Kim H. Veltman
Scientific Literature and Rise of the Quantitative Spirit
Written July 1990
To be Published as: “La littérature scientifique et l'essor de l'esprit quantitative,”
L'époque de la Renaissance 1520-1560, Budapest: Akadémiai Kiadó, vol. 3, (in press).
This is one of two contributions to a new four volume survey of the Renaissance which was initiated among others by the late Tibor Klaniczay of the Hungarian Academy of Sciences and is now being continued by Professor Eva Kushner. This essay covers the period 1520-1560. The other essay, “Mesure, Quantification et Science” covers the period 1560-1600. These essays serve as introductions to a planned larger work outlined in the author’s Mastery of Quantity (1990).
1. Introduction
2. Geometry
3. Arithmetic
4. Perspective and Surveying
5. Astrology
6. Astronomy
7. Tables
8. Instruments
9. Astronomy, Geography and Cosmology
10. Conclusions
1. Introduction
Historians of science frequently look back at the Renaissance in terms of isolated events and books that changed the course of early modern science. In this approach the period 1520-1560 is notable mainly for three works published in the year 1543: On the revolutions of the heavens by Nicholas Copernicus, On the fabric of the human body by Andreas Vesalius and the first vernacular edition of Euclid's Elements by Niccolo Tartaglia. There is also the widespread assumption that after Gutenberg every important idea was immediately published and hence only printed texts are significant. The story is not so simple. In 1471 Johannes Müller (Regiomontanus) established the first printing press devoted specifically to the publication of scientific books. About 1472 he issued a sheet 30x23 cm listing which books he planned to publish. These included the works of Euclid and Archimedes, the Conics of Apollonius, Serenus On the Cylinder, Ptolemy's Almagest, Geography, Music and Optics, Hero of Alexandria's Hydraulics, the Spherics of Menelaus and Theodosius, Astronomy of Hyginus, Arithmetic of Jordanus, the Optics of Witelo, plus a series of commentaries and books written by himself. When Regiomontanus died unexpectedly in 1474, his work was inherited first by Werner (1468-1528), then by Hartmann (1489-1564). As a result a number of the classics on his list were first published in the sixteenth century: e.g. the Almagest (1515), Witelo (1535), Hyginus (1535), Archimedes (1544).
Publication of both ancient and modern scientific texts progressed slowly. The half century between 1470 and 1520 saw some basic mediaeval works such as the Sphere of Sacrobosco 1499) and the Optics of Peckham (1482,1504); as well as modern works on astronomy, Stoffler (1514) and Lefèvre d'Etaples; perspective, Pélerin (1505,1509) and practical arithmetic, including Cirvelo (1505), Lefèvre (1510,1514), Köbel (1514), Bonini (1517) and Martini (1519). But it was not until the period 1520-1560 that a recognizable corpus of scientific literature emerged in published form. This included both early mediaeval texts such as Proclus' Two books on motion (1542) and late mediaeval manuscripts such as Saint Hildegard of Bingen's Physics (1533). As we are concerned specifically with the rise of systematic quantitative literature only passing reference will be made to isolated contributions in music by Walther (1538) or navigation by Saa (1549), or even to important advances in the life sciences such as botany, e.g. Brunfels (1533) and anatomy, Vesalius (1543,1545,1555), Estienne (1546), Columbus and Valverde (1559). Some mention must, however, be made of literature on weights and measures such as Agricola's Five books on weights and measures (1533), a second edition of which (1550) also contained a work by the lawyer Alciati, of emblem fame, on the topic of weights and measures. Also important in this context are The judgment of medical weights by Asculanus appended to Brunfel's Onomastikon of medicine (1534), Pasi's Tariff of corresponding weights and measures from the east to the west, from one country and place to another (1540); Cenalis' On the measures of liquids and pulses. On the truth of measures and weights (1546); a Synopsis of weights and measures by Neander (1555), Marheld's work on the weight and price of silver (1556) and Rudolff's study of comparative weights, lengths and coinage in different towns and countries (1557).
The incentives for these interests were various. One was obviously linked with trade and commerce. Medicine, and pharmacy in particular, which required accurate doses, provided another incentive. Agricola, for instance, was a town physician. In his spare time he also visited local mines and smelters which led to his classic study (1546,1557,1558) of weights and measures in connection with the emerging earth sciences, particularly metallurgy and mineralogy, a topic also treated by Biringuccio (1540,1556,1558) and Entzelt (1551,1557).
Our main purpose however is to focus on a phenomenon, whereby authors on traditionally abstract subjects such as arithmetic and geometry became increasingly concerned with practical topics involving measurement both on earth (notably perspective, surveying, geography) and in the heavens (astrology and astronomy). This created a new mathematical framework for a theoretical and practical treatment of nature amenable to verification by means of instruments. Without this the explosion of measuring devices and literature on quantification in the period 1560-1600 would have been unthinkable as would the subsequent contributions towards synthesis by Galileo, Descartes, Huygens and Newton in the seventeenth century frequently associated as the key moments in early modern science.
