Science and Technology

Diophantos of Alexandria
Arithmeticorum libri sex,
et de numeris multangulis liber unus
Paris: Sebastian Cramoisy, 1621

The Greek mathematician, Diophantos of Alexandria, one of the greatest algebraists in history, composed his Arithmetica in the second half of the third century A.D. Only six of the original thirteen books of this earliest extant work on algebra have survived, along with his tract on polygonal numbers. Some of the problems found in the Arithmetica result in various forms of determinate equations; the majority, however, lead to indeterminate equations (hence indeterminate analysis is often termed "Diophantine analysis"). While Latin translations of Diophantos had appeared as early as 1572, the Greek text was not available until Claude-Gaspar Bachet de Meziriac issued this edition in both Greek and Latin at Paris in 1621.

Augsburg: Erhard Ratdolt, 1489

The Julian calendar which was instituted in 46 B.C. exceeded the true solar year by more than eleven seconds per year. One consequence was that, with the advance of time, natural events such as the equinoxes fell increasingly earlier in the Julian "year." By the fifteenth century the discrepancy had grown to more than a week. Pope Sixtus IV (1471 ­ 1484), realizing the inaccuracy of the Julian system, summoned Regiomontanus (1436-1476), a renowned astrologer and astronomer, to Rome in 1474 to supervise the reformulation of the official Church calendar. Although Regiomontanus' premature death in 1476 prevented completion of the project (which would occur in 1582 under Pope Gregory XIII), his Kalendarium, calculated for the years 1475-1532, was the first calendar printed in Europe and became the standard for later efforts. The sixth edition of this immensely popular calendar, published in 1489, also contains volvelles, astronomical and astrological tables, and brass devices for constructing horoscopes.

Johann Kepler
Tabulae Rudolphinae
Ulm: Jonas Saurius, 1627

Since antiquity scientists and philosophers had speculated on the motions of celestial bodies and had sought an underlying harmony and order to the cosmos. Early in the sixteenth century Copernicus grafted aspects of Ptolemaic geometry onto the heliocentric system of Aristarchus; yet even this pioneer regarded planetary motion as uniformly circular. It remained for the inventive mathematician Johann Kepler (1571-1630) to derive new descriptive laws of planetary motion which challenged traditional views. Upon inheriting a vast quantity of accurate planetary observations from his mentor Tycho Brahe, Kepler derived new laws which demonstrated the elliptical nature of planetary orbits. In 1627, after a long delay and much labor, Kepler released to the world his Tabulae Rudolphinae (named after his first patron Rudolph II), which charted planetary positions according to these new laws.

Adriaan Vlacq
Tables de sinus, tangentes,
secantes, et de logarithmes
[Gouda: Pieter Rammaseyn, 1636?]

The trigonometric and logarithmic tables of Adriaan Vlacq (1600 ­ 1666), first published as Arithmetica logarithmica in 1628, were well received and frequently reprinted during the seventeenth century. In 1636, Vlacq, with his keen business instincts, published a smaller version in a more convenient format for the use of businessmen and scientists. Evidence suggests that this copy may have been taken to China by Jesuit missionaries who had introduced trigonometry and logarithms to the Chinese by the middle of the seventeenth century. The book also includes a note in French on Chinese paper stating that the emperor K'ang-hsi (1654 ­ 1722) made use of this book during his sessions with Jesuit tutors. Various functions are indicated by Chinese characters in red ink, while inserted before the printed text are eight handwritten pages on basic geometrical problems. The red morocco binding stamped in gold is similar to the bindings produced for the Jesuit library in China.

Leonhard Euler
Institutiones calculi differentialis
Pavia: Petrus Galeatus, 1787
Two volumes

Following the simultaneous invention of calculus by Newton and Leibniz, it remained for resourceful mathematicians such as Leonhard Euler (1707 ­ 1783) to perfect the new method of analysis. Euler, a brilliant and prolific man, made important advances in both differential and integral calculus. Among the many contributions found in Institutiones calculi differentialis, first published in 1755, are Euler's theorem on homogeneous functions; an elaboration of formulas of differentiation under substitution of variables; and the application of Taylor's series to finding extrema of f(x). To this day, Euler's name is associated with many formulas, such as that governing the relation between a sum and an integral (Euler-Maclaurin formula).

