepler as their subject. Having looked closely at one of the strangest events in Kepler’s unbelievably bizarre life, the arrest and trial of his mother, Katherina, on a charge of witchcraft – and having blogged about it twice – my interest was particularly piqued by an announcement of a new book on this topic. A decent, well-researched book in English devoted exclusively to the subject would be a very positive addition to the Kepler literature. Rublack’s book is just the bill.

Nearly all accounts of Katherina Kepler’s ordeal are merely chapters or sections in more general books about Kepler’s life and work and mostly deal chronologically with the original accusations of witchcraft, counter accusations, the attempted violent intimidation of Katherina, the frustrated strivings to bring charges against her tormentors, her arrest and finally the trial with its famous defence by Johannes. Except for thumbnail sketches of those involved very little attempt is ever made to place the occurrences into a wider or more general context and this is, as already said above, exactly the strength of Rublack’s book.

Rublack in having devoted an entire book to the whole affair draws back from the accusations, charges, counter charges and the trial itself to flesh out the story with the social, cultural, political and economic circumstances in which the whole sorry story took place. In doing so Rublack has created minor masterpiece of social history. Her research has obviously been deep and thorough and she displays a fine eye for detail, whilst maintaining a stirring narrative style that pulls the reader along at a steady pace.

One point in particular intrigued me having read all the prepublication advertising for the book, including several illuminating interviews on the subject with the author, as well as short essays by her. Rublack takes what might be seen as a strong feminist stand against the previous, exclusively male, characterisations of Katherina Kepler, all of which painted her as a mean spirited, crabby, old hag, who was, so to speak, largely to blame for the situation in which she found herself. Having over the years read almost all of these accounts I was curious how Rublack would justify her rejection of these portrayals of Katherina, which I knew were based on Kepler’s own accounts of his mother. Rublack does not disappoint. She points out quite correctly that Kepler’s description of his mother was written when he was still very young and is part of an almost psychopathic put down of himself and all those related or connected to him and calls rather his own mental state into question. Interestingly we have virtually no other accounts of Katherina from Johannes’ pen and to judge her purely on this one piece of strange juvenilia is probably, as Rublack makes very clear, a bridge too far. Piecing together all of the, admittedly scant, evidence Rublack paints a much more sympathetic picture of Katherina, a hard working, illiterate, sixteenth/seventeenth-century peasant woman, who had never had it easy in life but still managed to raise her children well and give them chances that she never had.

This book is not perfect, as Rublack relies in her accounts of Johannes on older standard biographies, whilst apparently not consulting some of the more recent scholarly studies of his life and work, and thus repeats several false claims concerning him. However I’m prepared to cut her some slack on this as none of the errors that she (unknowingly?) repeats have any direct bearing on the story of Katherina that she tells so skilfully.

The book is beautifully presented by the OUP. Printed in a pleasant, easy on the eyes typeface and charmingly illustrated with a large number of black and white pictures. The text is excellently annotated, but as always I would have preferred footnotes to endnotes, and there is an adequate index. I personally would have liked a separate bibliography but this might have been sacrificed on cost grounds, the hardback being available at a very civilised price for a serious academic volume. Although having called it that I should point out that the book is very accessible and readable for the non-expert or general reader.

I heartily recommend this book to anybody interested in seventeenth-century history, Johannes Kepler, the history of witchcraft or who just likes reading good informative, entertaining books, if one is allowed to call a book about the sufferings of an innocent woman entertaining. Put simply, it’s an excellent read that deserves to, and probably will, become the standard English text on the subject.

[1] Ulinka Rublack, *The Astronomer and the Witch*: *Johannes Kepler’s Fight for His Mother*. OUP, 2015

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Born in Aspenden in Hertfordshire on an unknown day in 1617, Seth Ward was the son of John Ward, an attorney, and his wife Mary Dalton. Having received a basic schooling he was admitted to Sidney-Sussex College, Cambridge on 1 December 1632, where he graduated B.A. in 1637 and M.A. on 27 July 1640, following which he was elected a fellow of the college. Ward was a keen mathematician, who, like many others in the Early Modern Period, was largely self-taught, studying William Oughtred’s *Clavis Mathematicae *together with fellow maths enthusiast Charles Scarburgh, a future physician to Charles II. Finding some passages difficult the two of them travelled to Albury in Surrey where Oughtred was rector. Here they took instruction from Oughtred and it was the start of a relationship between Ward and Oughtred that lasted until Oughtred’s death in 1660.

