Mathematics
Mathematics
Exhibit items on the subject of mathematics.
Exhibit Items
Map of the Moon Hevelius, Johann (1647) Accurate depiction of the topography of the Moon was accomplished by midcentury in this lunar atlas by Hevelius. It set a new standard for precision that remained unmatched for a century. 

The Great Art of Light and Shadow Kircher, Athanasius (1646) A “camera obscura” (“dark room”) consists of a box or container in which light enters via a small hole and projects an image on an opposite wall. The image will be reversed and upsidedown, but its proportions will be preserved. 

Elements of Geometry, 1570 Euclid, (1570) Euclid was the starting point for any further study of optics and perspective. Optics combined geometry, experiment, vision and art. In the presentation of the geometrical solids, this copy retains the original popups. 

Moral Essays Alberti, Leon Battista (1568) This anthology of the works of Alberti, a humanist scholar, contains the printed edition of his treatise, “On Painting,” a work he originally dedicated to Brunelleschi. 

Celestial Atlas, 1729 Flamsteed, John (1729) A globe maker for the French royal family, J. Fortin, prepared this edition of Flamsteed’s celestial atlas in a much reduced format. Flamsteed was the first Astronomer Royal, who oversaw the building of the Greenwich Observatory. Newton relied upon Flamsteed’s star positions in his Principia. 

Perspective Peckham, John (1556) The Perspectiva of Peckham (13th century) became the established university textbook on perspective. It was the text Galileo likely used in his early studies of optics. Renaissance artists were wellversed in the classic works on perspective. 

Celestial Globe Gores Coronelli, Vincenzo (1693; reprint ca. 1800) Coronelli, a Franciscan theologian and astronomer who worked in both Italy and France, was a founder of modern geography and an influential maker of celestial and terrestrial globes. 

Principles of Geometry Dürer, Albrecht (1535) This landmark work by Albrecht Dürer presents several variations on the technique of “Alberti’s window.” Here the artist is creating a drawing of a lute with true perspective by means of a string drawn from the object, through the canvas window, to the vanishing point on the wall. 

Essays of the Members of the Academy of Gelati (1671) This is the scarce first edition of writings by a leading learned society in Bologna, the Accademia dei Gelati. The volume includes striking woodcuts by the astronomer Geminiano Montanari of white stars against a black background. 

The Curiosities of Perspective Nicéron, Jean François (1663) While visiting Florence, Niceron was shown a unique perspective drawing tool devised by the painter Cigoli, one of Galileo’s friends. He viewed examples of anamorphic drawing techniques and Alberti’s perspective boxes. All of these make an appearance in this treatise. 

Measuring the Heavens Bayer, Johann (1661) In contrast to Piccolomini, who omitted constellation figures in favor of scientific accuracy, Bayer superimposed constellation figures upon the star maps without compromising positional accuracy. These figures were artfully drawn by Alexander Mair. 

The Divine Proportion Pacioli, Luca (1509) Consider this geometrical drawing, portrayed with true perspective and a mastery of light and shadow. It comes from a treatise on art and mathematics by Luca Pacioli, yet it was not drawn by Pacioli. 

On the Fixed Stars Piccolomini, Alessandro (1540) In contrast to the constellation figures in Hyginus and Abu Ma’shar, Piccolomini created a star atlas, measuring the positions of the stars according to an indicated scale (specific to each plate). He designated stars by Roman letters (a, b, c, etc.) in order of apparent brightness. 

The Practice of Perspective Sirigatti, Lorenzo (1596) This beautiful work by Sirigatti, published in 1596, brings the tradition of perspective drawing up to Galileo’s time. Sirigatti was a member of the Academy of Drawing (Accademia del Disegno), a school for artists and engineers where Galileo studied as a young man. 

On the New Star in the Foot of the Serpent Handler Kepler, Johann (1606) Kepler’s star map shows the constellations of Ophiuchus (the Serpent Handler), Sagittarius and Scorpius. The Milky Way runs diagonally down from the left, and the “ecliptic,” or annual path of the Sun, runs horizontally through Sagittarius and Scorpius. 

Treasury of Optics alHaytham, Ibn (1572) The frontispiece depicts a variety of optical phenomena: Reflection. Refraction. Perspective. The rainbow. Burning mirrors. 

On the Revolutions of the Heavenly Spheres, 1566 Copernicus, Nicolaus (1566) Copernicus argued that the Sun rather than the Earth lies in the center of the universe. The Earth moves as a planet around the Sun, carrying its Moon along as a satellite. In 1543 little proof was available that the Earth moves; there were many reasons not to accept it. 