François d'Aguilon Opticorum
Antwerp: Ex officina Plantiniana, 1613

As with the earlier rise of humanism, the growth of the exact sciences depended on able scholars who could marshal administrative as well as academic skills. After some years as instructor of syntax, logic, and theology, François d'Aguilon (1546 ­ 1617) was approached by Belgian officials with a bold and important request. He was asked to develop a program for the instruction of the new scientific ideas and methods which were of great use in a variety of fields. One result was Aguilon's magnum opus on optics, the Opticorum (1613), synthesizing the works of such luminaries as Euclid, Ibn al-Haytham (Alhazen), Vitellion, Roger Bacon, Ramus, Pena, Risner, and Kepler. A vital treatise for succeeding generations, the Opticorum is of importance to the history of science for its clear explication of orthographic, stereographic, and scenographic projections ­ intended for an audience of cosmographers, astronomers, navigators, military leaders, engravers, and painters.

Jean François Nicéron
La perspective curieuse
Paris: Jean Du Puis, 1663

In their examination of natural phenomena, many philosophers came to realize that what was previously regarded as "magic" could be described in mathematical language. La perspective curieuse, first published in 1638 by Jean François Nicéron (1613-1646), a student of the noted scientist Marin Mersenne, defines the range and nature of certain problems encountered in the study of perspective and geometrical optics. In sympathy with the "natural magic" prevalent during Nicéron's time, this contemporary of Galileo viewed optics not as the science of light, but as the art of illusion. Among the many practical applications of perspective, catoptrics, and dioptrics discussed, the work addresses the problem of establishing a perspective for paintings executed on irregular or curved surfaces, such as vaults or niches. Also found is the earliest published reference to Descartes' derivation of the law of refraction (1638). This fourth edition, in Latin and French, includes Mersenne's L'optique et la catoptrique.

Claude François Milliet de Challes
Cursus seu mundus
Lyons: Ex officina Anissoniana, 1674 Three volumes

Claude François Milliet de Challes (1621 ­ 1678) combined the talents of mathematician, teacher, and writer. Cursus seu mundus mathematicus, first published in 1674, is a remarkable and well-written course on mathematics and kindred subjects such as optics, magnetism, mechanics, navigation, pyrotechnics, astronomy, and music. De Challes was adept at incorporating the works of previous mathematicians into a coherent system and at explaining the intricacies of the mathematical sciences with ease and accuracy. Although somewhat old-fashioned for its time, being based largely on Euclid and Diophantos, the Cursus became a popular and widely used textbook which was instrumental in the diffusion of mathematical knowledge.

Johann Zahn
Oculus artificialis
teledioptricus sive telescopium
Würzburg: Quirinus Heyl, 1685-86
Three volumes in one

Soon after the invention of the telescope in the first decade of the seventeenth century, considerable numbers of the new instrument were made in Holland and from there found their way all over Europe. As the years passed, focal lengths grew, magnification increased, and the need arose for comprehensive manuals that dealt with the theory, construction, and application of telescopes and microscopes. One such text, Oculus artificialis, was provided by Johann Zahn (1641 ­ 1707), a German philosopher, physicist, and mathematician. An important treatise with many detailed illustrations, the work proceeds from basic theory on vision and optics through material selection and preparation of lenses to astronomical and biological applications. Included is a section on the uses of optical instruments for purposes of illusion and natural magic.