In 1643 Ward was appointed lecture for mathematics for the university but he did not exercise this post for very long. Some of the Cambridge colleges, and in particular Sidney-Sussex, Cromwell’s alma mater, became centres for the Puritan uprising and in 1644 Seth Ward, a devote Anglican, was expelled from his fellowship for refusing to sign the covenant. At first he took refuge with friends in and around London but then he went back to Albury where he received tuition in mathematics from Oughtred for several months. Afterwards he became private tutor in mathematics to the children of a friend, where he remained until 1649. Having used the *Clavis Mathematicae*, as a textbook whilst teaching at he university he made several suggestions for improving the book and persuaded Oughtred to publish a third edition in 1652

In 1648 John Greaves, one of the first English translators of Arabic and Persian scientific texts into Latin, also became a victim of a Puritan purge and was evicted from the Savilian Chair for Astronomy at Oxford. Greaves recommended Ward as his successor and in 1649, having overcame his scruples, Ward took the oath to the English Commonwealth and was appointed Savilian Professor.

These episodes, Wards expulsion from Sidney-Sussex and Greave’s from Oxford, serve to remind us that much of the scientific investigations that took place in the Early Modern Period, and which led to the creation of modern science, did so in the midst of the many bitter and very destructive religious wars that raged throughout Europe during this period. The scholars who carried out those investigations did not remain unscathed by these disturbances and careers were often deeply affected by them. The most notable example being, of course Johannes Kepler, who was tossed around by the Reformation and Counter-Reformation like a leaf in a storm. Anyone attempting to write a history of the science of this period has to, in my opinion, take these external vicissitudes into account; a history that does not do so is only a half history.

It was in his role as Savilian Professor that Ward made his greatest contribution to the development of the new heliocentric astronomy in an academic dispute with the French astronomer and mathematician Ismaël Boulliau (1605–1694).

Boulliau was an early supporter of the elliptical astronomy of Johannes Kepler, who however rejected much of Kepler’s ideas. In 1645 he published his own theories based on Kepler’s work in his *Astronomia philolaïca*. This was the first major work by another astronomer that incorporated Kepler’s elliptical astronomy. Ward another Keplerian wrote his own work *In Ismaelis Bullialdi Astronomiæ Philolaicæ Fundamenta Inquisitio Brevis*, which heavily criticised Boulliau’s theories and present his own, in his opinion superior, interpretations of Kepler’s ideas. He followed this with another more extensive presentation of his theories in 1656, *Astronomia Geometrica; ubi Methodus proponitur qua Primariorum Planetarum Astronomia sive Elliptica sive Circularis possit Geometrice absolve*. Boulliau responded in 1657 in his *Ismaelis Bullialdi Astronomiæ Philolaicæ Fundamenta clarius explicata et asserta*, printed in his* Exercitationes Geometricæ tres* in which he acknowledged errors in his own work but also pointing out inaccuracies in Ward’s. In final analysis both Boulliau and Ward were wrong, and we don’t need to go into detail her, but their dispute drew the attention of other mathematicians and astronomers to Kepler’s work and thus played a major role in its final acceptance as the preferred model for astronomy in the latter part of the seventeenth century.

The worst popular model of the emergence of modern astronomy in the Early Modern Period sees the inspiring creation of heliocentric astronomy by Copernicus in his *De revolutionibus* in the sixteenth century, the doting of a few ‘I’s and crossing of a few ‘T’s by Galileo and Kepler in the early seventeenth century followed by the triumphant completion of the whole by Newton in his *Principia* in 1687. Even those who acknowledge that Kepler created something new with his elliptical astronomy still spring directly to Newton and the *Principia*. In fact many scholars contributed to the development of the ideas of Kepler and Galileo in the decades between them and Isaac Newton and if we are going to correctly understand how science evolves it is important to give weight to the work of those supposedly minor figures. The scientific debate between Boulliau and Ward is a good example of an episode in the history of astronomy that we ignore at the peril of falsifying the evolution of a disciple that we are trying to understand.

Ward continued to make career as an astronomer mathematician. He was awarded an Oxford M.A. on 23 October 1649 and became a fellow of Wadham College in 1650. The mathematician John Wilkins was warden of Wadham and the centre of a group of likeminded enthusiasts for the emerging new sciences that at times included Robert Boyle, Robert Hooke, Christopher Wren, John Wallis and many others. This became known as the Philosophical Society of Oxford, and they would go on to become one of the founding groups of the Royal Society in the early 1660s.

