**Astronomical-Mathematical**CollectionThis is the oldest and best manuscript of a collection of early Greek astronomical works, mostly elementary, by Autolycus, Euclid, Aristarchus, Hypsicles, and Theodosius, as well as mathematical works. The most interesting, really curious, of these is Aristarchus's "On the Distances and Sizes of the Sun and Moon," in which he shows that the sun is between 18 and 20 times the distance of the moon. Shown here is Proposition 13, with many scholia, concerned with the ratio to the diameters of the moon and sun of the line subtending the arc dividing the light and dark portions of the moon in a lunar eclipse.

*Vat. gr. 204 fol. 116 recto math06 NS.02***Apollonius,**ConicsApollonius's "Conics," written about 200 B.C., on conic sections, the ellipse, parabola, and hyperbola, is the most complex and difficult single work of all Greek mathematics and was all but unknown in the west until the fifteenth century. This magnificent copy, probably the most elegant of all Greek mathematical manuscripts, was made in 1536 for Pope Paul III. The pages on display show the particularly elaborate figures illustrating Propositions 2-4 of Book III on the equality of areas of triangles and quadrilaterals formed by tangents and diameters of conics, and by tangents and lines parallel to the tangents.

*Vat. gr. 205 pp. 78-79 math07a NS.03***Pappus,**CollectionPappus's "Collection," consisting of supplements to earlier treatises on geometry, astronomy, and mechanics, dates from the late third century A.D. and is the last important work of Greek mathematics. This manuscript reached the papal library in the thirteenth century, and is the archetype of all later copies, of which none is earlier than the sixteenth century.

*Vat. gr. 218 fols. 39 verso-40 recto math08a NS.05***Ptolemy,**AlmagestClaudius Ptolemy, who lived in the second century A.D., did work of enormous importance in astronomy and geography in which the Vatican Library has particularly rich holdings. The "Almagest," written about A.D. 150, is a comprehensive treatise on all aspects of mathematical astronomy--spherical astronomy, solar, lunar, and planetary theory, eclipses, and the fixed stars. It made all of its predecessors obsolete and remained the definitive treatise on its subject for nearly fifteen hundred years. This, the most elegant of all manuscripts of the "Almagest," is one of the oldest and best witnesses to the text, and is very rich in notes.

*Vat. gr. 1594 fols. 73 verso-74 recto math09a NS.07***Ptolemy,**AlmagestIn Latin, Salernitan Translation, Late thirteenth or early fourteenth century

In about 1160 a very literal translation of the "Almagest" was made directly from the Greek by an unknown translator in Sicily. The version had little circulation, but in the early fifteenth century this manuscript, the only known complete copy, came into the hands of the great Florentine book collector Coluccio Salutati. Shown here is Book XII Chapters 8-9, the table of stations of the planets (the place on the epicycle where the planet appears stationary) written entirely in Roman numerals, and the method of computing a table of the greatest elongations of Mercury and Venus from the sun.

*Vat. lat. 2056 fols. 45 verso-46 recto, fols. 87 verso-88 recto math10a NS.09***Ptolemy,**AlmagestIn Latin, Translated by Gerard of Cremona, Thirteenth century

The most important medieval Latin translation of the "Almagest," which is found in many manuscripts, was made from the Arabic in Spain in 1175 by Gerard of Cremona, the most prolific of all medieval translators from Arabic into Latin. These pages show Book X Chapters 6-7, Ptolemy's description of his kinematic model for the motion of the superior planets--Mars, Jupiter, and Saturn. The separation of the center of uniform motion from the center of uniform distance of the center of the epicycle is explained, as well as the beginning of the derivation of the elements of the model for Mars, through a lengthy iterative computation. The earth is at rest at (e) and the planets move uniformly with respect to a point (r) which is separated from the center of their spheres, (d). This device closely approximated the elliptical orbit in which planets actually move.

*Vat. lat. 2057 fols. 70 verso-71 recto, fols. 146 verso - 147 recto math11a NS.10*