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.


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