twenty-six books De Animalibus, of Albertus Magnus (d. 1282) were not printed until 1478, but were apparently well known in manuscript copies. No great worker appears in this almost neglected field until we come to Conrad Gesner (or Gessner) (15161565), the first famous naturalist of modern times, on account of his vast erudition surnamed "the German Pliny." Professor of Greek at Lausanne and later of Natural History at Basel, he was almost as prolific an author as was della Porta fifty years later, for he wrote extensively upon plants, animals, milk, medicine, and theology, as well as various classical subjects. Yet he ranks high in the history of biology, both for the extent and the quality of his work in zoölogy and botany. It is significant that Gesner was a Swiss, and as such probably safe from persecution at a time when William Turner, an English ornithologist, worked and published in Cologne. At the end of the fifteenth and beginning of the sixteenth centuries Leonardo da Vinci (1452-1519) turned his attention in part from art to science, engineering, and inventions, making interesting studies in architecture, hydraulics, geology, etc. He is regarded as the first engineer of modern times, and has been called "the world's most universal genius." Palissy, "the Potter," later examined minutely various fossils and took the then advanced ground (as Xenophanes and Pythagoras had done, however, some two thousand years earlier) that these are in reality what they appear to be, i.e. petrified remains of plant and animal life, and not "freaks of nature." Palissy's bold stand on this subject marks one of the first steps in modern times toward rational geology. It was not until the end of the sixteenth century, when William Gilbert, an eminent practising physician of Colchester, England (1540-1603), published his now famous work on the magnet (De Magnete) that further progress was made through the first rational treatment of electrical and magnetic phenomena. To him is due the name electricity (vis electrica). He regarded the earth as a great magnet and, accepting the Copernican theory, attributed the earth's rotation to its magnetic character. He even extended this idea to the heavenly bodies, with an animistic tendency. Gilbert is also reputed to have done important work in chemistry, but none of this has survived. His work is one of the finest examples of inductive philosophy that has ever been presented to the world. It is the more remarkable because it preceded the Novum Organum of Bacon, in which the inductive method of philosophizing was first explained. Thomas Thomson. The most prolific writer on natural philosophy and physical science of the sixteenth century was G. della Porta (1543-1615), a native of Naples and a resident of Rome, founder of an early scientific academy there, and afterwards of the famous Accademia dei Lincei of Rome. His writings are voluminous and in many books, of which we need mention here only his Magia Naturalis, (1569), De Refractione (1593), Pneumatica (1691), De Distillatione (1604), De Munitione (1608) and De Aeris Transmutationibus (1609). In his Natural Magic, della Porta is the first to describe a camera obscura, besides touching on many interesting properties of lenses, and referring to spectacles, some forms of which had long been known. His work On Refraction deals largely with binocular vision, and is a criticism of the work of Euclid and Galen on that subject. The author hints also at a crude telescope, and may have known some form of stereoscope. Della Porta's compositions range all the way from natural magic to Italian comedies, and entitle him to high rank as a tireless and original, if not especially fruitful, thinker and worker. REFERENCES FOR READING BERRY. History of Astronomy. Chapters IV-VII. BREWSTER. Martyrs of Science. DREYER. Tycho Brahe; Planetary Systems. Chapters XII-XVI. GILBERT. On the Magnet. LOCY. Biology and its Makers. LODGE. Pioneers of Science. CHAPTER XI PROGRESS OF MATHEMATICS AND MECHANICS IN THE SIXTEENTH CENTURY It was not alone the striving for universal culture which attracted the great masters of the Renaissance, such as Brunelleschi, Leonardo da Vinci, Raphael, Michael Angelo and especially Albrecht Dürer, with irresistible power to the mathematical sciences. They were conscious that, with all the freedom of the individual phantasy, art is subject to necessary laws and, conversely, with all its rigor of logical structure, mathematics follows esthetic laws. Rudio. The miraculous powers of modern calculation are due to three inventions: the Arabic Notation, Decimal Fractions and Logarithms. - Cajori. The invention of logarithms and the calculation of the earlier tables form a very striking episode in the history of exact science, and, with the exception of the Principia of Newton, there is no mathematical work published in the country which has produced such important consequences, or to which so much interest attaches as to Napier's Descriptio. Glaisher. It is Italy, which is the fatherland of Archimedes, whose creative power embraces all domains of the mechanical