Treatise on Painting da Vinci, Leonardo (1651) Despite a lack of publications, Leonardo’s fame grew as word of his notebooks spread. The first book by Leonardo to be printed was his Treatise on Painting, published a century after his death. 

Works, Ptolemy Ptolemy, (1541) For this first edition of Ptolemy’s collected works, Johann Honter drew constellation figures after the manner of Albrecht Dürer. The figures appear in contemporary dress rather than in a classical style. 

Works… A New Science Tartaglia, Niccolo (1606) Niccolò Tartaglia argued for the use of mathematics in physics, engineering and art. Tartaglia’s frontispiece shows Euclid guarding the gate of knowledge. Just inside, Perspectiva stands among the sciences that open the way to Philosophia. 

Starry Messenger Galileo, (1610) Featuring Galileo's Handwriting. When Galileo heard news of telescopes invented in the Netherlands he worked out the underlying geometry and crafted one of his own design. In this work, Galileo published the first observations of the heavens made with the telescope. 

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Kepler's Universe Mitchell, Ron 

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Tellurian, Trippensee Planetarium Company (19081920) 

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Paul E. Klopsteg Collection of the History and Technology of Archery, miscellaneous items. Klopsteg, Paul E. 

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Mathematical Principles of Natural Philosophy, 1713 Newton, Isaac (1713) 

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Secret Book of the Quiver Ise, Heizo Sadatake (ca. 1846) Manuscript copy by Hajime Terai from original written in 1765 by Ise; illustrations copied by Odani. 

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The Operations of the Geometrical and Military Compass, 1606 Galilei, Galileo (1606) Featuring Galileo's Handwritting. Galileo dedicated the manual for his engineering compass to young Cosimo II de Medici, whom he had tutored in mathematics the previous summer. 

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Mathematical Principles of Natural Philosophy, 1729 Newton, Isaac (1729) This is the first English translation of Newton’s masterwork in physics. The Copernican idea that the Earth moves as a planet required a thorough revision of physics. Galileo undertook this task in his Discourse on Two New Sciences, published 80 years after Copernicus. 

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Almagest, ed. Regiomontanus Ptolemy, Claudius (1496) Ptolemy (Claudius Ptolemaios) lived in Alexandria, Egypt, in the second century. Ptolemy’s technical work on astronomy, originally written in Greek, was titled Almagest (“The Greatest”) by its Arabic translators. 

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Letters on Sunspots Galileo, (1613) In a 1611 book published by the Academy of the Lynx, the Jesuit astronomer Christoph Scheiner argued that sunspots are little planets circling the Sun like Venus. Galileo answered Scheiner with this book. 

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On the Christian Expedition to China Ricci, Matteo (1616) This book recounts the establishment of the Jesuit mission in China in the late 1500s led by Matteo Ricci. When Ricci predicted a solar eclipse in 1592 with greater accuracy than the astronomers of the Chinese court, Emperor Wanli invited Ricci to Beijing. 

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Sundial replica (2015) A sundial consists of a gnomon, which casts the Sun’s shadow, and a dial on which the shadow indicates the time. This simple portable sundial features a gnomon that can be adjusted according to one’s latitude. Sundials have ranged in size from pocketdials to monumental architecture. 

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Ecstatic Journey through the Heavens Kircher, Athanasius (1660) Six chief world systems were debated in Galileo’s world: • Ptolemaic: All planets revolve around the central Earth. Geocentric. • Platonic: Like the Ptolemaic, except switches the positions of Venus and Mercury. Geocentric. • Cappellan or Egyptian: Venus and Mercury revolve around the Sun. 

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The Divine Plato Plato, (1491) In his dialog entitled The Timaeus, Plato taught that the cosmos is constructed from regular geometrical figures known as the Pythagorean solids. Wherever one finds an emphasis upon mathematical demonstrations in science, one may credit Plato and the Pythagoreans. 

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Polyhedral Sundial replica This is a replica of an original polyhedral sundial created by Stefano Buonsignori in Florence in 1587, held in the Museo Galileo in Florence. 

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The Marriage of Philology and Mercury Capella, Martianus (1499) Capella described the seven liberal arts. The first three are grammar, logic or dialectic, and rhetoric. Then come the mathematical sciences, geometry and arithmetic. Geometrical circles in motion make astronomy. Numbers in motion make music. 

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Elements of Geometry, 1482 Euclid, (1482) Euclid was the starting point for a mathematical approach to physics. This is the 1st printed edition. The beautiful woodcuts are handcolored in this copy. The text of the first page was printed in both black and red ink. The geometrical diagrams were quite difficult to prepare. 