2. Arithmetic
With respect to arithmetic the period 1520-1560 brought at least 65 publications. In 1494 Luca Pacioli had published his great Summa of arithmetic, geometry, proportion and proportionality. This was reprinted in 1525 and remained a basic source. Adam Riese's classic work on arithmetic (1525) appeared together with Erhard Helm's book on gauging, i.e. the problem of volumetric measurement of wine barrels using rods with square roots or cube roots. Riese went through various editions (e.g. 1531 Erfurt; 1544 and 1550 Leipzig, the latter again with a section on gauging). Köbel's Reckoning book (1544, 1549) also combined arithmetic, geometry and gauging. Meanwhile with authors such as Frey (1543) and Helmreich (1561) gauging also emerged as an independent topic of publication.
The authors of this literature on arithmetic were often also engaged in a wide range of practical applications. For instance, Peter Apian, who was based at Ingolstadt, and wrote A new...instruction in all merchants' reckoning (1532, 1543); also published on geography (1529, 1553), surveying and astronomical instruments (1532, 1533), astronomy (1533,1539,1540) and sundials (1541). Gemma Frisius, who wrote an Easy method of practical arithmetic (1544), was the teacher of Mercator at Louvain, edited Apianus' work on cosmography (e.g.1539), published a basic text on surveying and cartography (1533) and also wrote on astronomy and geography (e.g. 1530, 1553) and new instru-ments (e.g. 1545). In Paris, Oronce Finé, who produced a treatise on practical arithmetic (1555) also published on geometry (1544), astronomy (1534, 1538,1553) as well as astronomy, geography and hydrography together (1555). A series of centres also emerged: chiefly Frankfurt, Nürnberg, Leipzig, Paris and Venice. Other centres, notably Basel, Strasbourg and Wittemberg (e.g Albert 1544, Ammon 1544 with a preface by Melanchthon; Gemma Frisius 1544 1548 1556 and Medler 1550), also played an important part in the early history of protestantism. Many of these publica-tions on arithmetic also involved geometry.
3. Geometry
In geometry, the period 1520-1560 was partly concerned with recovery and spread of the classics. There were six editions of Euclid's Elements (1533 1537 1550 Basel; 1536 Wittemberg; 1548 Frankfurt and 1555 Augsburg). There were also editions of Archimedes (1544 Basel, 1558 Venice) and Psellus (1558 Paris). Geometry also acquired a particular meaning. In Greek, geometry literally means "measurement of the earth", but the Greeks themselves had tended to keep a sharp distinc-tion between theoretical and practical geometry. From the time of Boethius onwards this literal meaning had gained increasing acceptance and by the sixteenth century practical geometry was frequently equated with geometry itself. Hence Dürer's basic textbook in geometry was entitled Instruction in measurement (1525).
A decade later Jakob Köbel published Geometry. On artful measuring and recording of all heights, surfaces, planes, widths and breadths such as towers, churches, buildings, trees, fields and lands (1535). A slightly more abstract approach was taken by Wolfgang Schmid in The first book of geometry. A brief instruction of what and whereupon geometry is based and how one can with the aid of the same, using a ruler and compass divide all lines, surfaces and bodies in a given propor-tion (1539). Even so the emphasis was now clearly on three-dimensional aspects of geometry. Oronce Finé, who founded a chair of mathematics at Paris pursued this in his Book of practical geometry or on the practices of lengths, planes and solids, that is, the measurement of lines, surfaces and bodies, and other mechanical matters which follow as a corollary from the demonstrations of Euclid's Elements (1544). This served as a starting point for Pierre de la Ramée (Ramus), which explains why Finé's successor included surveying and problems of volumetric measurement in his treatise on geometry.
Köbel's work was reprinted in 1556, a year which also saw the publication of the first two parts of Niccolo Tartaglia's General treatise on numbers and measures (1556-1560). Parts three to six followed in 1560, including, Part four, In which the great majority of figures, both superficial and corporeal are reduced to numbers; Part five, In which is shown the means of executing with the compass and the ruler all the propositions of Euclid and other philosophers and part six, which dealt with algebra. By this time other trends were evident. The Greeks had made a clear distinction between geometry (continuous quantity) and arithmetic (discrete quantity). The equation of geometry and measurement meant that geometrical lines, surfaces and solids could now be treated in terms of arithmetical numbers, which prepared the way for Descartes' new synthesis in the form of analytic geometry some 70 years later. It also meant that instruments and models could be used both for recording and demonstrating geometrical and arithmetical problems. The increased interplay between practical and theoretical thus forged a new nexus between mathematics, instrumentation and model making. By implication, surveying, geography, astronomy and cosmology were no longer problems for intellectual verbal debate. They involved a challenge of visual, mechanical, instrumental demonstration. That challenge led Kepler to make his famous models and eventually led him to see discrepancies that would never have emerged with such clarity in a traditional discussion.