Sebastian Münster
Fürmalung and künstlich
Beschreibung der Horologien
Basel: Heinrich Peter, 1537

Although the sixteenth century marked the initial development of clocks and watches into instruments of precision, sun dials were still the predominant timepieces and faded from use only during the eighteenth century. Among the earliest modern writers on dialling, or gnomonics, was the geographer, mathematician, and Hebraist Sebastian Munster (1489-1552), best known for his Cosmographia universalis (1544), an influential work of descriptive geography. In this first German edition of Münster's Compositio horologiorum, issued in Latin in 1531, Münster reviewed previous literature on the ancient craft of dialling, incorporated recent innovations allowing for greater accuracy, and presented the theory, construction, and employment of both sun and (Münster's own invention) moon dials. Accompanying the text are numerous woodcuts which illustrate, among other things, how to properly orient and mount a dial.

Nicolo Tartaglia
Quesiti et inventioni diverse
Venice: Nicolo de Bascarini, 1554

The rise of the exact sciences occurred in the context of the growth and consolidation of states in the sixteenth and seventeenth centuries. This relationship is evident in the extent to which scientists of the period frequently linked their services to the political and economic goals of contemporary governments. Nicolo Tartaglia (1499 ­ 1557) was an early exponent of scientific technology whose inventive efforts suggest the character of the Renaissance condottiere. Aware of the latest theoretical advances, Tartaglia made land- and sea-based military forces the proving ground of technology. His Quesiti et inventioni diverse, first published in 1546 with a dedication to King Henry VIII of England, discusses topographical surveying, the disposition of infantry, gunpowder, cannonballs, the firing of artillery, and other topics important to the security of states. Bound with this copy of the Quesiti is a portion of Tartaglia's first work, Nova scientia, treating the theory and practice of gunnery, and Regola generale di solevare ogni affondata nave, offering a solution to the problem of raising sunken ships, plans for a diving suit and bell, and advice for weather forecasting.

Francis Malthus
Traité des feux artificiels
pour la guerre,
et pour la recréation
Paris: Pierre Guillemot, 1632

As scientists applied themselves to the field of military technology and warfare, it became obvious that traditional methods of constructing cannons and projectiles, which resulted in an inefficient variety of sizes and poundages, were in need of standardization. Greater frequency and scale of conflict, increasingly distant fronts, and longer supply lines necessitated more efficient deployment and supply of field pieces. The French especially excelled in this direction, and the manual of Francis Malthus (fl. 1629), who held the position of "Commissaire des Feux Artificiels du Roy," is a typical handbook of the period. Dedicated to Cardinal Richelieu, the Traité deals with all aspects of contemporary gunnery and pyrotechnics, including cannons, gunpowder, projectiles, fortifications, siege, and fireworks. First issued in 1629, it was reissued several times during the seventeenth century.

Johan Sems and Johan Pietersz Dou
Von dem Gebrauch der geometrischen Instrumenten
Amsterdam: Wilhelm Jansz, [1616]

While general principles of surveying had been known to medieval scholars, it was not until the sixteenth century that cartography and instrumentation were sufficiently developed and seriously applied. By the middle of that century it became customary for textbooks on practical mathematics to include one or more chapters on how to survey a region or country. By the time of the Dutchmen Johan Sems (1572-1623) and Johan Pietersz Dou (1573-1635), specialized manuals such as Von dem Gebrauch der geometrischen Instrumenten, were being produced. The work, first issued in Dutch in 1600, details the employment of various recently invented instruments and provides many useful charts, tables, and illustrations. Surveying was particularly important in the Low Countries, where land reclamation was proceeding at a rapid pace.

Louis Georges Isaac Salivet
Manuel du tourneur
Paris: M. P. Hamelin Bergeron, 1792 ­ 96
Two volumes

The diffusion of scientific method and technology led, as Diderot hoped it would, to alternative ways of thinking. The machine became a dominant cultural metaphor and was seen as a veritable work of art and extension of the individual. Precision machinery and tooling in particular reflected the value and dignity attached to technological innovations. Lathes, which had become very popular in the sixteenth and seventeenth centuries, underwent great refinement during the eighteenth century. A contributor to Diderot's Encyclopédie, Louis Georges Isaac Salivet (1737-1805) summarized these latest advances in his Manuel du tourneur, a comprehensive guide to the art of turning, whose illustrations of machinery suggest the plates to Diderot's massive compilation. Typical of many eighteenth-century savants, Salivet was a versatile and inquisitive individual. Trained as a lawyer, he also edited classical texts and conducted experiments in physics and mechanics.

