Renaissance Science – XII

There is a popular misconception that the emergence of modern science during the Renaissance, or proto-scientific revolution as we defined it in episode V of this series, and the scientific revolution proper includes a parallel rejection of the so-called occult sciences. Nothing could be further from the truth. This period sees a massive revival of all sorts of occult studies, covering a wide spectrum, we will look at this in more details in further episodes, but today I wish to deal with astrology. It is generally acknowledged that the period we know as the Renaissance was the golden age of astrology in Europe. There are multiple reasons for this rise of interest in and practice astrology in the period from roughly fourteen hundred and the middle of the seventeenth century.

As already explained in the previous episode, one reason for the rise in the status of the mathematical sciences during the Renaissance was the rise of astrological-medicine, or iatromathematics, within school medicine, something that we will look at in more detail when discussing Renaissance medicine. This rise in iatromathematics was, naturally, also a driving force in the increasing acceptance of astrology, but it was by no means the only one. This brings us to the important fact, that whereas most people on hearing the term astrology automatically think of natal astrology (also known as genethliacal astrology), that is birth horoscopes, but this is only one branch of the discipline and often in a given context not the most important one.

As well as natal astrology and iatromathematics there are also mundane astrology, electional astrology, horary astrology, locational astrology also called astrogeography, and meteorological astrology, each of which played a significant role in the world of astrology in the Renaissance. 

Mundane astrology is the application of astrology to world affairs and world events rather than to individuals and is generally acknowledged as the oldest form of astrology.

Electional astrology is the attempt to determine the most auspicious time to stage an event or undertake a venture, or even to show that no time would be auspicious for a given event of venture. The range of events or ventures can and did include, starting a war, or staging a battle, but also peaceful activities such as launching a diplomatic mission, simply going on a journey, or planning the date for an important, i.e., political, wedding.  

Horary astrology attempts to answer questions, interrogations, posed to the astrologer by casting a horoscope at the time that question is received and understood by the astrologer. The range of possible questions is entirely open, but few would waste the time of the astrologer or incur the costs that they might levy with trivial questions.

Locational astrology assumes that geographical locations play a specific role in astrological interpretation. For example, although time and latitude are the principle initial condition for casting a horoscope, two babies born at exactly the same time on the same day but in differing locations would have differing horoscopes, even if born at the same latitude, because of the influence of the geographical location.

Meteorological astrology, or astrometeorology, is the belief that the weather is caused by the position and motion of celestial objects, and it is therefor possible to predict or forecast the weather through astrological means.  

There are also special procedures such as lots of fortune and prorogation to determine special or important events in a subjects life, too detailed for this general survey. 

Mundane, natal, electional, horary and locational astrology are all grouped together under the term judicial astrology. Iatromathematics and astrometeorology are referred to as natural astrology. Those who objected to or rejected astrology, including at times the Catholic Church, usually rejected judicial astrology but accepted natural astrology as a branch of knowledge.

Western astrology has its origins in the omen astrology of the Babylonians, which was originally purely mundane astrology. Individual horoscope astrology emerged in Babylon around the sixth century BCE, and it was this that the ancient Greeks adopted and developed further. This is basically the astrology that was still in use in Renaissance Europe. After some reluctance the Romans adopted the Greek astrology and in the second century CE Ptolemaeus produced the most comprehensive text on the philosophy and practice of astrology, his Tetrabiblos, also known in Greek as Apotelesmatiká (Ἀποτελεσματικά) “Effects”, and in Latin as Quadripartitum. It should, however, be noted that this is by no means the only astrology text from antiquity. 

With the general collapse of learning in Europe in the Early Middle Ages from the fifth century onwards, astrology disappeared along with other scholarly disciplines. It was first revived by the Arabic, Islamic culture via the Persians in the eighth century. Arabic scholars developed and expanded the Greek astrology. Astrological texts were amongst the earliest ones translated into Arabic during the big translation movement in the eighth and ninth centuries. The same was true when European scholars began translating Arabic texts into Latin in the twelfth century. They translated both Greek and Arabic texts on astrology.

The Church could have rejected Greek astrology in the High Middle Ages as it was deterministic and as such contradicted the theological principle of free will, which is fundamental to Church doctrine. However, Albertus Magnus and Thomas Aquinas, who made Aristotelian philosophy acceptable to the Church also did the same for astrology reinterpreting it as contingent rather than determinist. By the thirteenth century all the forms of astrology had become established in Europe.

So, astrology in its various forms were well established in Europe in the High Middle Ages. This raises the question, why did it flourish and bloom during the Renaissance? As already stated above it was not just the rise of iatromathematics although this was a contributary factor.

One factor was the rise of the court astrologer, as a member of the retinue serving the ruler at court. Several Roman emperors had employed court astrologers, but the practice re-entered Europe in the Middle Ages via the Islamic culture. The Abbasid Caliphs, who started the major translation movement of Greek knowledge into Arabic, adopted the practice of employing a court astrologer from the Persians. In the Middle Ages, one of the first European potentates to adopt the practice was the Hohenstaufen Holy Roman Emperor, Frederick II (1194–1250), whose court was on the island of Sicily an exchange hub between North African Arabic-Islamic and European cultures. Frederick was a scholar, who not only traded goods with his Islamic neighbours but also knowledge. Following the Abbasid example, he installed an astrologer in his court. Both the prominent astrologers Michael Scot (1175–c. 1232) and Guido Bonatti (c. 1210–c. 1300) served in this function. The fashion spread and by the fifteenth century almost all rulers in Europe employed a court astrologer, either as a direct employee at court or when employed elsewhere on a consultant basis. The role of the court astrologer was that of a political advisor and whilst casting birth horoscopes, their main activities were in electional and horary astrology. Many notable mathematicians and astronomers served as court astrologers including Johannes Regiomontanus (1436–1476), Georg von Peuerbach (1423–1461), Peter Apian (1495–1552), Tycho Brahe (1546–1601), Michael Mästlin (1550–1631), and Johannes Kepler (1571–1630).

The upper echelons were thus firmly anchored in an astrological culture but what of the masses? Here, an important factor was the invention of movable type printing. This, of course, meant that the major Greek and Arabic astrological volumes became available in printed form. Ptolemaeus’ Tetrabiblos, translated from Arabic into Latin in the twelfth century, was first printed and published in Venice by Erhard Ratdolt (1442–1528) in 1484. However, much more important for the dissemination and popularisation of astrology were the astrological ephemera that began to appear from the very beginning of the age of print–wall calendars, prognostica, writing calendars and almanacs. The wall calendars, and Guttenberg printed a wall calendar to help finance the printing of his Bible, and writing calendars were a product of the iatromathematics, whereas the prognostica and almanacs dealt with astrometeorology and mundane astrology. These ephemera were comparatively cheap and were produced in print runs that often ran into the tens of thousands, making them very profitable for printer-publishers. Often containing editorial sections, the prognostica and almanacs came in a way to fulfil the function of the tabloid press today. For most households the annual almanac was the only print item that the purchased, apart perhaps from a Bible. 

But what of the Humanist Renaissance, did its basic philosophy or principles play a role in the rise of astrology? The answer is yes, very much so. Although the Tetrabiblos was translated into Latin comparatively early, the majority of important astrological texts in the Middle Ages were Arabic ones and these also found their way early into print editions. This circumstance kicked off a back to Greek purity–remove the Arabic influence debate amongst Renaissance astrologers. The humanists insisted that the only permissible astrological methods were those found in the Tetrabiblos and anything else was Arabic corruption. This meant they wanted to eliminate elections and interrogations, which Ptolemaeus does not deal with. Ironical both practices came into Arabic astrology via Persian astrology from Greek astrology that was older than Ptolemaeus’ work.

We don’t need to discuss the details of this debate but leading scholars, and the astrologers were leading mathematicians, astronomers and physicians were exchanging theoretical broadsides in print over decades. This, of course, raised the public perception and awareness of astrology and contributed to the Renaissance rise in astrology.

The Renaissance surge in astrology held well into the seventeenth century. With the notable exception of Copernicus, who apparently had little interest in astrology, all of the astronomers, who contributed to the so-called astronomical revolution including Tycho, Kepler and Galileo were practicing astrologers. Later in the seventeenth century, astrology went into decline but we don’t need to address that here.

An eighteenth-century cartographical community in Nürnberg

If you walk up Burgstraße in the city of Nürnberg in the direction of the castle, you will see in front of you the impressive Baroque Fembohaus, which from 1730 to 1852 was the seat of the cartographical publishing house Homännische Erben, that is “Homann’s Heirs” in English. But who was Homann and why was the business named after his heirs?

Fembohaus Source: Wikimedia Commons

Johann Baptist Homann (1664–1724) was born in Öberkammlach in the south of Bavaria. He was initial educated at a Jesuit school and at some point, entered the Dominican Cloister in Würzburg, where he undertook, according to his own account, his “studia humaniora et philosophica.”

Johann Baptists Homann (1664–1725) Portrait by Johann Wilhelm Windter (c. 1696– 1765) Source: Wikimedia Commons

In 1687 he left the cloister moved to Nürnberg and converted to Protestantism. Over the next ten years he vacillated between Catholicism and Protestantism, leaving Nürnberg during the Catholic phases, and returning during the Protestant phases. In 1691 in Nürnberg, he was registered for the first time as a notary public. Around the same time, he started his career as a map engraver. It is not known how or where he learnt this trade, although there are claims that he was entirely self-taught. A map of the district surrounding Nürnberg, produced in 1691/92, shows Homann already as a master in cartographic engraving. From 1693 to 1695 he was in Vienna, then he returned for a time to Nürnberg, leaving again for Erlangen in 1696. Around 1696 to 1697, he was engraving maps in Leipzig.

He appears to have final settled on life as a protestant and permanent residency in Nürnberg in 1698. In 1702 he established a dealership and publishing house for cartography in the city, producing and selling maps, globes, and atlases. His dealership also produced and sold scientific instruments. The field that Homann had chosen to enter was by the beginning of the eighteenth century well established and thriving, with a lot of very powerful competition, in particular from France and Holland. Homann entered the market from a mercantile standpoint rather than a scientific one. He set out to capture the market with high quality products sold more cheaply than the competition, marketing copies of maps rather than originals. In a relatively short time, he had established himself as the dominant cartographical publisher in Germany and also a European market leader.

Planiglobii Terrestris Cum Utroq[ue] Hemisphærio Cælesti Generalis Exhibitio, Nürnberg 1707 Source: Wikimedia Commons

His dealership offered single sheet maps for sale, but he became the first German cartographer to sell atlases on a large scale and is considered the second most important German cartographer after Mercator. His first atlas with forty maps appeared in 1707. This was expanded to the Großen Atlas über die ganze Welt (The Big Atlas of the Entire World), with one hundred and twenty-six maps in 1716.

A fine example of Homann’s 1716 map of Burgundy, one of France’s most important wine regions. Extends to include Lake Geneva in the southwest, Lorraine in the north, Champaigne (Champagne) and Angers to the northwest and Bourgogne to the west. Depicts mountains, forests, castles, and fortifications and features an elaborate title cartouche decorated with cherub winemakers in the bottom right. A fine example of this rare map. Produced by J. H. Homann for inclusion in the Grosser Atlas published in Nuremberg, 1716. Source: Wikimedia Commons

By 1729 it had around one hundred and fifty maps. Johann Baptist’s success was richly acknowledged in his own lifetime. In 1715 he was appointed a member of the Preußischen Akademie der Wissenschaften (The Prussian Academy of Science) and in 1716 he was appointed Imperial Geographer by the Holy Roman Emperor, Karl VI.

