SCIENCE
AND TECHNOLOGY
62
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.
63
Regiomontanus
Kalendarium
Augsburg: Erhard Ratdolt, 1489
Image
Complete
Digital Version
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.
64
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.
65
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.
66
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).
67
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.
68
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.
69
Claude François Milliet de Challes
Cursus seu mundus
mathematicus
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.
70
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.
71
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.
72
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.
73
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.
74
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.
75
Louis Georges Isaac Salivet
Manuel du tourneur
Paris: M. P. Hamelin Bergeron, 1792 96
Two volumes
Image
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.
76
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.
77
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.
78
Georges Louis Leclerc Buffon
Histoire naturelle des oiseaux
[Paris: Imprimerie Royale, 1770-1783]
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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.
79
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.
80
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.
81
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.
82
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.
83
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.
84
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.
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