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Book on Calculation Borgi, Pietro (1517) Borgi’s book on the abacus was the most important commercial arithmetic manual in Renaissance Italy. Around 1200, Leonardo of Pisa, also known as Fibonnacci, wrote an earlier manual for the abacus which introduced a sign for zero, HinduArabic numerals, and a base10 place value system. 

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The Divine Comedy Dante, (1757) Dante’s love for astronomy pervaded this epic poem. Not by accident did he bring each of the three volumes to a close with the word “stelle,” or star. 

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Star Viewer Schickard, William (1698) Schickard, a friend of Kepler’s, designed this planisphere or “astroscopium” to calculate the positions of the stars for any day and hour of the year. Schickard also devised a calculating machine to produce astronomical tables according to Kepler’s laws. 

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Discourse on Floating Bodies Galileo, (1612) To provide entertainment at a dinner held by the Grand Duke of Tuscany, Galileo debated the Aristotelian physicist Lodovico delle Columbe on the topic of floating bodies. Galileo employed Archimedes’ mathematical analysis. 

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Galileo Compass replica Galileo’s engineering compass employed scales of his own innovative design, useful for an astonishing variety of calculations in the field. 

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Meteorology, 1556 Aristotle, (1556) In a discussion of optical effects of the atmosphere, Aristotle here addresses the formation of a halo around the Moon. This is one of the most interesting uses of mathematics in all of Aristotle’s writings. 

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Almagest, ed. Reinhold Ptolemy, Claudius (1549) Erasmus Reinhold, a professor at Wittenberg who was sympathetic to Copernicus, published the first Greek edition of Ptolemy’s Almagest. 

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Wonderful Machines of the Far West Schreck, Johann (1830) Schreck helped Galileo show the telescope to the Medici family and others in Rome. Once he arrived in China, he wrote this work on engineering in Chinese. 

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Principles of Astronomy Naibod, Valentin (1580) This Copernican cosmic section, the first published in Italy, appears in a sympathetic account, known to Tycho and to Kepler, which may have influenced Galileo. Naibod was a professor of mathematics at Padua who likely studied with Erasmus Reinhold in Wittenberg. 

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Works in Greek, vol. 1 Aristotle, (14951498) In a work entitled “On the Universe,” Aristotle argued that a 5th element, called ether or the quintessence, composes the celestial spheres that naturally rotate in place above the region where the four lower elements mix together beneath the Moon. 

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Natural Magic, 1589 Porta, Giambattista della (1589) In this postersized work, the first publication of observations made with a microscope, Cesi and Stelluti studied the anatomy of the bee. The text includes classical references to bees as well as new knowledge, integrated in a tabular outline. 

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Euclid's Elements of Geometry, 1594 AlTusi, Nasir adDin (1594) This Arabic text of Euclid came from the circle of the Persian astronomer alTusi (13th century). AlTusi worked in Baghdad and in the observatory of Maragha, in modern northwestern Iran. Printing Arabic with moveable type was a technological challenge. 

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Considerations on Galileo's Discourse on Floating Bodies Pannochieschi, Arturo (1612) Pannochieschi, head of the University of Pisa, defended Columbe, widening the debate over floating bodies and exemplifying the Aristotelian physicists’ reaction to Galileo’s use of Archimedean methods. In response, Galileo published a 2d ed. 

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Demonstration of the Halo Reinhold, Erasmus (c. 1550) This manuscript contains two transcriptions of a university lecture by Erasmus Reinhold. The diagrams are nearly identical to Aristotle’s discussion of halos in the Meteorology. Reinhold was a wellknown Wittenberg astronomer, sympathetic to Copernicus. 

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Historical Narration of the Origin and Progress of the Mission to China Schall, Adam (1665) This book is Schall’s account of the Jesuit mission in China after Ricci. Working closely with Chinese collaborators, Schall oversaw the publication of more than 30 scientific works in Chinese which drew upon Galileo, Copernicus, Tycho, Kepler and John Napier. 

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Commentary on the Sphere of Sacrobosco Clavius, Christoph (1570) Clavius taught mathematical astronomy in the Rome College (Collegio Romano), the leading Jesuit university in Rome. Aristotle did not emphasize mathematics, but Clavius’ lifelong work established mathematics and astronomy as essential areas of study for Jesuit schools. 

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On the Motion of Animals, 1685 Borelli, Giovanni (1685) This work of sports medicine analyzes the physics of bones and muscles. Borelli, a practicing mathematician and engineer as well as a physician, analyzed the musculoskeletal system in terms of the mechanics of the lever and other simple machines. 

