Boethius's Arithmetic

The Arithmetic of Boethius (480-524) dates from the early sixth century. This page is from a manuscript (Plimpton MS 165) that dates from approximately 1294, written on vellum. The above image is from page f. 13 and lists the powers of 2, 3, and 4 and also has some other tables representing multiplication by some of these powers. Note that the forms of the figures are not always identical to the modern form.

Boethius's Arithmetic

Galileo's Siderius Nuncius

This page from Galileo's Siderius Nuncius gives Galileo's initial sketches of the surface of the moon, with various craters, and the line between darkness and light clearly visible.

Jordanus de Nemore's Arithmetica

This is page 7 from an early printed edition of the Arithmetica of Jordanus de Nemore (early 13th century). The page contains theorems 14 through 19 of Book I. Rough translations are available here.

Jordanus de Nemore's Arithmetica

Galileo's Geometrical Compass

This image is from the 1640 printing of Galileo's Operation of the Geometrical and Military Compass. In this image, Galileo demonstrates how to find the height of a distant object by using the compass twice to sight the object at different distances.

Galileo's Geometrical Compass

Pacioli's Summa

This is the title page of the Summa de arithmetica, geometrica, proportioni et proportionalita, published by Luca Pacioli (1445-1509) in 1494. This was the most comprehensive mathematical text of the time and one of the earliest printed mathematical works. It contained not only practical arithmetic, but also algebra, practical geometry and the first published treatment of double-entry bookkeeping.

On this page (f. 36v), Pacioli illustrates one of the methods of finger counting prevalent at his time in Italy.

Pacioli's Summa