A detailed c. 1730 J. B. Homann map of Scandinavia. Depicts both Denmark, Norway, Sweden, Finland and the Baltic states of Livonia, Latvia and Curlandia. The map notes fortified cities, villages, roads, bridges, forests, castles and topography. The elaborate title cartouche in the upper left quadrant features angels supporting a title curtain and a medallion supporting an alternative title in French, Les Trois Covronnes du Nord . Printed in Nuremburg. This map must have been engraved before 1715 when Homann was appointed Geographer to the King. The map does not have the cum privilegio (with privilege; i.e. copyright authority given by the Emperor) as part of the title, however it was included in the c. 1750 Homann Heirs Maior Atlas Scholasticus ex Triginta Sex Generalibus et Specialibus…. as well as in Homann’s Grosser Atlas . Source: Wikimedia Commons

The publishing house continued to grow and prosper until Johann Baptist’s death in 1724, when it was inherited by his son Johann Christian Homann (1703–1730).

Johann Christian studied medicine and philosophy in Halle. He graduated doctor of medicine in 1725, following which he went on a study trip, first returning to Nürnberg in 1729. During his absence the publishing house was managed by Johann Georg Ebersberger (1695–1760) and later together with Johann Christian’s friend from university Johann Michael Franz (1700­–1761).

Hand coloured copper engraving by J. Chr. Homann, showing noth west Africa with the Canary Islands and two large cityviews. Source: Wikimedia Commons

When Johann Christian died in 1730, he willed the business to Ebersberger and Franz, who would continue to run the business under the name Homännische Erben. The publishing house passed down through several generations until Georg Christoph Fembo (1781­–1848) bought both halves of the business in 1804 and 1813. Fembo’s son closed the business in 1852 and in 1876 the entire collection of books, maps, engravings, and drawing were auctioned off, thus destroying a valuable source for the history of German cartography.

Today there is a big market for fictional maps based on fantasy literature such as Lord of the Rings. This is nothing new and Early Modern fiction also featured such fictional maps, for example Thomas More’s Utopia (1516). One very popular medieval myth concerns the Land of Cockaigne, a fictional paradise of pleasure and plenty also known as The Land of Milk and Honey. The German version is Schlaraffenland (literally the Land of the Lazy Apes). The most well-known version of the myth in the seventeenth century was written by Johann Andreas Schneblins (d. 1702) and based on Schneblins’ account of his travels in the utopia of Schlaraffenland Homann produced a map his very popular Accurata Utopiae Tabula.

“Accurata Utopiæ Tabula” (also named “Schlarraffenlandes”) designed by Johann Baptist Homann and printed in 1694 Source: Wikimedia Commons

From the very beginning one distinctive feature of the publishing house was Homann’s active cooperation with other scholars and craftsmen. From the beginning Johann Baptist worked closely with the engraver, art dealer, and publisher Christoph Weigel the Older (1665–1725).

Christoph Weigel, engraved by Bernhard Vogel of a portrait by Johann Kupetzky Source:Wikimedia Commons

Weigel’s most significant publication was his Ständebuch (1698) (difficult to translate but Book of the Trades and Guilds).

Gunpowder makers, engraving Regensburger Ständebuch, 1698, Christoph Weigel der Ältere (1654, 1725)

Weigel was very successful in his own right but he cooperated very closely with Homann on his map production.

Homann also cooperated closely with the scholar, author, schoolteacher, and textbook writer Johann Hübner (1668–1731).

Johann Hübner, engraving by Johann Kenckel Source: Wikimedia Commons

Together the two men produced school atlases according to Hübner’s pedagogical principles. In 1710 the Kleiner Atlas scholasticus von 18 Charten (Small School Atlas with 18 Maps) was published.

Kleiner Atlas scholasticus von 18 Charten

This was followed in 1719 by the Johann Baptist Homann / Johann Hübner: Atlas methodicus / explorandis juvenum profectibus in studio geographico ad methodum Hubnerianam accommodatus, a Johanne Baptista Homanno, Sacrae Caesareae Majestatis Geographo. Noribergae. Anno MDCCXIX. Methodischer Atlas / das ist, Art und Weise, wie die Jugend in Erlernung der Geographie füglich examiniret werden kann / nach Hübnerischer Lehr-Art eingerichtet von Johann Baptist Homann, Nürnberg, 1719. The title, given here in both Latin and German translates as Methodical Atlas in the manner in which the youth can be reasonably examined in the study of geography according to the pedagogic principles of Hübner, presented by Johann Baptist Homann.

Charte von Europa. Charte von Asia. Charte von Africa. Charte von America. Johanne Baptista Homanno, Norimbergae, 1719 Atlas methodicus / explorandis juvenum profectibus in studio geographico ad methodum Hubnerianam accommodatus

Johann Gottfried Gregorii (1685–1770) was a central figure in the intellectual life of eighteenth-century Germany. A geographer, cartographer, historian, genealogist, and political journalist, he put out a vast number of publications, mostly under the pseudonym Melissantes.

Johann Gottfried Gregorii Source: Wikimedia Commons

In his geographical, cartographical, and historical work he cooperated closely with both Johann Baptist Homann and Christoph Weigel.

 One of the Homann publishing house’s most important cooperation’s was with the Nürnberg astronomer Johann Gabriel Doppelmayr (1677–1750).

Johann Gabriel Doppelmayr Source: Wikimedia Commons

Doppelmayr was professor for mathematics at the Aegidianum, Germany’s first modern high school, and is best known for two publication his Historische Nachricht Von den Nürnbergischen Mathematicis und Künstlern (1730), an invaluable source for historian of science and his celestial atlas, Atlas Novus Coelestis (1742). Doppelmayr had been supplying celestial charts for the Homann atlases but his Atlas Novus Coelestis, which was published by Homännische Erben, contained thirty spectacular colour plates and was a leading celestial atlas in the eighteenth century.

PHÆNOMENA circa quantitatem dierum artificialium et solarium perpetuo mutabilem, ex Hypothesi copernicana deducta, cum aliis tam Veterum quam recentiorum Philosophorum, Systematibus mundi notabilioribus, exhibita – Engraved between 1735 and 1742.

Doppelmayr’s successor as professor of mathematics at the Aegidianum was Georg Moritz Lowitz (1722–1774), who went on to become professor for practical mathematics at the University of Göttingen.

Georg Moriz Lowiz Source: Wikimedia Commons

He worked together with Johann Michael Franz and produced several astronomical publications for the Homännische Erben. Franz as well as being co-manager of the publishing house was also an active geographer, who became professor in Göttingen in 1755. He also published a series of his own books on geographical themes. He sold his share of the publishing house on his younger brother Jacob Heinrich Franz (1713–1769) in 1759.

Johann Michael Franz: Belgium, Luxemburg; Johann Michael Franz – Circulus Burgundicus – 1758

Without any doubt Homann’s most important or significant employee, at least with hindsight, was the cartographer and astronomer Tobias Mayer (1723–1762), who is these days is best known for having calculated the Moon’s orbit accurately enough to make the lunar distance method of determining longitude viable. A self-taught mathematicus he had already published a town plan of Esslingen, two books on mathematics and one on fortifications, when he was appointed to the Homännische Erben in 1746.

Tobias Mayer Source: Wikimedia Commons

It was during his time in Nürnberg that he did his work on lunar astronomy. Like Lowitz, and Franz, Mayer also became a professor in Göttingen, in his case for economics and mathematics.

The three Göttingen professors–Lowitz, Franz, and Mayer–whilst still working for Homann in Nürnberg founded the Cosmographische Gesellschaft (Cosmographical Society), with the aim of improving the standards of cartography and astronomy. Due to lack of funding they never really got their plans of their grounds. Their only products being some propaganda publications for the society written by Franz and one publication from Mayer on his lunar research.

Each of the scholars, briefly sketched here was a leading figure in the intellectual landscape of eighteenth-century Germany and they were all to some extent rivals on the open knowledge market. However, they cooperated rather than competed with each other and in doing so increased the quality of their output.

Renaissance Science – IX

The part of mathematics that we most use in our lives is numbers, the building blocks of arithmetic. Today, we mostly use the Hindu-Arabic numerals and the associated place value decimal system, but this was not always the case. In fact, although this number system first entered Europe during the 12^th century translation movement, it didn’t become truly established until well into the Renaissance.

First, we will briefly track the Hindu-Arabic place value decimal system from its origins till its advent in Europe. The system emerged in India sometime late in the sixth century CE. Āryabhaṭa (476–550) a leading mathematician and astronomer doesn’t mention them in his Aryasiddhanta. The earliest known source being in the Āryabhaṭīyabhāṣya of Bhāskara I (c. 600–c. 680) another leading astronomer mathematician. The full system, as we know it today, was described in the Brāhmasphuṭasiddhānta of Brahmagupta (c. 598–c. 668 n. Chr.). The only difference is that he allows division by zero, which as we all learnt in the school is not on.

The Brāhmasphuṭasiddhānta was translated into Arabic in about 770 by Ibrahim ibn Habib ibn Sulayman ibn Samura ibn Jundab al-Fazri (d. 777), Muhammad ibn Ibrahim ibn Habib ibn Sulayman ibn Samura ibn Jundab al-Fazri (d. c. 800) and Yaʿqūb ibn Ṭāriq (d. c. 796). The first two are father and son. Having teams doing scientific translations in the middle ages was actually very common. I won’t go into detail, but it should be noted that it took several hundred years for this system to replace the existing number systems in Arabic culture, many mathematicians preferring their own systems, which they considered superior.

The system first came into Europe in the 12^th century through the translation of a work by Muhammad ibn Musa al-Khwārizmī (c. 780–c. 850) by an unknown translator. No Arabic manuscript of this work is known to exist, and it is only known by its Latin title Algoritmi de Numero Indorum, where Algoritmi is a corruption of al-Khwārizmī.

This translation only had a very limited impact. The new number system was adopted by the scholars at the universities as part of computus in order to calculate the date of Easter and the other moveable Church feasts. Leading scholars such as Sacrobosco wrote textbooks to teach the new discipline, which was Algorimus, another corruption of al-Khwārizmī. The other mostly university-based scholars, who used mathematics extensively, the astronomers, continued to use a sexagesimal i.e., base sixty, number system that they had inherited from both the Greek and the Arabic astronomers. This system would stay in use by astronomers down to Copernicus’ De revolutionibus (1543) and beyond.

This is the opening page of a 1490 manuscript copy of Johannes de Sacro Bosco’s Tractatus de Arte Numerandi, also referred to as his Algorismus Source:

What about the world outside of the universities? In the outside world the new number system was simply ignored. Which raises the question why? People generally believe that the base ten place value number system is vastly superior to the Roman numeral system that existed in Europe in the Middle ages, so why didn’t the people immediately adopt it? After all you can’t do arithmetic with Roman numerals. The thing is people didn’t do arithmetic with Roman numerals, although it would have been possible using different algorithm to the ones we use for the decimal place-value system. People did the calculations using either finger reckoning

of counting boards, also known as reckoning boards or abacuses. They only used the roman numerals to record the results.

Counting Board

In the hands of a skilled operator the counting board is a powerful instrument. It can be used very simply for addition and subtraction and using the halving and doubling algorithms, almost as simply for multiplication and division. A skilled operator can even extract roots using a counting board. The counting board also offers the possibility in a business deal for the reckoning masters of both parties to observe and control the calculations on the counting board.

The widespread use of counting boards over many centuries is still reflected in modern word usage. The serving surface in a shop is called a counter because it was originally the counting board on which the shop owner did their calculations. The English finance ministry is called the Exchequer after a special kind of counting board on which they did they calculations in the past. Nobody pays much attention to the strange term bankrupt, which also has its origins in the use of counting boards. The original medieval banks in Northern Italy were simply tables, Italian banca, on the marketplace, on which a printed cloth counting board was spread out. If the bankers were caught cheating their customers, then the authorities came and symbolically destroyed their table, in Italian, banca rotta, broken table.