During his time at Oxford Ward together with his friend John Wallis, the Savilian Professor of Geometry, became involved in a bitter dispute with the philosopher Thomas Hobbes on the teaching of geometry at Oxford and the latter’s claim to have squared the circle; he hadn’t it’s impossible but the proof of that impossibility came first a couple of hundred years later.

Ward however was able to expose the errors in Hobbes’ geometrical deductions. In some circles Ward is better known for this dispute than for his contributions to astronomy.

When the alchemist and cleric John Webster launched an attack on the curriculum of the English universities in his *Academiarum Examen* (1654) Ward joined forces with John Wilkins to write a defence refuting Webster’s arguments, *Viniciae Acadmiarum*, which also included refutations of other prominent critics of Oxford and Cambridge.

Ward’s career as an astronomer and mathematician was very successful and his work was known and respected throughout Europe, where he stood in contact with many of the leading exponents of his discipline. However, his career in academic politics was not so successful. He received a doctorate in theology (D.D.) from Oxford in 1654 and one from Cambridge in 1659. He was elected principle of Jesus College, Oxford in 1657 but Cromwell appointed somebody else promising Ward compensation, which he never delivered. In 1659 he was appointed president of Trinity College, Oxford but because he was not qualified for the office he was compelled to resign in 1660. This appears to have been the final straw and in 1660 he left academia, resigning his professorship to take up a career in the Church of England, with the active support of the recently restored Charles II.

He proceeded through a series of clerical positions culminating in the bishopric in Salisbury in 1667. He was appointed chancellor of the Order of the Garter in 1671. Ward turned down the offer of the bishopric of Durham remaining in Salisbury until his death 6 January 1689. He was a very active churchman, just as he had been a very active university professor, and enjoyed as good a reputation as a bishop as he had enjoyed as an astronomer.

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The first Englishmen to pick up on Kepler’s theories was the small group around Thomas Harriot, who did so immediately after the publication of the *Astronomia nova* in 1609.

The group included not only Harriot but also his lens grinder Christopher Tooke, the Cornish MP Sir William Lower (c.1570–1615) and his Welsh neighbour John Prydderch (or Protheroe). Lower had long been an astronomical pupil of Harriot’s and had in turn introduced his neighbour Prydderch to the science.

This group was one of the very earliest astronomical telescopic observing teams, exchanging information and comparing observations already in 1609/10. In 1610 they were enthusiastically reading *Astronomia nova* and discussing the new elliptical astronomy. It was Lower, who had carefully observed Halley’s comet in 1607 (pre-telescope) together with Harriot, who first suggested that the orbits of comets would also be ellipses. Kepler still thought that comets move in straight lines. The Harriot group did not publish their active support of the Keplerian elliptical astronomy but Harriot was well networked within the mathematical communities of both England and the Continent. He had even earlier had a fairly substantial correspondence with Kepler on the topic of atmospheric refraction. It is a fairly safe assumption that Harriot’s and Lower’s support of Kepler’s theories was known to other contemporary English mathematical practitioners.

Our next group of English Keplerians is that initiated by the astronomical prodigy Jeremiah Horrocks (1618–1641). Horrocks was a self-taught astronomer who stumbled across Kepler’s theories, whilst on the search for reliable astronomical tables. He quickly established that Kepler’s *Rudolphine Tables* were superior to other available tables and soon became a disciple of Kepler’s elliptical astronomy. Horrocks passed on his enthusiasm for Kepler’s theories to his astronomical helpmate William Crabtree (1610–1644). In turn Crabtree seems to have been responsible for converting another young autodidactic astronomer William Gascoigne (1612–1644) to the Keplerian astronomical gospel. Crabtree referred to this little group as Nos Keplari. Horrocks contributed to the development of Keplerian astronomy with an elliptical model of the Moon’s orbit, something that Kepler had not achieved. This model was the one that would eventually make its way into Newton’s *Principia*. He also corrected and extended the *Rudolphine Tables* enabling Horrocks and Crabtree to become, famously, the first people ever to observe a transit of Venus.