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Works in Greek, vol. 2 Aristotle, (14951498) In a work entitled “On the Universe,” Aristotle argued that a 5th element, called ether or the quintessence, composes the celestial spheres that naturally rotate in place above the region where the four lower elements mix together beneath the Moon. 

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Natural Magick, 1658 Porta, Giambattista della (1658) In Natural Magick, della Porta described an optical tube he designed to make far things appear as though they were near. The field of optics was often associated with magical tricks and illusions, and for that reason sometimes held suspect among nonmathematicians. 

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Chronicle of Mathematics Baldi, Bernardino Bernardino Baldi was an Italian mathematician whose work gives insight into the milieu of Galileo. This is one of two autograph manuscripts by Baldi held by the Collections. 

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On Mathematics Schott, Gaspar (1668) In this mathematics textbook, Schott explained the rodbased calculating machine designed by his fellow Jesuit, Athanasius Kircher. The philosopher Leibniz also created a calculating machine, described in 1666, which he offered to the emperor of China. 

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Euclide Tartaglia, Niccolo (1543) Tartaglia, a teacher of a teacher of Galileo, produced the first vernacular translation of Euclid’s Elements of Geometry. 

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Considerations on Tasso Galileo, (1793) Galileo employed his scientific acumen to engage in the literary debates of the day. Here he considered the merits of Tasso and Ariosto, comparing both with Dante. Using his new physics of tensile strength, Galileo refuted Ariosto’s indiscriminate descriptions of giants. 

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Harmonics Ptolemy, Claudius (1682) Ptolemy’s influential music theory was related to his astronomy. Through sight, we apprehend beauty through astronomy. Through hearing, we apprehend beauty through harmony. 

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Works in Greek, vol 3 pt. A Aristotle, (14951498) In a work entitled “On the Universe,” Aristotle argued that a 5th element, called ether or the quintessence, composes the celestial spheres that naturally rotate in place above the region where the four lower elements mix together beneath the Moon. 

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Response to the Opposition of Lodovico delle Colombe Galileo, (1615) Some of Galileo’s most avid opponents were Aristotelian physicists who, lacking training in mathematics, were unable to refute Galileo’s arguments. 

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A Description of the Marvelous Rule of Logarithms Napier, John (1614) In this book, Napier presented logarithmic methods of calculation in more than 50 pages of explanation, followed by 90 pages of numerical tables. “Logarithm” derives from “logos” (proportion) and “arithmos” (number). 

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Euclid's Elements of Geometry, 1589, vol. 1 Clavius, Christoph (1589) Not all versions of Euclid’s Elements were created equal. Clavius prepared this edition for his students at the Rome College (Collegio Romano). If these editions of Euclid were used in different courses, which course would you take? 

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On Secret Writing Porta, Giambattista della (1563) Members of the Academy of the Lynx preferred to communicate with each other in code. Della Porta was the most accomplished cryptographer of the Renaissance. This work includes a set of movable cipher disks to code and decode messages. 

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The Operations of the Geometrical and Military Compass, 1635 Galilei, Galileo (1635) After Capra, the design of Galileo’s compass became widely known. Later editions included illustrations of Galileo’s instrument. 

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Universal Geography Ptolemy, Claudius (1545) Although best known for his astronomy, Ptolemy (2nd century) brought the same mathematical methods to bear on various topics, including optics, geography, and astrology. This is the first printed edition of his geography, which established mathematical methods in cartography. 

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Galileo Thermoscope replica, National Weather Center Galileo’s thermoscope, ancestor to the thermometer: Galileo pioneered scientific investigations with the thermoscope along with his two Paduan friends, Giovanni Sagredo and Santorio Santorio. 

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Nocturnal Dial replica (2006) Nocturnal dials tell time by the stars. This instrument replicates an original nocturnal dial created by Girolano della Volpaia in Florence in 1569, held in the Museo Galileo in Florence. 

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On the Revolutions of the Heavenly Spheres, 1543 Copernicus, Nicolaus (1543) Copernicus argued that the Sun rather than the Earth lies in the center of the universe. The Earth moves as a planet around the Sun. In 1543 little proof was available that the Earth moves; there were many reasons not to accept it. 

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On the Snowflake, or the SixAngled Crystal Kepler, Johann (1611) Kepler’s contributions reached far beyond the realm of astronomy, to meteorology, mathematics, geology, mineralogy and crystallography. Kepler published this 24page pamphlet, a study of the snowflake, as a New Year’s greeting for a friend. 