Things first began to change slowly with the second introduction of Hindu-Arabic numerals by Leonardo from Pisa (c. 1175–c. 1250) in his Liber Abbaci (1202, 2^nd edition 1227).

Leonardo from Pisa Liber Abbaci

This was basically a book on commercial arithmetic, following its Arabic origins. The Arabic/Islamic culture used different number systems for different tasks and used the Hindu-Arabic numerals and the decimal place-value system extensively in commercial arithmetic, in general account keeping, to calculate rates of interest, shares in business deals and the division of inheritance according to the complex Islamic inheritance laws. Leonardo’s father was a customs officer in North Africa, and it was here that Leonard learnt of the Hindu-Arabic numerals and the decimal place-value system from Arab traders in its usage as commercial arithmetic.

This new introduction saw the gradual spread in Norther Italy of Scuole or Botteghe D’abbaco (reckoning schools) lead by a Maestri D’abbaco (reckoning master), who taught this new commercial arithmetic to apprentice traders from Abbaco Libro (reckoning books), which he usually wrote himself. Many leading Renaissance mathematici, including Peter Apian (1495–1552, Niccolò Fontana Tartaglia (c. 1500–1557), Gerolamo Cardano (1501–1576), Gemma Frisius (1508–1555) and Robert Recorde (c. 1512–1558), wrote a published abbacus books. The very first printed mathematics book the Arte dell’Abbaco also known as the Treviso Arithmetic (1478) was , as the title clearly states, an abacus book.

Un maestro d’abaco. Filippo Calandri, De arimetricha opusculum, Firenze 1491

This practice began to accelerate with the introduction of double entry bookkeeping. This was part of the more general so-called commercial revolution, which included the founding of the first banks and the introduction of bills of exchange to eliminate the necessity of traders carrying large amounts of gold or silver. Developments in Europe that lead to the Renaissance. The earliest known example of double entry bookkeeping is the Messari Report of the Republic of Genoa, 1340. The earliest account of double entry bookkeeping is the Libro dell’arte di mercatura by Benedetto Cotrugli (1416–1469), which circulated in manuscript but was never printed. The first printed account was in the highly successful Summa de arithmetica, geometria, proportioni et proportionalita of Fra. Luca Bartolemeo Pacioli (c.1447–1517) published in 1494, which contain the twenty-seven-page introduction to double entry bookkeeping, Particularis de computis et scripturis.

Particularis de computis et scripturis, about double-entry bookkeeping.

Beginning with the Southern German trading centres of Augsburg, Regensburg and Nürnberg, which all traded substantially with the Northern Italian commercial centres, the new commercial arithmetic and double entry bookkeeping began to expand throughout Europe. This saw the fairly rapid establishment of reckoning schools and the printing of reckoning books throughout the continent. We can see the partial establishment of the Hindu-Arabic numerals some four hundred years after their first introduction, although they were used principally for recording, the reckoning continuing to be done on a counting board, in many cases down to the eighteenth century.

Already in the fifteenth century we can see the glimmer of the base ten system moving into other mathematical areas. Peuerbach and Regiomontanus started using circles with radii of 10,000 or 100,000, suggesting base ten, to calculate their trigonometrical tables instead of radii of 60,000, base sixty. The use of such large radii was to eliminate the need for fractional values.

By the end of the sixteenth century, the base ten positional value number system with Hindu-Arabic numerals had become well established across the whole spectrum of number use, throughout Europe. The Indian decimal system had no fractions and decimal fractions were first introduced into the Hindu-Arabic numerals by Abu’l Hasan Ahmad ibn Ibrahim Al-Uqlidisi in his Kitab al-Fusul fi al-Hisab al-Hindi around 952 and then again independently by Ghiyāth al-Dīn Jamshīd Masʿūd al-Kāshī (c. 1380–1429) in his Key to Arithmetic (1427). They first emerged in Europe in 1585 in Simon Stevin’s De Thiende also published in French as La Disme. The decimal point or comma was first used in Europe by Christoph Clavius (1538–1612) in the goniometric tables for his astrolabe in 1593. Its use became widespread through its adoption by John Napier in his Mirifici Logarithmorum Canonis Descriptio (1614).

However, at the end of the seventeenth century we still find both John Evelyn (1620–1706) and John Arbuthnot (1667–1735) discussing the transition from Roman to Hindu-Arabic numerals in their writings; the former somewhat wistfully, the later thankfully.

In the eighteenth century, Pierre-Simon Laplace reputedly said:

‘It is India that gave us the ingenious method of expressing all numbers by ten symbols, each receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity, the great ease which it has lent to all computations, puts our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.’

A very positive judgement, with hindsight, of the base ten place value number system with Hindu-Arabic numerals but one that was obviously not shared in the Early Modern period when the system was initially on offer in Europe.

The alchemist, who became a cosmographer

As an Englishman brought up on tales, myths and legends of Francis Drake, Walter Raleigh, Admiral Lord Nelson, the invincible Royal Navy and Britannia rules the waves, I tend not to think about the fact that Britain was not always a great seafaring nation. As an island there were, of course, always fisher boats going about their business in the coastal waters and archaeology has shown us that people have been crossing the strip of water between Britain and the continent, as long as the island has been populated. However, British sailors only really began to set out onto the oceans for distant lands in competition to their Iberian brethren during the Early Modern Period. Before the start of these maritime endeavours there was a political movement in England to get those in power to take up the challenge and compete with the Spanish and the Portuguese in acquiring foreign colonies, gold, silver and exotic spices. One, today virtually unknown, man, whose writings played a not insignificant role in this political movement was the alchemist Ricard Eden[1] (c. 1520–1576).

Richard Eden[2] was born into an East Anglian family of cloth merchants and clerics, the son of George Eden a cloth merchant. He studied at Christ’s College Cambridge (1534–1537) and then Queen’s College, where he graduated BA in 1538 and MA in 1544. He studied under Sir Thomas Smith (1533–1577) a leading classicist of the period, who was also politically active and a major supporter of colonialism, which possibly influenced Eden’s own later involvement in the topic.

A c. 19th-century line engraving of Sir Thomas Smith. Source: Wikimedia Commons

Through Smith, Eden was introduced to John Cheke (1514–1557), Roger Ascham (c. 1515–1568) and William Cecil (1520–1598), all of whom were excellent classicists and statesmen. Cecil would go on under Elizabeth I to become the most powerful man in England. From the beginning Eden moved in the highest intellectual and political circles.

After leaving Cambridge Eden was appointed first to a position in the Treasury and then distiller of waters to the royal household, already indicating an interest in and a level of skill in alchemy. Eden probably acquired his interest in alchemy from his influential Cambridge friends, who were all eager advocates of the art. However, he lost the post, probably given to someone else by Somerset following Henry VIII’s death in 1547 and so was searching for a new employer or patron.

Through a chance meeting he became acquainted with the rich landowner Richard Whalley, who shared his interest in alchemy. Whalley provided him with a house for his family and an income, so that he could devote himself to both medicinal and transmutational alchemy. His activities as an alchemist are not of interest here but one aspect of his work for Whalley is relevant, as it marked the beginning of his career as a translator.

Whalley was obviously also interested in mining for metal ores, because he commissioned Eden to translate the whole of Biringuccio’s Pirotechnia into English. Although he denied processing any knowledge of metal ores, Eden accepted the commission and by 1552 he had completed twenty-two chapters, that is to the end of Book 2. Unfortunately, he lent the manuscript to somebody, who failed to return it and so the project was never finished. In fact, there was no English translation of the Pirotechnia before the twentieth century. Later he produced a new faithful translation of the first three chapters dealing with gold, silver and copper ores, only omitting Biringuccio’s attacks on alchemy, for inclusion, as we shall see, in one of his later works.

Title page, De la pirotechnia, 1540, Source: Science History Museum via Wikipedia Commons

In 1552, Eden fell out with Whalley and became a secretary to William Cecil. It is probable the Cecil employed him, as part of his scheme to launch a British challenge to the Iberian dominance in global trade. In his new position Eden now produced a translation of part of Book 5 of Sebastian Münster’s Cosmographia under the title A Treatyse of the New India in 1553. As I explained in an earlier blog post Münster’s Cosmographia was highly influential and one of the biggest selling books of the sixteenth century.

This first cosmographical publication was followed in 1555 by his The Decades of the newe worlde or west India, containing the nauigations and conquests of the Spanyardes… This was a compendium of various translations including those three chapters of Biringuccio, probably figuring that most explorers of the Americas were there to find precious metals. The main parts of this compendium were taken from Pietro Martire d’Anghiera’s De orbe novo decades and Gonzalo Fernández de Oviedo y Valdés’ Natural hystoria de las Indias.

Source: The British Library

Pietro Martire d’Anghiera (1457–1526) was an Italian historian in the service of Spain, who wrote the first accounts of the explorations of Central and South America in a series of letters and reports, which were published together in Latin. His De orbe novo (1530) describes the first contacts between Europeans and Native Americans.

Source: Wikimedia Commons

Gonzalo Fernández de Oviedo y Valdés (1478–1557) was a Spanish colonist, who arrived in the West Indies a few years after Columbus. His Natural hystoria de las Indias (1526) was the first text to introduce Europeans to the hammock, the pineapple and tobacco.

MS page from Oviedo’s La Natural hystoria de las Indias. Written before 1535, this MS page is the earliest known representation of a pineapple Source: Wikimedia Commons

Important as these writings were as propaganda to further an English involvement in the new exploration movement in competition to the Iberian explorers, it was probably Eden’s next translation that was the most important.

As Margaret Schotte has excellently documented in her Sailing School (Johns Hopkins University Press, 2019) this new age of deep-sea exploration and discovery led the authorities in Spain and Portugal to the realisation that an active education and training of navigators was necessary. In 1552 the Spanish Casa de la Contratación established a formal school of navigation with a cátedra de cosmografia (chair of cosmography). This move to a formal instruction in navigation, of course, needed textbooks, which had not existed before. Martín Cortés de Albacar (1510–1582), who had been teaching navigation in Cádiz since 1530, published his Breve compendio de la sphere y de la arte de navegar in Seville in 1551.

Retrato de Martín Cortés, ilustración del Breve compendio de la sphera y de la arte de navegar, Sevilla, 1556. Biblioteca Nacional de España via Wikimedia Commons

In 1558, an English sea captain from Dover, Stephen Borough (1525–1584), who was an early Artic explorer, visited Seville and was admitted to the Casa de la Contratación as an honoured guest, where he learnt all about the latest instruments and the instruction for on going navigators. On his return to England, he took with him a copy of Cortés’ Breve compendio, which he had translated into English by Richard Eden, as The Arte of Navigation in 1561. This was the first English manual of navigation and was immensely popular going through at least six editions in the sixteenth century.

In 1562, Eden became a companion to Jean de Ferrières, Vidame of Chartres, a Huguenot aristocrat, who raised a Protestant army in England to fight in the French religious wars. Eden, who was acknowledged as an excellent linguist, stayed with de Ferrières until 1573 travelling extensively throughout France and Germany. Following the St. Batholomew’s Day massacre, which began in the night of 23–24 August 1572, Eden together with de Ferrières party fled from France arriving in England on 7 September 1573. At de Ferrières request, Elizabeth I admitted Eden to the Poor Knights of Windsor, a charitable organisation for retired soldiers, where he remained until his death in 1576.

After his return to England Eden translated the Dutch musician and astrologer, Jean Taisnier’s Opusculum perpetua memoria dignissimum, de natura magnetis et ejus effectibus, Item de motu continuio, which was a plagiarism of Petrus Peregrinus de Maricourt’s (fl. 1269) Epistola de magnete and a treatise on the fall of bodies by Giambattista Benedetti (1530–1590) into English.