Like Harriot’s group, Nos Keplari published little but they were collectively even better networked than Harriot. Horrocks had been at ~~Oxford~~ Emmanual College Cambridge with John Wallis and it was Wallis, a convinced nationalist, who propagated Horrocks’ posthumous astronomical reputation against foreign rivals, as he also did in the question of algebra for Harriot. Both Gascoigne and Crabtree had connections to the Towneley family, landed gentry who took a strong interest in the emerging modern science of the period. Later the Towneley’s who had connections to the Royal Society ensured that the work of Nos Keplari was not lost and forgotten, bringing it, amongst other things, to the attention of a young John Flamsteed, who would later become the first Astronomer Royal. . Gascoigne had connections to William Cavendish, the later Duke of Newcastle, under whose command he served at the battle of Marston Moor, where he died. William, his brother Charles and his wife Margaret were all enthusiastic supporters of the new sciences and important members of the English scientific and philosophical community. Gascoigne also corresponded with William Oughtred who served as private mathematics tutor to many leading members of the burgeoning English mathematical community. It is to two of Oughtred’s students that we now turn

Seth Ward (1617–1689) studied at ~~Oxford~~ Cambridge University from 1636 to 1640 when he became a fellow of Sidney Sussex College.

In the same year he took instruction in mathematics from William Oughtred. In 1649 he became Savilian Professor of Astronomy at Oxford University the same year that John Wallis was appointed Savilian Professor of Mathematics. Whilst serving as Savilian Professor, Ward became embroiled in a dispute about Keplerian astronomy with the French astronomer and mathematician Ismaël Boulliau.

Boulliau was an early and strong defender of Keplerian elliptical astronomy, who however rejected Kepler’s attempts to create a physical explanation of planetary orbits. Boulliau published his Keplerian theories in his *Astronomia philoaïca* in 1645. Ward attacked Boulliau’s model in his *In Ismaelis Bullialdi astro-nomiae philolaicae fundamenta inquisitio brevis* from 1653, presenting his own model for Kepler’s planetary laws. Boulliau responded to Ward’s attack in his *De lineis spiralibus* from 1657. Ward had amplified his own views in his *Astronomia geometrica* from 1656. This public exchange between two heavyweight champions of the elliptical astronomy did much to raise the general awareness of Kepler’s work in England. It has been suggested that the dispute was instrumental in bringing Newton’s attention to Kepler’s ideas, a claim that is however disputed by historians.

Ward went on to make a successful career in the Church of England, eventually becoming Bishop of Salisbury his successor, as Savilian Professor of Astronomy was another one of Oughtred’s student, Christopher Wren (1632–1723).

Wren is of course much better known as the foremost English architect of the seventeenth-century but started out as mathematician and astronomer. Wren studied at Wadham College Oxford from 1650 to 1653, where he was part of the circle of scientifically interested scholars centred on John Wilkins (1614–1672), the highly influential early supporter of heliocentric astronomy. The Wilkins group included at various times Seth Ward, John Wallis, Robert Boyle, William Petty and Robert Hooke amongst others and would go on to become one of the groups that founded the Royal Society. Wren was a protégé of Sir Charles Scarborough, a student of William Harvey who later became a famous physician in his own right; Scarborough had been a fellow student of Ward’s and was another student of Oughtred’s. Wren was appointed Gresham Professor of Astronomy and it was following his lectures at Gresham College that the meetings took place that would develop into the Royal Society. As already noted Wren then went on to succeed Ward as Savilian Professor for astronomy in 1661, a post that he resigned in 1673 when his work as Surveyor of the King’s Works (a post he took on in 1669), rebuilding London following the Great Fire of 1666, became too demanding. Wren enjoyed a good reputation as a mathematician and astronomer and like Ward was a convinced Keplerian.

Our final English Keplerian is Nicolaus Mercator (1620–1687), who was not English at all but German, but who lived in London from 1658 to 1682 teaching mathematics.

In his first years in England Mercator corresponded with Boulliau on the subject of Horrock’s Transit of Venus observations. Mercator stood in contact with the leading English mathematicians, including Oughtred, John Pell and John Collins and in 1664 he published a defence of Keplerian astronomy *Hypothesis astronomica nova*. Mercator’s work contained an acceptable mathematical proof of Kepler’s second law, the area law, which had been a bone of contention ever since Kepler published it in 1609; Kepler’s own proof being highly debateable, to put it mildly. Mercator continued his defence of Kepler in his *Institutiones astronomicae* in 1676. It was probably through Mercator’s works, rather than Ward’s, that Newton became acquainted with Kepler’s astronomy. We still have Newton’s annotated copy of the latter work. Newton and Mercator were acquainted and corresponded with each other.

As I hope to have shown there was a strong continuing interest in England in Keplerian astronomy from its very beginnings in 1609 through to the 1660s when it had become de facto the astronomical model of choice in English scientific circles. As I stated at the outset, to become accepted a new scientific theory has to find supporters who are prepared to champion it against its critics. Kepler’s elliptical astronomy certainly found those supporters in England’s green and pleasant lands.

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