4. Surveying and Perspective
In addition to textbooks, which treated geometry literally as measurement of the earth there were also books specifically devoted to the topic of surveying. One of the classics in this context was Gemma Frisius' Booklet on the means of describing places and finding their distances (1533), which described the use of timepieces in determining longitude (cf. Pogo, Isis, 1933). Johann Stoeffler, adapted an astrolabe for the purposes of surveying in On artful measurement of all sizes, planes and declines in length, height, breadth and depth (1536). Kaspar Peucer was interested in the extension of these surveying principles to longitudes, latitudes and cartography in his book On the dimension of the earth (1550).
There was yet another context for these interests. From the early fifteenth century there had been significant connections between geometry, perspective and surveying, through Alberti, Filarete, Piero della Francesca, Francesco di Giorgio Martini and Leonardo da Vinci. The first of these to be published was Alberti (1540). Meanwhile, Dürer included a section on perspective in his Instruction of measurement (1525, 1532, 1535, 1538). Rodler who edited A beautiful useful booklet (1531,1546), set out to popularize Dürer and explicitly equated perspective and measurement. Hirschvogel (1543) who wrote on geometry and perspective also wrote a treatise on suveying. Ryff, wrote a large compendium (1547, 1558) of treatises on both perspective (Alberti, Serlio) and surveying. Consequently surveying was more than a question of recording isolated points on a terrain: it was also a question of recording graphically the features of a terrain in a perspectival form.
A number of artists were trained as surveyors and it was no coincidence therefore that such artists were frequently called in to settle land disputes in the latter sixteenth century, as Père De Dainville has shown. An understanding of these connections helps explain the close connections between geometry, surveying and perspective evidenced in the latter sixteenth century: e.g. Bartoli (1564), Barbaro (1568) or Danti in his edition of Vignola (1583), plus the interplay between surveying and perspective instruments from early examples such as Besson's cosmolabe to the sector in the seventeenth century.
5. Astrology
In astrology there was also a movement to publish classic texts, particularly Ptolemy (e.g. 1538, 1541, 1543, 1550, 1553,and 1556) and mediaeval manuscripts from both the Jewish ,e.g. Abraham ben Ezra (1537, 1545) and the Arabic tradition: Alchabitius (1521, 1560); Albohali (1546); and Ali-Ibn Abi al-Rajjal (1551), as well as the Latin west, notably, Pietro d'Abano (1552). Here too there was a rise of literature on quantitative measurement. A number of works simply attempted to predict the future on the basis of positions of the stars: e.g. Carion 1529, 1549, Grünbeck 1531, Torquatus 1535, Gauricus 1539. Frequently they gave a forecast of the current year as in Heller's Practice books for 1548, 1549, 1551, 1553, 1554, 1557, 1560, 1561, 1580. Or they predicted the coming year, as in Gasser's Prognosticum for the year 1545 (1544), Brotbeyel (1547) and Rheticus (1550). Other books contained technical tables, lists and instruments. In 1532, for instance, there appeared an anonymous: Geomancy...With accompanying tables, which hours of the day and night are governed by each planet. Two years later there was another anonymous: Geomancy...together with five tables with an appended technical instrument and rules which hour of the day and night is governed by each planet (1532). Another instrument was decribed by the mathematician, Finé, in his book On the twelve houses of the heavens and unequal hours (1536).
Besides superstition, one incentive for these studies was medicine, as in Dariot's Easy introduction to judgment of the stars. Fragment on knowing diseases and critical days from the motions of the stars (1557). A more pressing incentive was religion. At the time there was a widespread conviction that the end of the world was imminent. Knowing when it would happen might not save one's skin but it could save one's soul. Hence those involved in astrology included the foremost astronomers: Regiomontanus' A new calendar of all kinds of medicine...with eclipses of the sun and moon until the year 1563 (1540) and Rheticus' Astronomical tables... On the ascensions of the signs in the level and oblique sphere for the latitude of 52 degrees (1545). This tradition explains why the Wolfenbüttel copy of an anonymous German astronomy. On the nature, property and effect of the 7 signs of the heavens, of the 7 planets and the 36 celestial images and their stars...(1545) should be bound with technical works: Münster's Outline and technical description of sundials and Schöner's Gnomonics. This also explains why comets, which were seen as barometers for disaster, emerged as an important topic: e.g. Brelochs (1531), Sch”ner (1531) Gasser (1538) or why, a generation later, even the great Kepler was both an astrologer and an astronomer. Often, of course, the same term served to describe both astrology and astronomy, with the result that both fields remained interdependent.