This was published posthumously together with his Arte of Navigation in 1579. His final translation was of Ludovico de Varthema’s (c. 1470–1517) Intinerario a semi-fictional account of his travels in the east. This was published by Richard Willes in The History of Travayle an enlarged version of his Decades of the newe worlde in 1577.

Eden’s translations and publications played a significant role in the intellectual life of England in the sixteenth century and were republished by Richard Hakluyt (1553–1616) in his The Principal Navigations, Voiages, Traffiques and Discoueries of the English Nation (1589, 1598, 1600), another publication intended as propaganda to promote English colonies in America.

Unlike Sebastian Münster or Richard Hakluyt, Eden has been largely forgotten but he made important and significant contributions to the history of cosmography and deserves to be better known.

[1] I want to thank Jenny Rampling, whose book The Experimental Fire, which I reviewed here, made me aware of Richard Eden, although, I have to admit, he turns up, managing to slip by unnoticed in other books that I own and have read.

[2] The biographical details on Eden are mostly taken from the ODNB article. I would like to thank the three wonderful people, who provided me with a pdf of this article literally within seconds of me asking on Twitter

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

The event that would eventually lead to Isaac Newton writing and publishing his magnum opus, the Philosophiæ Naturalis Principia Mathematica (the Mathematical Principles of Natural Philosophy), took place in a London coffee house.

Title page of ‘Principia’, first edition (1687). Source: Wikimedia Commons

This is not quite as strange as it might at first appear, shortly after their first appearance in England around 1650 coffee houses became the favourite meeting places of the English scientific intelligentsia, the astronomers, mathematicians and natural philosophers. Here, these savants would meet up to exchange ideas, discuss the latest scientific theories and pose challenges to each other. These institutions also earned the appellation Penny Universities, as some of those savants, such as William Whiston, Francis Hauksbee and Abraham de Moivre, bettered their incomes by holding lectures or demonstrating experiments to willing audiences, who paid the price of a cup of coffee, a penny, for their intellectual entertainment. Later, after he had become Europe’s most famous living natural philosopher, Isaac Newton would come to hold court in a coffee shop, surrounded by his acolytes, the original Newtonians, distributing words of wisdom and handing round his unpublished manuscripts for scrutiny. However, all that still lay in the future.

One day in January 1684 Christopher Wren, Robert Hooke and Edmond Halley were discussing the actual astronomical theories over a cup of coffee. Wren, today better known as one of England most famous architects, was a leading mathematician and astronomers, who had served both as Gresham and Savilian professor of astronomy. Newton would name him along with John Wallis and William Oughtred as one of the three leading English mathematicians of the seventeenth century.

Wren, portrait c.1690 by John Closterman Source: Wikimedia Commons

Hooke was at the time considered to be the country’s leading experimental natural philosopher and Halley enjoyed an excellent reputation as a mathematician and astronomer.

Portrait by Richard Phillips, before 1722 Source: Wikimedia Commons

The topic of discussion was Kepler’s elliptical, heliocentric astronomy and an inverse, squared law of gravity. All three men had arrived separately and independently at an inverse, squared law of gravity probably derived from Huygens’ formula for centrifugal force. Wren posed the question to the other two, whether they could demonstrate that such a law would lead to Kepler’s elliptical planetary orbits.

Hooke asserted that he already had such a demonstration but he would first reveal it to the others after they had admitted that they couldn’t solve the problem. Wren was sceptical of Hooke’s claim and offered a prize of a book worth forty shillings to the first to produce such a demonstration.  Hooke maintained his claim but didn’t deliver. It is worth noting that Hooke never did deliver such a demonstration. Halley, as already said no mean mathematician, tried and failed to solve the problem.

In August 1684 Halley was visiting Cambridge and went to see Newton in his chambers in Trinity College, who, as we know, he had met in 1682.

Trinity College Cambridge, David Loggan’s print of 1690 Source: Wikimedia Commons

According the Newton’s account as told to Abraham DeMoivre, Halley asked Newton, “what he thought the Curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of the distance from it. Sir Isaac replied immediately that it would be an Ellipse…” Here was Newton claiming to know the answer to Wren’s question. Halley asked Newton how he knew it and he replied, “I have calculated it…” Newton acted out the charade of looking for the supposed solution but couldn’t find it. However he promised Halley that he would send him the solution.

In November Edward Paget, a fellow of Trinity College, brought Halley a nine page thesis entitled De motu corporum in gyrum (On the Motion of Bodies in an Orbit).

Page of the De motu corporum in gyrum

When Halley read Newton’s little booklet he was immediately aware that he held something truly epoch making in the history of astronomy and physics in his hand. Newton had delivered up a mathematical proof that an elliptical orbit would be produced by an inverse square force situated at one of the foci of the ellipse, thus combining the inverse square law of gravity with Kepler’s first law. He went on to also derive Kepler’s second and third laws as well as laying down the beginnings of a mathematical theory of dynamics. Halley reported details of this extraordinary work to the Royal Society on 10 December 1684:

Mr Halley gave an account, that he had lately seen Mr. Newton at Cambridge, who had shewed him a curious treatise, De motu: which, upon Mr. Halley’s desire, was he said promised to be sent to the Society to be entered upon their register.

Mr. Halley was desired to put Mr. Newton in mind of his promise for securing his invention to himself till such time as he could be at leisure to publish it. Mr. Paget was desired to join with Mr. Halley.

The interest in and the demand to read Newton’s new production was very high but the author decided to improve and rewrite his first offering, triggering one of the most extraordinary episodes in his life.

Although he was Lucasian Professor and would turn forty-two on 25 December 1684, Newton remained a largely unknown figure in the intellectual world of the late seventeenth century. Following the minor debacle that resulted from the publication of his work in optics in the 1670s he had withdrawn into his shell, living in isolation within the walls of Cambridge University. He carried out his duties as Lucasian Professor but had almost no students to speak of and definitely no disciples. Thanks to the word of mouth propaganda of people like his predecessor as Lucasian Professor, Isaac Barrow, and above all the assiduous mathematics groupie, John Collins, it was rumoured that a mathematical monster slumbered in his chambers in Trinity College but he had done nothing to justify this bruited reputation. His chambers were littered with numerous unfinished scientific manuscripts, mostly mathematical but also natural philosophical and an even larger number of alchemical and theological manuscripts but none of them was in a fit state to publish and Newton showed no indication of putting them into a suitable state. Things now changed, Newton had found his vocation and his muse and the next two and a half years of his life were dedicated to creating the work that would make him into a history of science legend, the reworking of De motu into his Principia.

Over those two and a half years Newton turned his nine-page booklet into a major three-volume work of science. The modern English translation by I B Cohen runs to just over 560 large format pages, although this contains all the additions and alterations made in the second and third editions, so the original would have been somewhat shorter. Halley took over the editorship of the work, copyediting it and seeing it through the press. In 1685 the Royal Society had voted to take over the costs of printing and publishing Newton’s masterpiece, so everything seemed to be going smoothly and then disaster struck twice, firstly in the form of Robert Hooke and secondly in the form of a financial problem.

Hooke never slow to claim his priority in any matter of scientific discovery or invention stated that he alone had first discovered the inverse square law of gravity and that this fact should, indeed must, be acknowledged in full in the preface to Newton’s book. Halley, realising at once the potential danger of the situation, was the first to write to Newton outlining Hooke’s claim to priority, stating it, of course, as diplomatically as possible. Halley’s diplomacy did not work, Newton went ballistic. At first his reaction was comparatively mild, merely pointing out that he had had the inverse square law well before his exchanges with Hook in 1679 and had, in fact, discussed the matter with Wren in 1677, go ask him, Newton said. Then with more time to think about the matter and building up a head of steam, Newton wrote a new letter to Halley tearing into Hooke and his claim like a rabid dog. All of this ended with Newton declaring that he would no longer write volume three of his work. Halley didn’t know this at the time but this was in fact, as we shall see, the most important part of the entire work in which Newton presented his mathematical model of a Keplerian cosmos held together by the law of gravity. Halley remained calm and used all of his diplomatic skills to coax, flatter, persuade and cajole the prickly mathematician into delivering the book as finished. In the end Newton acquiesced and delivered but acknowledgements to Hooke were keep to a minimum and offered at the lowest level of civility.

The financial problem was of a completely different nature. In 1685 the Royal Society had taken over the cost of printing and publishing the deceased Francis Willughby’s Historia piscium as edited by John Ray.

Source

This was an expensive project due to the large number plates that the book contained and the book was, at the time, a flop. This meant when it came time to print and publish Newton’s work the Royal Society was effectively bankrupt. One should note here that the popular ridicule poured out over Willughby’s volume, it having almost prevented Newton’s masterpiece appearing, is not justified. Historia piscium is an important volume in the history of zoology. Halley once again jumped into the breach and took over the costs of printing the volumes; on the 5 July 1687 Halley could write to Newton to inform him that the printing of his Philosophiæ Naturalis Principia Mathematica had been completed.

 

 

 

 

 

 

 

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

 

From about 1630 onwards there were only two serious contenders under European astronomers, as the correct scientific description of the cosmos, on the one hand a Tychonic geo-heliocentric model, mostly with diurnal rotation and on the other Johannes Kepler’s elliptical heliocentric system; both systems had their positive points at that stage in the debate.

A 17th century illustration of the Hypothesis Tychonica from Hevelius’ Selenographia, 1647 page 163, whereby the Sun, Moon, and sphere of stars orbit the Earth, while the five known planets (Mercury, Venus, Mars, Jupiter, and Saturn) orbit the Sun. Source: Wikimedia Commons

A lot of the empirical evidence, or better said the lack of that empirical evidence spoke for a Tychonic geo-heliocentric model. The first factor, strangely enough spoke against diurnal rotation. If the Earth was truly rotating on its axis, then it was turning at about 1600 kilometres an hour at the equator, so why couldn’t one feel/detect it? If one sat on a galloping horse one had to hang on very tightly not to get blown off by the headwind and that at only 40 kilometres an hour or so. Copernicus had already seen this objection and had actually suggested the correct solution. He argued that the Earth carried its atmosphere with it in an all-enclosing envelope. Although this is, as already mentioned, the correct solution, proving or explaining it is a lot more difficult than hypothesising it. Parts of the physics that was first developed in the seventeenth century were necessary. We have already seen the first part, Pascal’s proof that air is a material that has weight or better said mass. Weight is the effect of gravity on mass and gravity is the other part of the solution and the discovery of gravity, in the modern sense of the word, still lay in the future. Copernicus’ atmospheric envelope is held in place by gravity, we literally rotate in a bubble.

In his Almagestum Novum (1651), Giovanni Battista Riccioli (1598–1671) brought a list of 126 arguments pro and contra a heliocentric system (49 pro, 77 contra) in which religious argument play a minor role and carefully argued scientific grounds a major one.

Frontispiece of Riccioli’s 1651 New Almagest. Mythological figures observe the heavens with a telescope and weigh the heliocentric theory of Copernicus in a balance against his modified version of Tycho Brahe’s geo-heliocentric system Source: Wikimedia Commons

Apart from the big star argument (see below) of particular interest is the argument against diurnal rotation based on what is now know as the Coriolis Effect, named after the French mathematician and engineer, Gaspard-Gustave de Coriolis (1792–1843), who described it in detail in his Sur les équations du mouvement relatif des systèmes de corps (On the equations of relative motion of a system of bodies) (1835). Put very simply the Coriolis Effect states that in a frame of reference that rotates with respect to an inertial frame projectile objects will be deflected. An Earth with diurnal rotation is such a rotating frame of reference.

Riccioli argued that if the Earth rotated on its axis then a canon ball fired from a canon, either northwards or southwards would be deflected by that rotation. Because such a deflection had never been observed Riccioli argued that diurnal rotation doesn’t exist. Once again with have a problem with dimensions because the Coriolis Effect is so small it is almost impossible to detect or observe in the case of a small projectile; it can however be clearly observed in the large scale movement of the atmosphere or the oceans, systems that Riccioli couldn’t observe. The most obvious example of the effect is the rotation of cyclones.