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Works in Greek, vol 3 pt. B Aristotle, (14951498) In a work entitled “On the Universe,” Aristotle argued that a 5th element, called ether or the quintessence, composes the celestial spheres that naturally rotate in place above the region where the four lower elements mix together beneath the Moon. 

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Discourse on Two New Sciences, vol. 1 Galileo, (1656) In this masterwork of physics, Galileo studied the two sciences of tensile strength and motion. The science of tensile strength considers how larger objects must bear more and more weight to perform the same action. 

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Description and Use of an Instrument, Called the Double Scale of Proportion Partridge, Seth (1692) After a century of calculating instrument innovation, Partridge created the sliderule. Edmund Gunter designed a logarithmic scale in 1620. William Oughtred placed two logarithmic scales sidebyside to perform multiplication and division in 1630. 

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Euclid's Elements of Geometry, 1589, vol. 2 Clavius, Christoph (1589) Not all versions of Euclid’s Elements were created equal. Clavius prepared this edition for his students at the Rome College (Collegio Romano). If these editions of Euclid were used in different courses, which course would you take? 

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Cosmography, 1574 Munster, Sebastian (1574) Munster’s Cosmography was one of the most popular books of the 16th century. In addition to the map of the world, it includes separate maps for America, Africa, Asia and Europe. First published in 1540, at least 24 editions were published in the following century. 

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The Assayer, early state Galileo , (1623) The crest of the Barberini family, showing three busy bees, appears at the top of the frontispiece. Galileo’s supporter, Cardinal Maffeo Barberini, had become Pope Urban VIII. The election of Barberini seemed to assure Galileo of support at the highest level in the Church. 

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Demonstration Slide Rule The slide rule is based on logarithms. With a slide rule, one may quickly and reliably calculate to a precision of about 3 digits. Until the pocket calculator became available in the mid1970‘s, slide rules were in constant use by scientists and engineers. 

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Discourse on Two New Sciences, vol. 2 Galileo, (1656) In this masterwork of physics, Galileo studied the two sciences of tensile strength and motion. The science of tensile strength considers how larger objects must bear more and more weight to perform the same action. 

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Problems and Exercises in Aristotle’s Mechanics Baldi, Bernardino (1621) Aristotle’s Mechanics contained an analysis of the principles of motion and simple machines. While no longer accepted as an authentic work by Aristotle, its influence among Renaissance scientistengineers was profound, as illustrated in this commentary by Baldi. 

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Instruments for the Restoration of Astronomy Brahe, Tycho (1602) For two decades, Tycho and his assistants at Uraniborg produced thousands of astronomical observations of unprecedented quality. Tycho’s largescale observing instruments, together with sophisticated new error correction techniques, increased observational precision by a factor of twenty. 

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Works in Greek, vol. 4 Aristotle, (14951498) In a work entitled “On the Universe,” Aristotle argued that a 5th element, called ether or the quintessence, composes the celestial spheres that naturally rotate in place above the region where the four lower elements mix together beneath the Moon. 

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The Rudolphine Tables Kepler, Johann (1627) From his new astronomy, using Tycho’s observations, Kepler calculated these tables of the positions of the Sun, Moon and planets. Kepler adopted John Napier’s recently invented computational method of logarithms, published in 1614. 

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New Science Tartaglia, Niccolo (1558) Tartaglia’s compass (also known as a “sector”) incorporated the functions of a quadrant and a caliper measuring device. His “new science” investigated the ballistics of cannonballs, laying a foundation for Galileo’s studies of projectile motion and free fall. 

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The Assayer, later state Galileo , (1623) Although Galileo eloquently championed mathematical methods in science, the main target of his wit and sarcasm in The Assayer was Grassi, a fellow astronomer, whose mathematical methods proved that comets move above the Moon. 

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On the Sizes and Distances of the Sun and Moon Samos, Aristarchus of (1572) Aristarchus, the Copernicus of antiquity, proposed in the 3rd century B.C.E. that the Sun lies at the center of the universe and that the Earth and other planets revolve around the Sun. 

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Astronomical Letters Brahe, Tycho (1596) In this work, Tycho explained two problems posed for Copernicus by the absence of stellar parallax: 1. Due to the annual movement of the Earth around the Sun, one would expect to see stars appear to shift in position. This parallax evaded detection, even at Uraniborg. 2. 

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Sacred Mystery of the Structure of the Cosmos Kepler, Johann (1596) By far the best known 16thcentury defender of Copernicus was Johann Kepler. In this work he demonstrated that vast empty regions lying between the planetary spheres, which were required by Copernicus, were not wasted space. 