Johannes Goedaert
Metamorphosis naturalis
Middelburg: Jaques Fierens, [1662 ­ 1669]
Three volumes

Like many experimental "virtuosi" of the seventeenth century, Johannes Goedaert (1617 ­ 1668) began his explorations of the natural realm from the standpoint of an artist and craftsman. Goedaert, who never attended a university, was not only a skilled naturalist and observer, but a fine watercolorist. Aided by recent advances in optics and instrumentation, he was able to train "flea-glasses" upon a great variety of insect life. Goedaert's sole work, Metamorphosis naturalis, written in Dutch, was the earliest study of the insect populations of the Netherlands, and it describes observations of and experiments with insects made between 1635 and 1658. Capturing "worms" (larvae) in the field and raising them to maturity, Goedaert observed and recorded the metamorphoses of a number of species. Using his expertise as a painter, he depicted the life cycles of beetles, flies, wasps, bees, butterflies, and moths.

Jakob Christian Schäffer
Icones insectorum circa Ratisbonam indigenorum
Ratisbon: Heinrich Gottfried Zunkel, [1766 ­ 79]
Three volumes

In their efforts to grasp the precision and beauty of nature, many eighteenth-century scientists turned to a variety of pursuits. Jakob Christian Schäffer (1718-1790) was trained as a priest and became adept in the arts and sciences. Excelling in manual arts such as sculpture, cabinet- and instrument-making, Schäffer also conducted experiments in electricity and optics. He is best known for his work in zoology, especially in entomology and botany. Among his major productions was Icones insectorum circa Ratisbonam indigenorum, the result of field research on several hundred insect species in the area of Ratisbon, Bavaria. Schäffer's exact descriptions and fidelity of illustration made the three-volume work a mine of information for zoologists and brought it to the attention of scientists and royalty throughout Europe.

Georges Louis Leclerc Buffon
Histoire naturelle des oiseaux
[Paris: Imprimerie Royale, 1770-1783]

A major feature of eighteenth-century science was the attempt to systematize the various results of research and to make that system philosophically attractive. The massive, forty-four-volume Histoire naturelle of the Count de Buffon (1707 ­ 1788), a basic text of Enlightenment science, was the first work to collect the diverse facts of natural history and to present them in a lucid and popular fashion. The Histoire naturelle moves from cosmology and anthropology to geology, geography, zoology, and many other topics. The nine monumental volumes on ornithology, published separately, contain over 1000 hand-colored plates executed by the artist and engraver François Nicolas Martinet and others. Buffon's great encyclopedia of natural history became an immensely popular work and was translated into numerous languages.

Alexander von Humboldt
Monographie des mélastomacées
Paris: A la librairie grecque-latine-allemande
and chez Gidefils, 1816 ­ 1823
Two parts

Alexander von Humboldt (1769-1859), the celebrated naturalist, explorer, and politician, required more than twenty years to publish the encyclopedic mass of materials ­ scientific, archaeological, and political ­ gathered during his 1799 ­ 1804 expedition to equatorial regions of the Americas. Included among the sixth part of Voyage aux régions équinoxiales du Nouveau Continent, under which title the results of his voyage were to be known, is the Monographie des mélastomacées. A monograph on tropical flora, the work is illustrated with superb color engravings prepared by Aimé Bonpland (1773 ­ 1858), a botanist who accompanied Humboldt during his journey. Heir to the Enlightenment, Humboldt excelled in many fields. In addition to botany, his scientific interests included astronomy, mathematics, physics, zoology, physical geography, and meteorology.