Illustration from Riccioli’s 1651 New Almagest showing the effect a rotating Earth should have on projectiles.[36] When the cannon is fired at eastern target B, cannon and target both travel east at the same speed while the ball is in flight. The ball strikes the target just as it would if the Earth were immobile. When the cannon is fired at northern target E, the target moves more slowly to the east than the cannon and the airborne ball, because the ground moves more slowly at more northern latitudes (the ground hardly moves at all near the pole). Thus the ball follows a curved path over the ground, not a diagonal, and strikes to the east, or right, of the target at G. Source: WIkimedia Commons

Riccioli was not alone in using the apparent absence of the Coriolis Effect to argue against diurnal rotation. The French Jesuit mathematician Claude François Milliet Deschales (1621–1678) in his Cursus seu Mundus Mathematicus (1674) brought a very similar argument against diurnal rotation.

Source: WIkimedia Commons

Image from Cursus seu Mundus Mathematicus (1674) of C.F.M. Dechales, showing how a cannonball should deflect to the right of its target on a rotating Earth, because the rightward motion of the ball is faster than that of the tower. Source: Wikimedia Commons

It was first 1749 that Euler derived the mathematical formula for Coriolis acceleration showing it to be two small to be detected in small projectiles.

A nearby star’s apparent movement against the background of more distant stars as the Earth revolves around the Sun is referred to as stellar parallax. Source:

The second empirical factor was the failure to detect stellar parallax. If the Earth is really orbiting the Sun then the position of prominent stars against the stellar background should appear to shift when viewed from opposite sides of the Earth’s orbit, six months apart so to speak. In the seventeenth century they didn’t. Once again supporters of heliocentricity had an ad hoc answer to the failure to detect stellar parallax, the stars are too far away so the apparent shift is too small to measure. This is, of course the correct answer and it would be another two hundred years before the available astronomical telescopes had evolved far enough to detect that apparent shift. In the seventeenth century, however, this ad hoc explanation meant that the stars were quite literally an unimaginable and thus unacceptable distance away. The average seventeenth century imagination was not capable of conceiving of a cosmos with such dimensions.

The distances that the fixed stars required in a heliocentric system produced a third serious empirical problem that has been largely forgotten today, star size.  This problem was first described by Tycho Brahe before the invention of the telescope. Tycho ascribed a size to the stars that he observed and calculating on the minimum distance that the fixed stars must have in order not to display parallax in a heliocentric system came to the result that stars must have a minimum size equal to Saturn’s orbit around the Sun in such a system. In a geo-heliocentric system, as proposed by Tycho, the stars would be much nearly to the Earth and respectively smaller.  This appeared to Tycho to be simply ridiculous and an argument against a heliocentric system. The problem was not improved by the invention of the telescope. Using the primitive telescopes of the time the stars appeared as a well-defined disc, as recorded by both Galileo and Simon Marius, thus confirming Tycho’s star size argument. Marius used this as an argument in favour of a geo-heliocentric theory; Galileo dodged the issue. In fact, we now know, that the star discs that the early telescope users observed were not real but an optical artefact, now known as an Airy disc. This solution was first hypothesised by Edmond Halley, at the end of the century and until then the star size problem occupied a central place in the astronomical system discussion.

With the eccentricity of the orbits exaggerated: Source

The arguments in favour of Kepler’s elliptical, heliocentric system were of a very different nature. The principle argument was the existence of the Rudolphine Tables. These planetary tables were calculated by Kepler using Tycho’s vast collection of observational data. The Rudolphine Tables possessed an, up till that time, unknown level of accuracy; this was an important aspect in the acceptance of Kepler’s system. Since antiquity, the principle function of astronomy had been to provide planetary tables and ephemerides for use by astrologers, cartographers, navigators etc. This function is illustrated, for example, by the fact that the tables from Ptolemaeus’ Mathēmatikē Syntaxis were issued separately as his so-called Handy Tables. Also the first astronomical texts translated from Arabic into Latin in the High Middle Ages were the zījes, astronomical tables.

Source

The accuracy of the Rudolphine Tables were perceived by the users to be the result of Kepler using his elliptical, heliocentric model to calculate them, something that was not quite true, but Kepler didn’t disillusion them. This perception increased the acceptance of Kepler’s system. In the Middle Ages before Copernicus’ De revolutionibus, the astronomers’ mathematical models of the cosmos were judge on their utility for producing accurate data but their status was largely an instrumentalist one; they were not viewed as saying anything about the real nature of the cosmos. Determining the real nature of the cosmos was left to the philosophers. However, Copernicus regarded his system as being a description of the real cosmos, as indeed had Ptolemaeus his system before him, and by the middle of the seventeenth century astronomers had very much taken over this role from the philosophers, so the recognition of the utility of Kepler’s system for producing data was a major plus point in its acceptance as the real description of the cosmos.

The other major point in favour of Kepler’s system, as opposed to a Tychonic one was Kepler’s three laws of planetary motion. Their reception was, however, a complex and mixed one. Accepting the first law, that the planetary orbits were ellipses with the Sun at one focus of the ellipse, was for most people fairly easy to accept. An ellipse wasn’t the circle of the so-called Platonic axioms but it was a very similar regular geometrical figure. After Cassini, using a meridian line in the San Petronio Basilica in Bologna, had demonstrated that either the Earth’s orbit around the Sun or the Sun’s around the Earth, the experiment couldn’t differentiate, Kepler’s first law was pretty much universally accepted. Kepler’s third law being strictly empirical should have been immediately accepted and should have settled the discussion once and for all because it only works in a heliocentric system. However, although there was no real debate with people trying to refute it, it was Isaac Newton who first really recognised its true significance as the major game changer.

Strangely, the problem law turned out to be Kepler’s second law: A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This seemingly obtuse relationship was not much liked by the early readers of Kepler’s Astronomia Nova. They preferred, what they saw, as the purity of the Platonic axiom, planetary motion is uniform circular motion and this despite all the ad hoc mechanism and tricks that had been used to make the anything but uniform circulation motion of the planets conform to the axiom. There was also the problem of Kepler’s proof of his second law. He divided the ellipse of a given orbit into triangles with the Sun at the apex and then determined the area covered in the time between two observations by using a form of proto-integration. The problem was, that because he had no concept of a limit, he was effectively adding areas of triangles that no longer existed having been reduced to straight lines. Even Kepler realised that his proof was mathematically more than dubious.

Ismaël Boulliau portrait by Pieter van Schuppen Source: Wikimedia Commons

The French astronomer and mathematician Ismaël Boulliau (1605–1694) was a convinced Keplerian in that he accepted and propagated Kepler’s elliptical orbits but he rejected Kepler’s mathematical model replacing it with his own Conical Hypothesis in his Astronomica philolaica published in 1645.

He criticised in particular Kepler’s area rule and replaced it in his work with a much simpler model.

Boulliau’s Conical Hypothesis [RA Hatch] Source: Wikimedia Commons

The Savilian Professor of astronomy at Oxford University, Seth Ward (1617–1689)

Bishop Seth Ward, portrait by John Greenhill Source: Wikimedia Commons

attacked Boulliau’s presentation in his In Ismaelis Bullialdi astro-nomiae philolaicae fundamenta inquisitio brevis (1653), pointing out mathematical errors in the work and proposing a different alternative to the area law.

Source: Wikimedia Commons

Boulliau responded to Ward’s criticisms in 1657, acknowledging the errors and correcting but in turn criticising Ward’s model.

Source: Wikimeda Commons

Ward in turn had already presented a fully version of his Keplerian system in his Astronomia geometrica (1656).

The whole episode is known as the Boulliau-Ward debate and although it reached no satisfactory conclusion, the fact that two high profile European astronomers were disputing publically over the Keplerian system very much raised the profile of that system. It is probable the Newton was first made aware of Kepler’s work through the Boulliau-Ward debate and he is known to have praised the Astronomica philolaica, which as Newton was later to acknowledge contained the first presentation of the inverse square law of gravity, which Boulliau personally rejected, although he was the one who proposed it.

The Boulliau-Ward debate was effectively brought to a conclusion and superseded by the work of the German mathematician Nikolaus Mercator (c. 1620–1687), whose birth name was Kauffman. His birthplace is not certain but he studied at the universities of Rostock and Leiden and was a lecturer for mathematics in Rostock (1642–1648) and then Copenhagen (1648–1654). From there he moved to Paris for two years before emigrating to England in 1657. In England unable to find a permanent position as lecturer he became a private tutor for mathematics. From 1659 to 1660 he corresponded with Boulliau on a range of astronomical topics. In 1664 he published his Hypothesis astronomica, a new presentation of the Keplerian elliptical system that finally put the area law on a sound mathematical footing. In 1676 he published a much-expanded version of his Keplerian astronomy in his two-volume Institutionum astronomicarum.

Mercator’s new mathematical formulation of Kepler’s second law ended the debate on the subject and was a major step in the eventual victory of Kepler’s system over its Tychonic rival.

Addendum: Section on Coriolis Effect added 21 May 2020

 

 

 

 

 

 

 

 

 

 

 

A uniform collection of maps should have been a Theatre but became an Atlas instead but it might have been a Mirror.

Early Modern cartography was centred round a group of pioneers working in the Netherlands in the sixteenth century. The two best-known cartographers being Gerhard Mercator and Abraham Ortelius but they were by no means the only map publishers competing for the market. One notable engraver cartographer, who has slipped out of public awareness, is Gerard de Jode.

Source: Wikimedia Commons

He was born in Nijmegen, then part of the Spanish Lowlands in 1509, which appears to be the sum total of all that is know about his origins or early life; a not uncommon situation with Renaissance figures. At some point he moved to Antwerp and in 1547 he was admitted to the Guild of St Luke. At the time Antwerp was a booming trading city, the second biggest city in Northern Europe after Paris and probably the richest city in Europe. Because of its large population and accumulated wealth it was also a major centre for both the book and map trades.

Map of Antwerp around 1598 Hoefnaegels, cartographer XVIth century Source: Wikimedia Commons

The Guild of St Luke was principally the guild for painters and other artists and De Jode was an engraver. To become a guild member he would have had to have been a master, so we can assume that he had served an apprenticeship and worked as a journeyman engraver prior to becoming a guild member.  He received permission to set up a printing office in Antwerp in 1551.

Coat of arms of the Antwerp Guild of Saint Luke

This was not a one-man business and he employed a number of skilled engravers, who are well known craftsmen. His workshop produced a wide range of engraved products but he appears to have specialised to a certain extent in cartography and map production. Antwerp was a major centre for the map trade and De Jode printed and published single maps by notable cartographers.

In 1555 he issued an edition of the world map of the renowned Venetian cartographer Giacomo Gastaldi (c. 1500–1566). Gastaldi had originally been an engineer working for the Venetian Republic but in the 1640s he turned to cartography. His 1648 edition of Ptolemaeus’ Geographia is notable for including regional maps of the Americas and for being reduced in size to produce the first ‘pocket’ atlas. It also represents a shift from woodblock to copper plate printing in cartography. His world map is interesting in that it shows the Americas and Asia as a single conjoined landmass, a common geographical misconception of the period.

Paolo Forlani & Ferando Bertelli, world map based on world map of Giacomo Gastaldi Source: Library of Congress

In 1558 he produced an edition of Jacob van Deventer’s map of Brabant.

hertogdom Brabant uit 1540 door Jacob van Deventer Source

Jacob van Deventer (c. 1500–1575) was born in Kampen, also in the Spanish Lowlands. He is part of the mathematical heritage of the University of Leuven, where he registered as a student in 1520. It was in Leuven that he developed his interest in geography and cartography. He later moved to Mechelen and in 1572 to Köln to escaped the Dutch Revolt against the Spanish. In 1536 he produced the map of Brabant that De Jode would later reprint. It is the earliest known map to use the method of triangulation first described in print by Gemma Frisius (1508–1555) in his Libellus de locorum describendorum ratione (1533).