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Works, Archimedes Archimedes, (1543) Archimedes (d. 212 B.C.) developed the law of the lever with his Treatise on the Balance. He contributed to arithmetic by devising methods for expressing extremely large numbers. He deduced many new geometrical theorems on spheres, cylinders, circles and spirals. 

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Notes Lovelace, Ada (1843) These notes comprise one of the most important papers in the history of computing. Lovelace explained how Babbage’s “analytical engine,” if constructed, would amount to a programmable computer rather than merely a calculator. 

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Works in Greek, vol. 5 Aristotle, (14951498) In a work entitled “On the Universe,” Aristotle argued that a 5th element, called ether or the quintessence, composes the celestial spheres that naturally rotate in place above the region where the four lower elements mix together beneath the Moon. 

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Apple Computer (1984) The original 256K Macintosh computer was the first consumermarketed personal computer to support mouse input and a windowsbased graphical user interface. 

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Treatise on the Measuring Stick Orsini, Latino (1583) This book is Orsini’s manual for using a measuring stick instrument which he designed and called a “radio latino.” With its changing angles, multiple sight lines, and various scales, it was useful for making astronomical measurements, surveying uneven topography, measuring a cannon’s bore or... 

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Treatise on the Sphere Grassi, Oratio (1623) In the same year that Galileo published The Assayer, Grassi delivered these lectures to Jesuit students in the Rome College (Collegio Romano). 

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On the Sphere, 1511 Proclus, (1511) This work was attributed to Proclus (5th century), one of the most important Neoplatonic philosophers of late antiquity. It became one of the most popular introductions to astronomy during the Italian Renaissance, appearing in more than 70 16thcentury editions. 

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On Meteorology Descartes, René (1637) This essay on meteorology contains Descartes’ explanation of the optics of the rainbow and his law of refraction. Descartes’ ambitious aim was to produce a new body of writings that would completely displace the Aristotelian corpus. 

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Complete Works Brahe, Tycho (1648) In De mundi aetherei (1588), Tycho reported that the comet of 1577 displayed no detectable parallax and thus moved, contrary to Aristotle, in the regions of the heavens beyond the Moon, passing through multiple celestial spheres. The ancient solid spheres melted. 

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A Geometrical Reconstruction of On Conic Sections by Aristaeus Viviani, Vincenzo (1701) In this work, Viviani reconstructed an ancient study of conic sections by Aristaeus the Elder (4th century B.C.E.). Viviani became Galileo’s student and assistant in 1639. 

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Admonition to Astronomers Kepler, Johann (1630) The Rudolpine Tables were not a best seller. Three years later, Kepler and his soninlaw Jacob Bartsch published this little extract to stir up interest in the Rudolphine Tables and boost sales. It contains predictions of the transits of Mercury and Venus across the disk of the Sun in 1631. 

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On Conic Sections Apollonius, (1710) Apollonius (3rd century B.C.E.) examined the properties of conic sections; namely, the: • circle (cuts a cone horizontally, perpendicularly to the axis of the cone) • ellipse (cuts a cone to make a closed curve) • parabola (cuts a cone parallel to a side of the cone) • hyperbola (cuts a cone in... 

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On the Use and Fabrication of the Astrolabe Danti, Egnazio (1578) Danti was a cosmographer in the court of Cosimo I de Medici. Visitors to Florence today may view his stunning maps of the world in the Hall of Maps of the Palazzo Vecchio, as well as armillary spheres and a quadrant he mounted on the facade of the church of Santa Maria Novella. 

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Abacus model The abacus, an ancient calculating machine, is still in use around the world. Counters consisting of pebbles in the sand, beads on a wire or knots on a string are shifted back and forth on each level to represent different quantities, such as units and tens. 

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On the Revolutions of the Heavenly Spheres, 1617 Copernicus, Nicolaus (1617) In De revolutionibus, Copernicus placed the Sun in the center of the universe and set the Earth in annual motion around the Sun. This is the 3d edition, printed in 1617, the year after the Inquisition stimulated fresh interest in the work by placing it on the Index of Prohibited Books. 

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Galileo Thermoscope replica, Bird Health Sciences Library Galileo’s thermoscope, developed in the context of pneumatic engineering, was an ancestor to the thermometer. Galileo pioneered scientific investigations with the thermoscope along with his two Paduan friends, Giovanni Sagredo and Santorio Santorio. 

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The Burning Mirror Cavalieri, Bonaventura (1632) Archimedes died defending the ancient city of Syracuse, on the island of Sicily, from the Carthaginian navy. Reports attributed the defense of the city to his ingenuity, including giant mirrors capable of setting attacking ships in the harbor on fire. 