Carl Linnaeus
Systema naturae
Leiden: Theodorus Haak, 1756

One of the greatest advances made in biology during the eighteenth century was the binomial taxonomy proposed by Carl Linnaeus (1707-1778). Embracing the animal, vegetable, and mineral kingdoms, the Linnean system of classification imposed order on a burgeoning mass of data that had confronted biologists since the sixteenth century. By 1600 some six thousand distinct plants had been described, and the number trebled during the next century. Traditional classification systems such as those of Aristotle, Theophrastus, Dioscorides, and the medieval herbalists were poorly equipped to organize such data. In 1735 Linnaeus published his Systema naturae, in which he applied the principle of plant sexuality demonstrated by Rudolf Jakob Camerarius (1694) to the material collected and initially ordered by John Ray, Joseph Tournefort, and others.

Jacob Theodor Klein
Summa dubiorum circa classes
quadrupedum et amphibiorum
Leipzig: Johann Friedrich Gleditsch, 1743

Following the publication and success of Linnaeus' Systema naturae, a number of subsequent books and monographs questioned the Linnean classification and outlined the latest research. One such text was the Summa dubiorum, written by zoologist Jacob Klein (1685-1759). Klein's taxonomic method, based entirely upon external characteristics such as number and position of limbs, was incompatible with those systems, including the Linnean, based on criteria not externally visible. In addition to questioning the Linnean classes of quadrupeds and amphibians, Summa dubiorum discusses crustaceans and ruminants and compares human longevity with that of other primates. Of additional interest are the engravings, which suggest a style of animal portraiture much closer to the fantastic and legendary creatures of old than to modern scientific illustration.

Marcus Elieser Bloch
Allgemeine Naturgeschichte der Fische
Berlin, 1782-1795
Twelve volumes and atlas of plates

The accomplishment of Linnean binomial taxonomy, combined with pioneering work by the Swedish naturalist Peter Artedi, led to a vigorous period of research in ichthyology. Students travelled the globe in search of new species of fish to describe. Amidst mounting reports of new discoveries from the field, ichthyologists were faced with the task of coordinating a fixed matrix of classification with an expanding range of species. Marcus Elieser Bloch (1723 ­ 1799), a Berlin physician, was fifty-six when he began writing on fish. His enthusiasm was such that he set out to describe, illustrate, and systematize virtually every known species. The result was the monumental Naturgeschichte der Fische whose collection of exquisitely hand-colored engraved plates makes it one of the most handsome books on fish ever produced.

Louis Bourguet
Traité des pétrifications
Paris: Chez Briasson, 1742

Along with the classification of new living species came the discovery of increasing numbers of fossils, evidence which suggested that many species had completely disappeared from the world. This conclusion drew the wrath of religious authorities, since it challenged the traditional Judeo-Christian notion of the fixity of species. In the face of such opposition, scholars such as Louis Bourguet (1678-1742) explored fossil sites throughout Europe and sought to systematize their findings. Professor of mathematics, skilled naturalist, and a correspondent of Leibniz, Bourguet provided in this first edition of his major work a theory of crystallization, a list of fossil sites, and a bibliography of nearly a hundred works on petrification. Countering the notion that fossils were simply "freaks" of nature, he argued for their animal and vegetable origins.

Jean Louis Rodolphe Agassiz
On the Principles of
Classification in the Animal Kingdom;
On the Structure of the Halcyonoid Polypi;
On the Morphology of the Medusae
Charleston, S.C.: Walker and James, 1850

The work of Jean Louis Rodolphe Agassiz (1807-1873), Swiss zoologist, ichthyologist, geologist, and paleontologist, reflects the transition of the natural sciences from classical to evolutionary biology during the mid-nineteenth century. A student of French naturalist Georges Cuvier (1769-1832), Agassiz pursued his career both in Europe and in America. He blended an insistence on close empirical study with a metaphysical view of the Creator's role in the formation of each species, a position which would make him the leading American opponent of Darwinism. Following his acceptance of a professorship at Harvard in 1847, Agassiz issued a series of monographs on comparative embryology, including On the Principles of Classification in the Animal Kingdom in 1850. In this work he argued that zoologists must consider embryological changes as criteria in the classification of animal species.