It was once thought that Deventer had learnt the technique from Gemma but given that Gemma’s book was only published in 1533 and Van Deventer’s map already in 1536 it seems improbable. Two other possibilities are that Gemma learnt the technique from Deventer or they both learnt it from a third unknown source. We will probably never know.

Deventer was appointed Imperial Cartographer by Charles V in 1540, the title being changed to Royal Cartographer after the emperor’s abdication in 1555. In 1559 he was commissioned to survey and map all of the cities in the Spanish Lowlands, a task that he completed with great competence. Due to their military significance the maps were never published.

Town plan of Asperen c. 1560 by Jacob van Deventer Source: Wikimedia Commons

In 1564 De Jode published another world map by a famous cartographer, the eight-sheet wall map of Abraham Ortelius (1527–1598), which would later appear in reduced form in Ortelius’ Theatrum Orbis Terrarum (1570).

Ortelius World Map in reduced form from Theatrum Orbis Terrarum (1570) Source: Wikimedia Commons

This was actually Ortelius’ first published map and De Jode would also produce a reduced version of it. The two cartographers would go on to become serious rivals.

It is not known if De Jode independently came up with the idea of producing a book of uniform maps, what we now call an atlas, or whether he was inspired by Ortelius’ endeavour but he produced his own Speculum Orbis Terrarum.

Gerade de Jode’s World Map 1578 Source: Wikimedia Commons

Whereas Ortelius presented the world on a stage as a theatre, De Jode held a mirror up to the globe reflecting it in his maps.  It appears that Ortelius used his reputation and his influential connections to enforce his monopoly and De Jode’s Speculum first appeared in 1578, when Ortelius’ official printing privilege for Antwerp ended. However, by that time Ortelius had established himself so well in the market that De Jode’s atlas suffered the same fate as Mercator’s and flopped, although it was considered at least as good as if not actually superior to Ortelius’ Theatrum.

However, De Jode appears not to have been too dispirited by the failure of his project as he set about preparing a second expanded edition. Rather like Mercator, he died in 1591 before he could complete this work and like Mercator, it was his son Cornelius de Jode (1568–1600), who completed the work and issued the Speculum Orbis Terrae in 1593.

Title page of Speculum Orbis Terrae. 1593 Source: Wikimedia Commons

Africa Gerade de Jode 1593 Source: Wikimedia Commons

Map Quiviræ Regnum cum aliis versus Boream from the Speculum Orbis Terræ. This map is one of the earliest depictions of the North American West Coast based on a veröffentlichten world map published by Petrus Plancius 1592 Source: Wikimedia Commons

This too failed to sell well. The book however, features a pair of interesting polar projection world maps strongly influenced by Guillaume Postel’s polar planisphère from 1578.

Guillaume Postel polar projection world map 1578

Guillaume Postel (1510-1581) was a French polymath principally known as a linguist, he was also an astronomer, cosmologists, cartographer, cabbalist, diplomat and religious universalist.

Postel as depicted in Les vrais pourtraits et vies des hommes illustres grecz, latins et payens (1584) by André Thevet Source: Wikimedia Commons

Tried by the Inquisition in 1553 for heresy he was found insane and imprisoned in the Papal prisons in Rome. He was released in 1559 but then confined in a monastery in Paris from 1566 till his death. Postel did not invent the polar projection; it had already been used by Walter Ludd (1448–1547)–administrator of the Gymnasium Vosagense, whose most well known member was the cartographer Martin Waldseemüller(c. 1470–1520)–for a diagram in Gregor Reisch’s Margarita philosophica (1512), but Postel’s was the first large scale use of the projection and it influenced not just De Jode.

Gerard de Jode polar projection map of the Northern hemisphere. Color print from copper engraving (printer Arnold Coninx), Antwerp, 1593. Source: Wikimedia Commons

Gerard de Jose polar projection map of the Southern Hemisphere Source: Wikimedia Commons

Following Cornelius’ death the plates for the De Jode Speculum were sold to the Antwerp book and print seller Joan Baptista Vrients, who also acquired the plates for Ortelius’ Theatrum at about the same time. Although Vrients published several very successful editions of the Theatrum in the early years of the seventeenth century, he never reissued the Speculum, so it appears he only acquired it to remove a potential competitor from the market.

It should not be thought that because his atlas project failed that De Jode was not in general successful. His business in Antwerp was very successful turning out prints of all kinds and he also had a flourishing stand at the Frankfurt Book Fair where he not only sold his wares but acquired foreign prints and maps that he then copied for his own printing office back home. Following the death of Gerard and his oldest son Cornelius the family business was set forth by his second son Pieter de Jode the elder (1570–1634), an artist and engraver, who became a master of the Guild of St Like in Antwerp in 1599.

Pieter de Jode the Elder by Lucas Emil Vorsterman after Sir Anthony van Dyck Source: Wikimedia Commons

He in turn was succeeded by his son Pieter de Jode (1606–1674) the younger, also an artist and engraver.

Portrait of Pieter de Jode the younger based on portrait by Thomas Willeboirts Bosschaert

The line ended with Pieter the younger’s son Arnold born in 1638, who although he studied engraving under his father never rose to the standards of his illustrious forebears.

I find it an interesting speculation that if De Jode’s Speculum had been successful, we today take down a mirror from the bookshelf to look at maps of the world.

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

In the previous episode of this series we looked into the academic literature that spread knowledge of the heliocentric system during the seventeenth century. However, there was another genre of literature during the century that was also partially dedicated to introducing and explaining the heliocentric system, fiction and popular literature and that is what we are going to look at now.

It should come as no surprise that the earliest author to produce a fictional account of the heliocentric system was Johannes Kepler with his posthumously published proto-science-fiction novel, Somnium (The Dream) (1634).

Source: Wikimedia Commons

Kepler first wrote the core of this book as a student dissertation, written for his teacher Michael Mästlin, explaining how the movement of the Earth, in a heliocentric system, would appear to somebody observing it from the Moon. Around 1605 he added a frame story to his student dissertation the dream of the title. Kepler relates that in 1608 he was reading a book on Bohemian legends when he fell asleep and began to dream. In his dream he takes down another book from the shelf and reads the story of Duracotus, an Icelander, and his mother Fiolxhilda, who is obviously a witch, although Kepler never explicitly states that. The boy open a herb charm that his mother has made to sell to sailors and removes the herbs making the charm useless. Outraged, his mother sells him instead to the ship’s captain, who takes him to Scandinavia, where he ends up on Hven with Tycho Brahe under whom he studies astronomy for five years. Returning to Iceland he reconciles himself with his mother, who reveals to him that she has magical knowledge of astronomy. Fiolxhilda summons a daemon, who tells Duracotus how they could travel to the moon and then holds a long discourse on the moon and its inhabitants, part science, part science fiction. To go into more detail would turn this post into book, however, because of the obvious autobiographical element Kepler thought that somebody had gained access to the manuscript and this was why his mother was charged with witchcraft; he was almost certainly mistaken in this belief.

Kepler did not publish his story but put it aside. Between 1620 and 1630 Kepler added 223 extensive endnotes, which elucidate the story, explaining his sources, his motivations and the content of the story itself. Even with these explanatory additions Kepler did not publish the book, leaving it unpublished at his death in 1630. Because his death had left his wife, Susanna, and his family in financial difficulties, his son in law, Jacob Bartsch (c. 1600–1633) edited the manuscript for publication with hope of generating an income for his mother-in-law. However, he too died before he could publish the book, which was then finally brought to press by Kepler’s son Ludwig (b. 1607).

Kepler’s Somnium was the first of a series of fictional books describing journeys to the moon in the seventeenth century nearly all of which promoted a heliocentric astronomy and it is to these that we now turn.

Our first author is the Anglican clergyman and natural philosopher, John Wilkins (1614–1672).

John Wilkins portrait attributed to John Greenhill Source: Wikimedia Commons

Although he produced no real new scientific discoveries or theories Wilkins was a highly influential figure in the scientific revolution in England. He published a series of popular and speculative science books and was a founding member of and a driving force behind the Royal Society. One of Wilkins’ popular science books, Mathematical Magick (1648) is said to have had a strong influence on a young Isaac Newton but it is two of his other books that interest us here, The Discovery of a World in the Moone (1638) and A Discourse Concerning a New Planet (1640), the second being a revised and expanded version of the first.

Cover and frontispiece. Note the heliocentric system diagram

Both books present a heliocentric astronomical system and, based on Galileo’s telescopic discoveries of the earth like nature of the moon, hypothesise an inhabited moon, as had Kepler’s Somnium, which however predated Galileo’s Sidereus Nuncius. Wilkins two books were a popular source for disseminating the heliocentric hypothesis in England.

Five months after the publication of The Discovery of a World in the Moone another journey to the moon fantasy by an Anglican clergyman was published, Francis Goodwin’s The Man in the Moone or A Discourse of a Voyage thither (1638), under the pseudonym Domingo Gonsales.

Francis Godwin artist unknown Source: Wikimedia Commons

Godwin (1562–1633) had died five years previously and although his book was published after Wilkins’ tome, it is thought to have been written in the 1620s and it is known to have influenced Wilkins’ book.

Source: Houghton Library via Wikimedia Commons

The ‘author’, Gonsales, a Spaniard on the run after killing a man in a duel, invents a flying machine powered by gansa, a species of wild swans, which after a series of adventures flies him to the moon, a twelve day journey. Here he discovers a utopian Christian society. After six months he returns to earth landing in China, where he has some more adventures. For our purposes what is important here is that like Wilkins, Godwin is a Copernican and although he only mentions Copernicus by name the influence of Kepler, Gilbert and Galileo is clearly discernable in his science fantasy.

Frontispiece and title page of the second edition (1657), now with the pseudonym replaced by “F.G. B. of H.” (“Francis Godwin, Bishop of Hereford”) Source: Wikimedia Commons

The books of Wilkins and Godwin were both best sellers and were translated into various other European languages including French, where they influenced another book in the genre, Cyrano de Bergerac’s L’Autre monde ou les états et empires de la Lune (The Other World: Comical History of the States and Empires of the Moon 1657), and his Les États et Empires du Soleil (The States and Empires of the Sun, 1662), both published posthumously.

Cyrano de Bergerac artist unknown Source: Wikimedia Commons

L’Autre monde is a satire on Godwin’s book and Cyrano’s hero, who is also called Cyrano, makes various failed attempts to reach the moon, including trying to rise up to the moon levitated by bottles of evaporating dew before he finally gets there.

Cyrano uses bottles of dew to float upwards. Illustration from the second volume of an edition of Cyrano de Bergerac’s complete works printed in Amsterdam in 1708 Source: Wikimedia Commons

When he does arrive on the moon one of the people he meets is Gonsales, with whom he has a religious debate. It might seem that Cyrano de Bergerac (1619–1655) as a literary author was just riffing off the success of Wilkins’ and Godwin’s works but he was a pupil of Pierre Gassendi (1592–1655) and so was well informed about the ongoing cosmology and astronomy debate.

Godwin’s The Man in the Moone and the English translation of Cyrano’s L’Autre monde inspired two later stage productions on the theme Aphra Behn’s (1640–1689) farce The Emperor of the Moon 1687, her second most successful play, and Elkanah Settle’s (1648–1724) opera The World in the Moon (1697).