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The Generous Muse of the Heavens Cunitz, Maria (1650) Prior to Newton, fewer than half a dozen astronomers accepted Kepler’s three laws. Galileo was typical in ignoring everything Kepler did. Yet this beautiful book is an exception: it clearly demonstrated that Kepler’s laws were more accurate than anything that had come before. 

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Introduction to the Astrolabe Lansbergen, Philip van (1635) Astronomers use astrolabes for dozens of astronomical operations including telling time by the Sun or stars and determining the positions of planets. 

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Treatise on Painting da Vinci, Leonardo (1716) Despite a lack of publications, Leonardo’s fame grew as word of his notebooks spread. The first work by Leonardo to be printed was his Treatise on Painting, published a century after his death. That 1651 Italian edition is on display at the Fred Jones Jr. Museum of Art in Spring 2016. 

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Commentary on AlQabisi AlQabisi, (1512) This medieval introduction to astrology was frequently translated from Arabic into Latin. AlQabisi lived in the 10th century in Syria. 

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On the Sphere of the Universe bar Hiyya, Abraham (1546) Abraham bar Hiyya, also known as Savasorda, was a 12th century Jewish mathematician and astronomer in Barcelona. In this beautiful introduction to astronomy, bar Hiyya’s text appears in Hebrew alongside a Latin translation. 

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On the Motion of Animals, 1680  81 Borelli, Giovanni (168081) The physics of bones and muscles: Borelli, a practicing mathematician and engineer as well as a physician, analyzed the musculoskeletal system in terms of the mechanics of the lever and other simple machines. Borelli studied under Galileo’s student Castelli, along with Torricelli. 

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Commentary on Aristotle’s Posterior Analytics Philoponus, (1504) In the 6th century, the Greek physicist and theologian Philoponus constructed an antiAristotelian theory of motion. For Philoponus, an “impressed incorporeal motive force” explains the motion of a top, a projectile, and falling bodies. 

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The Elements of Euclid , (1847) Colorcoded, graphical proofs occur in this masterpiece of visual presentation and design. Text is dramatically reduced in favor of a strategy of visual thinking. 

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On the Quadrant Lansbergen, Philip van (1635) Astronomers use quadrants and sextants to measure angular distances in the night sky, such as the angular divergence between a planet and the nearest bright star. One may also measure the height of the North Star above the horizon, which is equal to one’s latitude on the Earth. 

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Mathematical Works Stevin, Simon (1634) Stevin’s work represents that of a scientistengineer in the Low Countries, whose major works appeared in Dutch. Like the scientistengineers of Italy, Stevin maintained water systems and improved fortifications. He investigated the mechanics of motion, falling bodies and hydraulics. 

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Sextant replica An astronomer might use a sextant or quadrant to measure the distance between a planet and a notable bright star, or the altitude of a star above the horizon. 

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On the Sphere Sacro Bosco, Joannes de (1490) In University study from the 13th through 16th centuries, the most common introduction to the geocentric cosmos was the medieval work, On the Sphere, by Sacrobosco. 

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Cosmography, 1585 Barozzi, Francesco (1585) The illustrations in this cosmography show its indebtedness to the Sacrobosco tradition. Barozzi, a humanist scholar who lectured at the University of Padua, provided an updated introduction to observational astronomy, intended as a replacement for Sacrobosco and Peurbach. 

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On the Center of Gravity of Solids, 1661 Valerio, Luca (1661) Analyzing the center of gravity of an object was a traditional problem addressed using the methods of Archimedes. Galileo referred to Valerio as “the Archimedes of our age” and recommended him for membership in the Academy of the Lynx. 

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The New Almagest, part 1 Riccioli, Giambattista (1651) The frontispiece of Riccioli’s treatise depicts not two, but three major systems of the world. The Ptolemaic system rests discarded (lower right corner) because of the phases of Venus and Mercury (upper left corner). Allseeing Argus looks on, holding a telescope. 

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Description and Use of Both the Globes, the Armillary Sphere, and Orrery Martin, Benjamin (ca. 1760) This book explains how to use the terrestrial and celestial globes, an armillary sphere (which shows the movements of the sky), and an orrery (which models the motions of the planets). Martin operated an instrument shop in London. 

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On the Magnet Gilbert, William (1600) Gilbert, a physician to Queen Elisabeth I, wrote the first experimental treatise devoted to magnetism. Gilbert discerned analogies between the Earth and magnets, and reasoned that the Earth itself is a magnet. 

