##### Galileo’s World at a Glance

Gallery at the Exhibit Website

Location: Bizzell Memorial Library, 5th floor Exhibit Hall.

How did Galileo create a mathematical physics?

In 1638, Galileo published his masterwork of physics, *Discourse on Two New Sciences*. The two sciences were tensile strength and mechanics, the study of machines in motion. Instead of basing physics on logic and qualitative principles, Galileo exemplified a new experimental and mathematical approach to physics. With Newton’s mathematical physics the following generation, this approach would transform understanding of motion and even of the universe itself.

“Philosophy (i.e., physics) is written in that great book which ever lies before our eyes — I mean the universe — but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.” Galileo Galilei,

Il Saggiatore(The Assayer, 1623)

Introductory video: Letter from Galileo’s Daughter

### Section 1: Machines in Motion

Scientist-engineers of the 16th century debated the theoretical principles of machines in motion. Ancient sources included a treatise on mechanics attributed to Aristotle; the mathematical methods of Archimedes; and Hero of Alexandria’s analysis of five simple machines: the lever, pulley, wheel, wedge and screw. The design of large-scale, complex machines drew attention to weaknesses in existing theoretical frameworks which Galileo resolved in his new science of motion.

**Euclid**,*Preclarissimus liber elementorum*(Venice, 1482), “Elements of Geometry”- Nasir ad-Din
**al-Tusi**,*Kitab tahrir usul l-Uqlidus*(Rome, 1594), “Euclid’s*Elements of Geometry*“ - Niccolo
**Tartaglia**,*Euclide*(Venice, 1543), “Euclide” - Christoph
**Clavius**,*Euclidis elementorum*(Rome, 1589), 2 vols, “Euclid’s*Elements of Geometry*, 2 vols. - Bernardino
**Baldi**,*In mechanica Aristotelis problema exercitationes*(Mainz, 1621), “Problems and Exercises in Aristotle’s Mechanics” **Archimedes**,*Opera*(1543), “Works”**Apollonius**,*Conicorum*(Oxford, 1710), “On Conic Sections”- Bonaventura
**Cavalieri**,*Lo Specchio Ustorio*(Bologna, 1632), “The Burning Mirror” - John
**Philoponos**,*In posteriora resolutoria Aristotelis Comentaria*(Venice, 1504), “Commentary on Aristotle’s Posterior Analytics” - Simon
**Stevin**,*Les Oeuvres Mathematiques*(Leiden, 1634), “Mathematical Works” - Luca
**Valerio**,*De centro gravitatis solidorum*(Bologna, 1661), “On the Center of Gravity of Solids” - Guidobaldo del Monte,
*Perspectivae*(Pesaro, 1600), “On Perspective” - Guidobaldo del Monte,
*Mechanicorum*(Pisa, 1577), “On Mechanics” - Marin
**Mersenne**,*Les Mechaniques du Sieur Galilée*(Paris, 1634), “Galileo, Mechanics” **Galileo**,*Mathematical Discourses*(London, 1730), trans. Thomas Weston- Inclined plane, crafted by Ron Mitchell (University of Oklahoma Libraries, 2015).
- Nobutoyo, Yahon Hiden, “Book of the Arrow” (ca. 1846). Manuscript copy by Hajime Terai from 1556 original written by Nobutoyo, illustrations copied by Odani
- Nobutoyo, Koto no sho, “Book of Leggings” (ca. 1846). Manuscript copy by Hajime Terai from 1556 original written by Nobutoyo, illustrations copied by Odani
- Ise, Heizo Sadatake, Kasakake zenki, “Secret Book of Hunger for the Target” (ca. 1846). Manuscript copy by Hajime Terai from original written in 1758 by Ise; illustrations copied by Odani
- Ise, Heizo Sadatake, Fuku (no) Sho, “Secret Book of the Quiver” (ca. 1846). Manuscript copy by Hajime Terai from original written in 1765 by Ise; illustrations copied by Odani.
- Paul E. Klopsteg Collection of the History and Technology of Archery, miscellaneous items.

### Section 2: The Universe

Galileo was one of a generation of mathematicians who believed they understood physics better than the physicists. Physicists, then trained in logical methods, understood neither the theoretical basis of mechanics nor the tradition of mathematical astronomy which they regarded as hypothetical and uncertain. A generation after Galileo, the new mathematical approach to physics triumphed in Newton’s *Principia, or Mathematical Principles of Natural Philosophy*, which unified physics with the mathematical study of the universe.

**Plato**,*Diuus Plato*(Venice, 1491), ed. Marsilio Ficino, “The Divine Plato”**Aristotle**,*Opera Graece*(Venice,1495-1498), 5 vols. bound in 6, “Works in Greek”.**Aristarchus**,*De magnitudinibus et distantiis solis, et lunae*(Pesaro, 1572), “On the Sizes and Distances of the Sun and Moon”**Proclus**,*Sphaera*(Vienna, 1511), “On the Sphere”**Al-Qabisi**,*Alchabitius cum commento*(Venice, 1512), “Commentary on Al-Qabisi”- Abraham bar Hiyya,
*Sphaera mundi*(Basel, 1546), “On the Sphere of the Universe” **Sacrobosco**,*De Sphaera*(Venice, 1490), “On the Sphere”; with Georg Peurbach,*Theoricae novae planetarum*, “New Theory of the Planets”**Sacrobosco**,*De sphaera*(Wittenberg, 1545), “On the Sphere”- Francesco
**Barozzi**,*Cosmographia*(Venice, 1585), “Cosmography” - William
**Gilbert**,*De magnete*(London, 1600), “On the Magnet” - René
**Descartes**,*Principia philosophiae*(Amsterdam, 1644), “Principles of Philosophy” **Fontenelle**,*Conversations on the Plurality of Worlds*(London, 1728)- Isaac
**Newton**,*Philosophiae naturalis principia mathematica*(London, 1687), “Mathematical Principles of Natural Philosophy” - Francesco
**Algarotti**,*Il Newtonianismo per le dame*(Naples, 1737), “Newtonianism for Women” - James
**Bradley**, “An Account of a New Discovered Motion of the Fix’d Stars,”*Philosophical Transactions of the Royal Society of London*(London, 1729), no. 406, pp. 637-660 - Wilhelm
**Bessel**, “De motu proprio stellarum fixarum” (1827); reprinted in*Abhandlungen von Friedrich Wilhelm Bessel*(Leipzig, 1875), “On the Proper Motion of Fixed Stars” - Léon
**Foucault**, “Démonstration Physique du Mouvement de la Rotation de la Terre,”*Comptes Rendus*(Paris, 1851), pp. 135ff, “Physical Demonstration of the Rotational Movement of the Earth” - Albert
**Einstein**: The Centenary of General Relativity, 1915-2015, miscellaneous items

###### Further reading:

- Galileo,
*Dialogue on the Two Chief World Systems*, trans. Stillman Drake (Modern Library, 2001). - John L. Heilbronn,
*Galileo*(Oxford, 2010). - Stillman Drake,
*Galileo at Work: His Scientific Biography*(Chicago, 1978).