science, the land of the Renaissance, from out of which those mighty waves of new ideas and new impulses in science and art have come forth into the world — the fatherland of Galileo the creator of experimental physics, of Leonardo da Vinci the engineer, of Lagrange who has given its form to modern analytical mechanics. W. v. Dyck. - Dynamics is really a product of modern times, and affords the rare example of a development fulfilled in a single great personage Galileo. Nothing is finer than how he, beginning in the Aristotelian spirit, gradually frees himself from its bondage and, instead of empty metaphysics, introduces well-directed methodical investigations of nature. Timerding. The period from the invention of printing about 1450 to that of analytic geometry in 1637 was one of very great importance for mathematics and mechanics as well as for astronomy. At the beginning, Arabic numerals were known, but the mathematics even of the universities hardly extended beyond the early books of Euclid and the solution of simple cases of quadratic equations in rhetorical form. At the end of the period the foundations of modern mathematics and mechanics were securely laid. AIMS AND TENDENCIES OF MATHEMATICAL PROGRESS. — In the centuries just preceding, the chief applications of mathematics had connected themselves with the relatively simple needs of trade, accounts and the calendar, with the graphical constructions of the architect and the military engineer, and with the sines and tangents of the astronomer and the navigator. During the period in question some of these applications became increasingly important, and at the same time mathematics was more and more cultivated for its own sake. Mathematicians became gradually a more and more distinctly differentiated class of scholars; mathematical textbooks took shape. The beginnings of this evolution have been dealt with already; its further progress is now to be traced. The larger achievements and tendencies of the period in mathematical science were the following: In Arithmetic, decimal fractions and logarithms were introduced, regulating and immensely simplifying computation; a general theory of numbers was developed; in Algebra, a compact and adequate symbolism was worked out, including the use of the signs +, ÷, X, −, =, (), √, and of exponents; equations of the third and fourth degree were solved, negative and imaginary roots accepted, and many theorems of our modern theory of equations discovered. In Geometry, the computation of π was carried to many decimals, the beginnings of projective geometry were made, and a so-called method of indivisibles developed, foreshadowing the integral calculus; in plane and spherical Trigonometry, the theorems and processes now in use were worked out, and extensive tables computed. In Mechanics, ideas about force and motion, equilibrium and centre of gravity, were gradually clarified. Underlying some of these new developments are the dawning fundamental concepts: function, continuity, limit, derivative, infinitesimal, on which our modern mathematics has been built up. Descartes, Newton and Leibnitz are soon to make their revolutionary discoveries in analytic geometry and the calculus. We have seen that up to about 1500 the chief stages in the development of mathematics have been the introduction and improvement of Arabic arithmetic for commercial purposes (though accounts were kept in Roman numerals until 1550 to 1650), the rediscovery of Greek geometry, and the improvement of trigonometry in connection with its increasing use in astronomy, navigation and military engineering. The development of science has been powerfully promoted by the general intellectual emancipation of the Renaissance, while mathematical progress, beginning earlier, has been both a cause and a consequence of the general advance. The diffusion and the preservation of scientific knowledge have derived immense advantage from the new art of printing and from expanding commercial intercourse. Algebra, almost helpless in Greek times because, for lack of proper symbolism, expressed only in geometrical or rhetorical form, has been converted by a process of abbreviation, at first into a syncopated form, intermediate between the rhetorical and our modern purely symbolic notation. PACIOLI.—The earliest printed book on arithmetic and algebra was published at Venice in 1494 by Lucas Pacioli, a Franciscan monk born in Tuscany about 1450. Rules are here given for the fundamental operations of arithmetic, and for extracting square roots. Commercial arithmetic is treated at considerable length by the newer algoristic or Arabic methods. The method of arbitrary assumption corrected by proportion is used effectively, for example: To find the original capital of a merchant who spent a quarter of it in Pisa and a fifth of it in Venice, who received on these transactions 180 ducats, and who has in hand 224 ducats. Assume that his original capital was 100 ducats; then the surplus would be 100 25 2055, but this is of his actual surplus 224180, therefore his original capital was of 100 = 80 ducats. |