Aphra Behn by the Anglo-Dutch artist Sir Peter Lely, Courtesy of the Yale Center for British Art, Yale University via Wikimedia Commons

All of the texts that we have looked at so far contain a common theme that emerged strongly during the seventeenth century, the possibility of life on other worlds, in this case the moon. Our final work, in this case not a fictional but a factual one, continues this theme, Bernard Le Bovier de Fontenelle’s popular presentation of the heliocentric hypothesis, Entretiens sur la pluralité des mondes (Conversations on the Plurality of Worlds, 1686). Bernard Le Bovier de Fontenelle (1657–1757) was an author and Cartesian philosopher, commentator rather than initiator, who was a member of both the Académie française and the Académie des sciences of which he was secretary for forty-two years beginning in 1697; in this function he wrote Histoire du renouvellement de l’Académie des Sciences (Paris, 3 vols., 1708, 1717, 1722).

Bernard Le Bovier de Fontenelle artist unknown Source: Wikimedia Commons

His Entretiens sur la pluralité des mondes was an early example of a popular science book written in French not Latin.

In the preface, Fontenelle addresses female readers and suggests that the offered explanation should be easily understood even by those without scientific knowledge. The book is presented as a dialogue between a philosopher and a marquise and elucidates the heliocentric system with a discussion of the possibility of extra-terrestrial life. The book is interesting in that Fontenelle explains that there is now only one system to consider because the Tychonic system was now considered to be too complex in comparison with the heliocentric system. This is one of the few real applications of Ockham’s razor in the history of science and comes long before there was any empirical proof for the heliocentric system. There was an English translation by John Glanville (c. 1664–1735) in 1687 and another by Aphra Behn A Discovery of New Worlds in 1688.

A Gentleman of the Inner Temple is John Glanville

This all too brief survey of the fictional and popular literature published in the seventeenth century demonstrates that the discussion on the cosmological/astronomical system had escaped the narrow confines of academia and entered the public forum.

 

 

 

 

 

 

 

 

 

How Renaissance Nürnberg became the Scientific Instrument Capital of Europe

This is a writen version of the lecture that I was due to hold at the Science and the City conference in London on 7 April 2020. The conference has for obvious reasons been cancelled and will now take place on the Internet. You can view the revised conference program here.

The title of my piece is, of course, somewhat hyperbolic, as far as I know nobody has ever done a statistical analysis of the manufacture of and trade in scientific instruments in the sixteenth century. However, it is certain that in the period 1450-1550 Nürnberg was one of the leading European centres both for the manufacture of and the trade in scientific instruments. Instruments made in Nürnberg in this period can be found in every major collection of historical instruments, ranging from luxury items, usually made for rich patrons, like the column sundial by Christian Heyden (1526–1576) from Hessen-Kassel

Column Sundial by Christian Heyden Source: Museumslandschaft Hessen-Kassel

to cheap everyday instruments like this rare (rare because they seldom survive) paper astrolabe by Georg Hartman (1489–1564) from the MHS in Oxford.

Paper and Wood Astrolabe Hartmann Source: HSM Oxford

I shall be looking at the reasons why and how Nürnberg became such a major centre for scientific instruments around 1500, which surprisingly have very little to do with science and a lot to do with geography, politics and economics.

Like many medieval settlements Nürnberg began simply as a fortification of a prominent rock outcrop overlooking an important crossroads. The first historical mention of that fortification is 1050 CE and there is circumstantial evidence that it was not more than twenty or thirty years old. It seems to have been built in order to set something against the growing power of the Prince Bishopric of Bamberg to the north. As is normal a settlement developed on the downhill slopes from the fortification of people supplying services to it.

A fairly accurate depiction of Nürnberg from the Nuremberg Chronicle from 1493. The castles (by then 3) at the top with the city spreading down the hill. Large parts of the inner city still look like this today

Initially the inhabitants were under the authority of the owner of the fortification a Burggraf or castellan. With time as the settlement grew the inhabitants began to struggle for independence to govern themselves.

In 1200 the inhabitants received a town charter and in 1219 Friedrich II granted the town of Nürnberg a charter as a Free Imperial City. This meant that Nürnberg was an independent city-state, which only owed allegiance to the king or emperor. The charter also stated that because Nürnberg did not possess a navigable river or any natural resources it was granted special tax privileges and customs unions with a number of southern German town and cities. Nürnberg became a trading city. This is where the geography comes into play, remember that important crossroads. If we look at the map below, Nürnberg is the comparatively small red patch in the middle of the Holy Roman Empire at the beginning of the sixteenth century. If your draw a line from Paris to Prague, both big important medieval cities, and a second line from the border with Denmark in Northern Germany down to Venice, Nürnberg sits where the lines cross almost literally in the centre of Europe. Nürnberg also sits in the middle of what was known in the Middle Ages as the Golden Road, the road that connected Prague and Frankfurt, two important imperial cities.

You can also very clearly see Nürnberg’s central position in Europe on Erhard Etzlaub’s  (c. 1460–c. 1531) pilgrimage map of Europe created for the Holy Year of 1500. Nürnberg, Etzlaub’s hometown, is the yellow patch in the middle. Careful, south is at the top.

Over the following decades and centuries the merchant traders of Nürnberg systematically expanded their activities forming more and more customs unions, with the support of various German Emperors, with towns, cities and regions throughout the whole of Europe north of Italy. Nürnberg which traded extensively with the North Italian cities, bringing spices, silk and other eastern wares, up from the Italian trading cities to distribute throughout Europe, had an agreement not to trade with the Mediterranean states in exchange for the Italians not trading north of their northern border.

As Nürnberg grew and became more prosperous, so its political status and position within the German Empire changed and developed. In the beginning, in 1219, the Emperor appointed a civil servant (Schultheis), who was the legal authority in the city and its judge, especially in capital cases. The earliest mention of a town council is 1256 but it can be assumed it started forming earlier. In 1356 the Emperor, Karl IV, issued the Golden Bull at the Imperial Diet in Nürnberg. This was effectively a constitution for the Holy Roman Empire that regulated how the Emperor was to be elected and, who was to be appointed as the Seven Prince-electors, three archbishops and four secular rulers. It also stipulated that the first Imperial Diet of a newly elected Emperor was to be held in Nürnberg. This stipulation reflects Nürnberg’s status in the middle of the fourteenth century.

The event is celebrated by the mechanical clock ordered by the town council to be constructed for the Frauenkirche, on the market place in 1506 on the 150^th anniversary of the Golden Bull, which at twelve noon displays the seven Prince-electors circling the Emperor.

Mechanical clock on the Frauenkirche overlooking the market place in Nürnberg. Ordered by the city council in 1506 to celebrate the 150th anniversary of the issuing of the Golden Bull at the Imperial Diet in 1356

Over time the city council had taken more and more power from the Schultheis and in 1385 they formally bought the office, integrating it into the councils authority, for 8,000 gulden, a small fortune. In 1424 Emperor, Sigismund appointed Nürnberg the permanent residence of the Reichskleinodien (the Imperial Regalia–crown, orb, sceptre, etc.).

The Imperial Regalia

This raised Nürnberg in the Imperial hierarchy on a level with Frankfurt, where the Emperor was elected, and Aachen, where he was crowned. In 1427, the Hohenzollern family, current holders of the Burggraf title, sold the castle, which was actually a ruin at that time having been burnt to the ground by the Bavarian army, to the town council for 120,000 gulden, a very large fortune. From this point onwards Nürnberg, in the style of Venice, called itself a republic up to 1806 when it was integrated into Bavaria.

In 1500 Nürnberg was the second biggest city in Germany, after Köln, with a population of approximately 40,000, about half of which lived inside the impressive city walls and the other half in the territory surrounding the city, which belonged to it.

Map of the city-state of Nürnberg by Abraham Ortelius 1590. the city itself is to the left just under the middle of the map. Large parts of the forest still exists and I live on the northern edge of it, Dormitz is a neighbouring village to the one where I live.

Small in comparison to the major Italian cities of the period but even today Germany is much more decentralised with its population more evenly distributed than other European countries. It was also one of the richest cities in the whole of Europe.

Nürnberg, Plan by Paul Pfinzing, 1594 Castles in the top left hand corner

Nürnberg’s wealth was based on two factors, trading, in 1500 at least 27 major trade routes ran through Nürnberg, which had over 90 customs unions with cities and regions throughout Europe, and secondly the manufacture of trading goods. It is now time to turn to this second branch of Nürnberg’s wealth but before doing so it is important to note that whereas in other trading centres in Europe individual traders competed with each other, Nürnberg function like a single giant corporation, with the city council as the board of directors, the merchant traders cooperating with each other on all levels for the general good of the city.

In 1363 Nürnberg had more than 1200 trades and crafts masters working in the city. About 14% worked in the food industry, bakers, butchers, etc. About 16% in the textile industry and another 27% working leather. Those working in wood or the building branch make up another 14% but the largest segment with 353 masters consisted of those working in metal, including 16 gold and silver smiths. By 1500 it is estimated that Nürnberg had between 2,000 and 3,000 trades and crafts master that is between 10 and 15 per cent of those living in the city with the metal workers still the biggest segment. The metal workers of Nürnberg produced literally anything that could be made of metal from sewing needles and nails to suits of armour. Nürnberg’s reputation as a producer rested on the quality of its metal wares, which they sold all over Europe and beyond. According to the Venetian accounts books, Nürnberg metal wares were the leading export goods to the orient. To give an idea of the scale of production at the beginning of the 16^th century the knife makers and the sword blade makers (two separate crafts) had a potential production capacity of 80,000 blades a week. The Nürnberger armourers filled an order for armour for 5,000 soldiers for the Holy Roman Emperor, Karl V (1500–1558).

The Nürnberger craftsmen did not only produce goods made of metal but the merchant traders, full blood capitalists, bought into and bought up the metal ore mining industry–iron, copper, zinc, gold and silver–of Middle Europe, and beyond, (in the 16th century they even owned copper mines in Cuba) both to trade in ore and to smelt ore and trade in metal as well as to ensure adequate supplies for the home production. The council invested heavily in the industry, for example, providing funds for the research and development of the world’s first mechanical wire-pulling mill, which entered production in 1368.

The wirepulling mills of Nürnberg by Albrecht Dürer

Wire was required in large quantities to make chainmail amongst other things. Around 1500 Nürnberg had monopolies in the production of copper ore, and in the trade with steel and iron.  Scientific instruments are also largely made of metal so the Nürnberger gold, silver and copper smiths, and toolmakers also began to manufacture them for the export trade. There was large scale production of compasses, sundials (in particular portable sundials), astronomical quadrants, horary quadrants, torquetum, and astrolabes as well as metal drawing and measuring instruments such as dividers, compasses etc.

The city corporation of Nürnberg had a couple of peculiarities in terms of its governance and the city council that exercised that governance. Firstly the city council was made up exclusively of members of the so-called Patrizier. These were 43 families, who were regarded as founding families of the city all of them were merchant traders. There was a larger body that elected the council but they only gave the nod to a list of the members of the council that was presented to them. Secondly Nürnberg had no trades and crafts guilds, the trades and crafts were controlled by the city council. There was a tight control on what could be produced and an equally tight quality control on everything produced to ensure the high quality of goods that were traded. What would have motivated the council to enter the scientific instrument market, was there a demand here to be filled?

It is difficult to establish why the Nürnberg city corporation entered the scientific instrument market before 1400 but by the middle of the 15^th century they were established in that market. In 1444 the Catholic philosopher, theologian and astronomer Nicolaus Cusanus (1401–1464) bought a copper celestial globe, a torquetum and an astrolabe at the Imperial Diet in Nürnberg. These instruments are still preserved in the Cusanus museum in his birthplace, Kues on the Mosel.