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On Perspective Monte, Guidobaldo del (1600) Kepler, Galileo and Guidobaldo were the leading optical theorists of their generation. Galileo studied with Guidobaldo while he was composing this treatise. 

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Delamarche Orrery An orrery, also called a planetarium, shows the choreography of planets as they dance with coordinated precision around the Sun. From antiquity, geocentric (Earthcentered) models of the moving planets were constructed, such as the Antikythera device and large mechanical clocks. 

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The New Almagest, part 2 Riccioli, Giambattista (1651) The frontispiece of Riccioli’s treatise depicts not two, but three major systems of the world. The Ptolemaic system rests discarded (lower right corner) because of the phases of Venus and Mercury (upper left corner). Allseeing Argus looks on, holding a telescope. 

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On Mechanics Monte, Guidobaldo del (1577) Hero described five simple machines: the lever, pulley, wheel, wedge and screw. In this theoretical investigation of the foundations of mechanics, Guidobaldo demonstrated that all five machines could be deduced from the principle of the lever. 

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Galileo, Mechanics Marsenne, Marin (1634) As a young scientistengineer, Galileo wrote two manuscripts on motion. The first, Delle macchine, written ca. 1592; reflected the tradition of Aristotle’s Mechanics. It was never printed. The second, revised study, Le mechaniche, written ca. 

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Astronomy Explained upon Sir Isaac Newton's Principles Ferguson, James (1809) Ferguson’s books, orreries, clocks and mechanical devices were studied with interest by Benjamin Franklin, Thomas Paine and William Herschel, among others. 

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Mathematical Principles of Natural Philosophy, 1687 Newton, Isaac (1687) The Copernican idea that the Earth moves as a planet required a thorough revision of physics. Galileo undertook this task in his Discourse on Two New Sciences, published 80 years after Copernicus. 

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Mathematical Discourses Galileo , (1730) This is the first separate English edition of Galileo’s Discourse on Two New Sciences, his masterwork in mathematical physics. The “two new sciences” are tensile strength and motion. 

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Army Sanitary Administration and its Reform under the late Lord Herbert Nightingale, Florence (1862) Organization of nursing as a profession: Florence Nightingale championed social reform and the organization of nursing as a profession. 

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Newtonianism for Women Algarotti, Francesco (1737) Algarotti’s popular introduction to Newtonian science went through many editions and aided in the dissemination of Newtonian ideas on the European continent. It was dedicated to Fontenelle. Like Fontenelle’s Plurality of Worlds, it was written as an entertaining dialogue. 

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Book of the Arrow Nobutoyo, (ca. 1846) Galileo’s mechanics demonstrated that projectiles follow a parabolic path. This is true whether the projectile is a cannonball, an arrow or a football. This set of four Japanese Samurai manuscripts, drawn on rice paper in the mid 1800’s, was copied by hand from mid16thcentury sources. 

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An Account of a New Discovered Motion of the Fix’d Stars Bradley, James (1729) Direct observational proof of the motion of the Earth remained difficult to find, even as late as the generation of Isaac Newton. 

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On the Proper Motion of Fixed Stars Bessel, Wilhelm Scientific theories may be accepted on the basis of a weighing of many complex factors rather than a single determinative observation or crucial experiment. From antiquity, Copernicanism had been rejected due to a failure to observe stellar parallax. 

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Book of Leggings Nobutoyo, (ca. 1846) Galileo’s mechanics demonstrated that projectiles follow a parabolic path. This is true whether the projectile is a cannonball, an arrow or a football. This set of four Japanese Samurai manuscripts, drawn on rice paper in the mid 1800’s, was copied by hand from mid16thcentury sources. 

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Physical Demonstration of the Rotational Movement of the Earth Foucault, Léon (1851) The Foucault pendulum swings in a constant plane or direction, and thus reveals the rotation of the Earth turning underneath. 

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Secret Book of Hunger for the Target Ise, Heizo Sadatake (ca. 1846) Galileo’s mechanics demonstrated that projectiles follow a parabolic path. This is true whether the projectile is a cannonball, an arrow or a football. This set of four Japanese Samurai manuscripts, drawn on rice paper in the mid 1800’s, was copied by hand from mid16thcentury sources. 

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Physical Demonstration of the Rotational Movement of the Earth Foucault, Léon (1851) The Foucault pendulum swings in a constant plane or direction, and thus reveals the rotation of the Earth turning underneath. 

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The Centenary of General Relativity, misc. items Einstein, Albert (19152015) The 20152016 year is the centenary of Einstein’s General Theory of Relativity. Einstein attributed the formulation of the principle of the relativity of motion to Galileo. 