Oliver Byrne's Euclid

Page 117 of Oliver Byrne’s 1847 edition of Euclid's Elements discusses Proposition 32 of Book II.

Oliver Byrne's Euclid

Seki Kowa's Essentials of Mathematics

These are two pages from volume one of Seki Kowa’s (1642-1708) Katsuyo sampo [Essentials of Mathematics]. These pages show the table employed to obtain “Bernoulli” numbers. They are given in the right column and were obtained by a technique called Ruisai Shosa-ho.

Seki Kowa's Essentials of Mathematics

Nasir al-Din al-Tusi's Commentary on Euclid's Elements

Nasir al-Din al-Tusi (1201 – 1274) was a Persian astronomer and mathematician. He is noted for writing the first major work on pure trigonometry as well as for his commentaries on Greek works.

This is a page from a later Arabic edition of his commentary on Euclid’s Elements, a page dealing with Euclid's method of exhaustion.

Nasir al-Din al-Tusi's Commentary on Euclid's Elements

Benedetto da Firenze's Trattato d'arismetriche

Benedetto da Firenze (1429 – 1479) was a respected Florentine maestro d’abaco. Here, on page 114 of his unpublished manuscript Trattato d’arismetricha (ca 1460), a work on mercantile arithmetic, is a discussion of regula del chataina, the chain rule, used to compute exchange rates.

Benedetto da Firenze's Trattato d'arismetriche

Euclid's Elements in a 14th century manuscript

This image is from a late 14th century manuscript containing the first five books of Euclid's Elements in Latin translation. The manuscript probably comes from England, but the scribe is unknown.

This page is f. 10, and contains three results from Book II, often characterized as results in geometric algebra.

Euclid's Elements in a 14th century manuscript