The Cusanus Museum in Kue

In fact the demand for scientific instrument rose sharply in the 15^th & 16^th centuries for the following reasons. In 1406 Jacopo d’Angelo produced the first Latin translation of Ptolemy’s Geographia in Florence, reintroducing mathematical cartography into Renaissance Europe. One can trace the spread of the ‘new’ cartography from Florence up through Austria and into Southern Germany during the 15^th century. In the early 16^th century Nürnberg was a major centre for cartography and the production of both terrestrial and celestial globes. One historian of cartography refers to a Viennese-Nürnberger school of mathematical cartography in this period. The availability of the Geographia was also one trigger of a 15^th century renaissance in astronomy one sign of which was the so-called 1^st Viennese School of Mathematics, Georg von Peuerbach (1423–1461) and Regiomontanus (1436–176), in the middle of the century. Regiomontanus moved to Nürnberg in 1471, following a decade wandering around Europe, to carry out his reform of astronomy, according to his own account, because Nürnberg made the best astronomical instruments and had the best communications network. The latter a product of the city’s trading activities. When in Nürnberg, Regiomontanus set up the world’s first scientific publishing house, the production of which was curtailed by his early death.

Another source for the rise in demand for instruments was the rise in interest in astrology. Dedicated chairs for mathematics, which were actually chairs for astrology, were established in the humanist universities of Northern Italy and Krakow in Poland early in the 15^th century and then around 1470 in Ingolstadt. There were close connections between Nürnberg and the Universities of Ingolstadt and Vienna. A number of important early 16th century astrologers lived and worked in Nürnberg.

The second half of the 15^th century saw the start of the so-called age of exploration with ships venturing out of the Iberian peninsular into the Atlantic and down the coast of Africa, a process that peaked with Columbus’ first voyage to America in 1492 and Vasco da Gama’s first voyage to India (1497–199). Martin Behaim(1459–1507), son of a Nürnberger cloth trading family and creator of the oldest surviving terrestrial globe, sat on the Portuguese board of navigation, probably, according to David Waters, to attract traders from Nürnberg to invest in the Portuguese voyages of exploration.  This massively increased the demand for navigational instruments.

The Erdapfel–the Behaim terrestial globe Germanische National Museum

Changes in the conduct of wars and in the ownership of land led to a demand for better, more accurate maps and the more accurate determination of boundaries. Both requiring surveying and the instruments needed for surveying. In 1524 Peter Apian (1495–1552) a product of the 2^nd Viennese school of mathematics published his Cosmographia in Ingolstadt, a textbook for astronomy, astrology, cartography and surveying.

The Cosmographia went through more than 30 expanded, updated editions, but all of which, apart from the first, were edited and published by Gemma Frisius (1508–1555) in Louvain. In 1533 in the third edition Gemma Frisius added an appendix Libellus de locorum describendum ratione, the first complete description of triangulation, the central method of cartography and surveying down to the present, which, of course in dependent on scientific instruments.

In 1533 Apian’s Instrumentum Primi Mobilis 

was published in Nürnberg by Johannes Petreius (c. 1497–1550) the leading scientific publisher in Europe, who would go on ten years later to publish, Copernicus’ De revolutionibus, which was a high point in the astronomical revival.

All of this constitutes a clear indication of the steep rise in the demand for scientific instruments in the hundred years between 1450 and 1550; a demand that the metal workers of Nürnberg were more than happy to fill. In the period between Regiomontanus and the middle of the 16^th century Nürnberg also became a home for some of the leading mathematici of the period, mathematicians, astronomers, astrologers, cartographers, instrument makers and globe makers almost certainly, like Regiomontanus, at least partially attracted to the city by the quality and availability of the scientific instruments.  Some of them are well known to historians of Renaissance science, Erhard Etzlaub, Johannes Werner, Johannes Stabius (not a resident but a frequent visitor), Georg Hartmann, Johannes Neudörffer and Johannes Schöner.**

There is no doubt that around 1500, Nürnberg was one of the major producers and exporters of scientific instruments and I hope that I have shown above, in what is little more than a sketch of a fairly complex process, that this owed very little to science but much to the general geo-political and economic developments of the first 500 years of the city’s existence.

One of the most beautiful sets on instruments manufactured in Nürnberg late 16th century. Designed by Johannes Pretorius (1537–1616), professor for astronomy at the Nürnberger University of Altdorf and manufactured by the goldsmith Hans Epischofer (c. 1530–1585) Germanische National Museum

**for an extensive list of those working in astronomy, mathematics, instrument making in Nürnberg (542 entries) see the history section of the Astronomie in Nürnberg website, created by Dr Hans Gaab.

3 into 2 does go!

It would of course be totally unethical for me to review a book of which I am one of the authors. However, as my contribution is only six of two-hundred pages, of which three are illustrations, and the book is one that could/would/should interest some (many) of my readers, I’m going to be unethical and review it anyway.

Thinking 3D is an intellectual idea, it is a website, it is exhibitions and other events, it is a book but above all it is two people, whose idea it is: Daryl Green, who was Fellow Librarian of Magdalen College, Oxford and is now Special Collections Librarian of the University of Edinburg and Laura Moretti, who is Senior Lecturer in Art History at the University of St Andrews. The Thinking 3D idea is the historical investigation of the representation of the three-dimensional world on the two-dimensional page particular, but not exclusively, in print.

The Thinking 3D website explains in great detail what it is all about and contains a full description of the activities that have been carried out. For those quarantined there is a fairly large collection of essays on various topics from the project.

In 2019 Thinking 3D launched a major exhibition with The Bodleian Libraries Oxford as part of the commemorations of the 500^th anniversary of Leonardo da Vinci’s death, Thinking 3D From Leonardo to the Present, which ran from March 2019 to February 2020 and which I have been told was quite exceptional.

As an extension and permanent record of that exhibition Bodleian Libraries published a book, Thinking 3D: Books, Images and Ideas from Leonardo to the Present[1], which appeared in autumn 2019. This is both a coffee table book but also, at the same time, a piece of serious academic literature.

The book opens with a long essay by Green and Moretti, The history of thinking 3D in forty books, which delivers exactly what the title says. This is an excellent survey of the topic and it is worth reading the book just for this. However, it does contain one historical error that I, in my alter ego of the HIST_SCI HULK, simply cannot ignore, at least not if I want to maintain my hard won reputation. Having introduced the topic of Copernicus’ De revolutionibus the authors write:

As mentioned above, the oft-published heliocentric diagram, and its theoretical propositions, are what launched this book into infamy (the book was immediately put on the Catholic Church’s Index of Prohibited Books [my emphasis]), but the execution of this relational illustration is simple and reductive.

De revolutionibus was published in 1543 but was first placed on the Index sixty-three years later in 1616 and more importantly, as I wrote very recently, not for the first time, it was placed on the Index until corrected. These corrections, which were fairly minimal, were carried out surprisingly quickly and the book became available to be studied by Catholics already in 1621.

Other than this I noticed no other errors in the highly informative introductory essay, which is followed by an essay from Matthew Landrus, Leonardo da Vinci, 500 years on, which examines Leonardo’s three-dimensional perception of the world and everything in it. It was for me an interesting addition to my previous readings on the Tuscan polymath.

The main body of the book is taken up by sixteen fairly short essays in four categories: Geometry, Astronomy, Architecture and Anatomy.

Geometry starts off with Ken Saito’s presentation of a ninth century manuscript of The Elements of Euclid, where he demonstrates very clearly that the author has no real consistent, methodology for presenting a 3D space on a 2D page.   This is followed by Renzo Baldasso’s essay on Luca Pacioli’s De divina proportione (1509). Here the three dimensional solids are presented perfectly by Pacioli’s friend, colleague and one time pupil Leonardo. We return to Euclid for Yelda Nasifoglu’s investigation of the English translation of The Elements by Henry Billingsley in 1570. This volume is totally fascinating as three-dimensional figures are present as pop-up figure like those that we all know from our children’s books. The geometry section closes with a book that I didn’t know, Max Brückner’s Vielecke und Vielflache (1900) presented by George Hart. This is a vast collection of photographs of paper models of three-dimensional figures, which I learnt also influenced M. C. Escher a master of the third dimension.

Luca Pacioli De divina proportione

 

Karl Galle, Renaissance Mathematicus friend and guest blogger, kicks of the astronomy section with Johannes Kepler’s wonderfully bizarre presentation of the planetary orbits embedded in the five regular Platonic solids from his Mysterium Cosmographicum (1596). Yours truly is up next with an account of Galileo’s Sidereus Nuncius (1610) and it’s famous washes of the Moon displaying three-dimension features. Also covered are the later pirate editions that screwed up those illustrations. Stephanie O’Rourke presents one of the most extraordinary nineteenth century astronomy books James Nasmyth’s and James Carpenter’s The Moon: Considered as a Planet, a World, and a Satellite(1874). This contains stunningly realistic photographic plates of the Moon’s surface but which are not actually real. The two Jameses constructed plaster models that they then lit and photographed to achieve the desired effect. We close the astronomy section with Thinking 3D’s co-chef, Daryl Green, taking on a survey of the surface of Mars with the United Stated Geological Survey, Geological Map of Mars (1978).

Johannes Kepler Mysterium Cosmographicum

Turning our attention to architecture, we travel back to the twelfth century, with Karl Kinsella as our guide, to Richard of St Victor’s In visionen Ezekielis; a wonderfully modern in its presentation but somewhat unique medieval architectural manuscript. The other half of the Thinking 3D team, Laura Moretti now takes us up to the sixteenth century and Sebastiano Serlio’s catalogue of the buildings of Rome (1544), which has an impossibly long Italian title that I’m not going to repeat here. We remain in the sixteenth century for Jacques Androuet du Cerceau’s Le premier [et second] volume des plus excellent bastiment de France (1576–9), where our guide is Frédérique Lemerle. Moving forward a century we close out the architecture section with Francesco Marcorin introducing us to Hans Vredeman de Vries’s absolutely stunning Perspective (1604–5).

Hans Vredeman de Vries Perspective

It would not be too difficult to guess that the anatomy section opens with one of the greatest medical books of all time, Andreas Vesalius’ De fabrica but not with the full version but the shorter (cheaper?) De humani corporis fabrica libroum epitome, like the full version published in 1543 in Basel. Our guide to Vesalius’ masterpiece is Mark Samos. Camilla Røstvik introduces us to William Hunter’s The Anatomy of the Human Gravid Uterus (1774), as she makes very clear a milestone in the study of women’s bodies with its revolutionary and controversial study of the pregnant body. For me this essay was a high point in a collection of truly excellent essays. We stay in the eighteenth century for Jacques Fabien Gautier D’Agoty’s Exposition anatomique des organes des sens (1775). Dániel Margócsy present a fascinating guide to the controversial work of this pioneer of colour printing. Anatomy, and the book as a whole, closes with Denis Pellerin’s essay on Arthur Thomson’s Anatomy of the Human Eye (1912). Thomson’s book was accompanied by a collection of stereoscopic images of the anatomy of the eye together with a stereoscope with which to view the 3D images thus created; a nineteenth century technology that was already dying out when Thomson published his work.

William Hunter The Anatomy of the Human Gravid Uterus

The book closes with a bibliography of five books for further reading for each essay, brief biography of each of the authors, a glossary of technical terms and a good general index. All sixteen of the essays are short, informative, light to read, easily accessible introductions to the volumes that they present and maintain a high academic quality throughout the entire book.

I said at the outset that this is also a coffee table book and that was not meant negatively. It measures 24X26 cm and is printed on environmentally friendly, high gloss paper. The typeface is attractive and light on the eyes and the illustrations are, as is to be expected for a book about the history of book illustration, spectacularly beautiful. The publishing team of the Bodleian Libraries are to be congratulated on an excellent publication. If you leave this on your coffee table then your visitors will soon be leafing though it admiring the pictures, whether they are interested in book history or not. I don’t usually mention the price of books that I review but at £35 this beautifully presented and wonderfully informative volume is very good value for money.

[1] Thinking 3D: Books, Images and Ideas from Leonardo to the Present, edited by Daryl Green and Laura Moretti, Bodleian Library, Oxford, 2019.