## Saturday, December 24, 2011

### Boethius's Liber Circuli

## Saturday, December 17, 2011

### Billingsley Euclid

*: The elements of geometrie of the most ancient philosopher Euclide of*

*Megara*[sic].

*Elements*. This page contains three pop up models of pyramids. These pop-up models occur throughout Book XI on solid geometry and were hand-glued into each copy of the work.

## Saturday, December 10, 2011

### Maria Agnesi's Analytical Institutions

*Instituzioni analitche ad uso della gioventu italiana*(

*Foundations of Analysis for the Use of Italian Youth*) of Maria Agnesi (1718-1799). The text was one of the earliest treatments of calculus written on the European continent. Because Agnesi originally wrote this to instruct her younger brothers in analysis, she explained concepts very clearly and gave numerous examples.

## Saturday, December 3, 2011

### Leonhard Euler's Integral Calculus

*Integral Calculus*, vol. 1 (1768). Note that Euler used

*lx*to represent what we write as ln(

*x*).

*Integral Calculus*in three volumes appeared in the interval 1768 – 1770. This was the first complete textbook published on the integral calculus.

## Saturday, November 26, 2011

### Christopher Clavius's Opera Mathematica

## Saturday, November 19, 2011

### Giuseppe Alberti's Instruzioni pratiche per l’ingenero civile

Plate VII from Giuseppe Alberti’s Instruzioni pratiche per l’ingenero civile, (1774) [Practical Instructions for Civil Engineers]. Alberti (1712 - 1768) was an Italian engineer and architect. This illustration on page 298 explains the triangulation method of land measurement employing a sighting staff or surveyor’s cross. The instrument shown contains a compass for marking bearings.

## Saturday, November 12, 2011

### Peter Apianus's trigonometry and geography

*A Geographical Introduction*(1534). In this book, he reviews the theories of Vernerus [Johannes Werner (1468-1522), a Nuremburg priest and mathematician who devised a method of using lunar observations to find longitude] and explains the applications of trigonometry (i.e. sines and chords) in geography.

## Saturday, November 5, 2011

### Tycho Brahe's astronomical instruments

## Saturday, October 29, 2011

### Oliver Byrne's Euclid

*Euclid's Elements*discusses Proposition 32 of Book II.

## Oliver Byrne's Euclid

## Saturday, October 22, 2011

### Seki Kowa's Essentials of Mathematics

## Saturday, October 15, 2011

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

*Elements,*a page dealing with Euclid's method of exhaustion.

## Saturday, October 8, 2011

### 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.

## Saturday, October 1, 2011

### Euclid's Elements in a 14th century manuscript

*Elements*in Latin translation. The manuscript probably comes from England, but the scribe is unknown.

## Saturday, September 24, 2011

### Opus Arithmetica of Honoratus

*Opus Arithmetica D. Honorati veneti monachj coenobij S. Lauretij*. Honoratus was a Venetian monk, and the manuscript was written in the second half of the 16th century. But the manuscript was copied by a pupil, probably also a monk, who also did the illustrations.

## Saturday, September 17, 2011

### Qadi Zada al-Rumi's Geometry

*Geometry*(1412) of Qadi Zada al-Rumi (1364-1436). Al-Rumi's book was a commentary on the Fundamental Theorems, written by al-Samarqandi (1250-1310), where he discusses twenty-five of Euclid's propositions in detail. The book shown in the image is a later copy of al-Rumi's work, probably written in the sixteenth century. At the top of the page is a discussion of Euclid's Proposition I-5, the "Bridge of Asses" proposition that the base angles of an isosceles triangle are equal. At the bottom, there is a discussion of I-6, the converse of I-5. Al-Rumi was an astronomer and mathematician in the court of Ulugh Beg (1393-1449) in Samarkand. He and his colleagues compiled the first complete star catlogue since the time of Ptolemy.

## Saturday, September 10, 2011

### The Grounde of Artes by Robert Recorde

## Saturday, September 3, 2011

### Omar Khayyam's Algebra

*Algebra*(

*Maqalah fi al-jabra wa-al muqabalah*) of Omar Khayyam (1048-1131). This work is known for its solution of the various cases of the cubic equation by finding the intersections of appropriately chosen conic sections. On this page, Omar is discussing the case "a cube, sides and numbers are equal to squares", or, in modern notation, x

^{3}+ cx + d = bx

^{2}. Read more about Omar Khayyam's Algebra.

## Saturday, August 27, 2011

### Margarita philosophica of Gregor Reisch

*Margarita philosophica*(

*Pearl of Wisdom*) of Gregor Reisch (1467 - 1525). The first edition was published in 1503. This work was used as a university textbook in the early sixteenth century. Among its twelve chapters are seven dealing with the seven liberal arts commonly taught at the universities: the trivium of logic, rhetoric, grammar and the quadrivium of arithmetic, music, geometry, and astronomy. There are also several chapters on more advanced topics.

## Saturday, August 20, 2011

### De Divina Proportione by Luca Pacioli

## Saturday, August 6, 2011

### Leonhard Euler's Calculus of Variations

## Saturday, July 30, 2011

### Omar Khayyam's Algebra

*Algebra*(

*Maqalah fi al-jabra wa-al muqabalah*) of Omar Khayyam (1048-1131). This work is known for its solution of the various cases of the cubic equation by finding the intersections of appropriately chosen conic sections.

## Saturday, July 23, 2011

### A Treatise of Algebra by John Wallis

*A Treatise of Algebra* (1685) by John Wallis (1616-1703). This is probably the first attempt at a history of the subject of algebra, presented in the context of a text on the subject.

## Thursday, July 14, 2011

### Boethius's Arithmetic

## Thursday, July 7, 2011

### Galileo's Siderius Nuncius

## Thursday, June 30, 2011

### Jordanus de Nemore's Arithmetica

## Wednesday, June 8, 2011

### Galileo's Geometrical Compass

## Wednesday, June 1, 2011

### Pacioli's Summa

*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.

## Wednesday, May 25, 2011

### Gaspard Monge's Descriptive Geometry

*Descriptive Geometry*of Gaspard Monge (1746-1818). This book deals with methods for representing three-dimensional objects in two dimensions. It was written to accompany Monge's courses at the Ècole Polytechnique in Paris.

## Wednesday, May 18, 2011

### Niccolo Tartaglia's General Trattato di Numeri et Misure

Detail of the title page of part I of the *General Trattato di Numeri* (*General Treatise on Number and Measure*) (1556) of Niccolo Tartaglia (1500-1557). This is an extensive work on elementary mathematics that was popular in Italy for several decades after its publication.

Here Tartaglia is showing how to determine the area of an irregular curved shape.

## Wednesday, May 11, 2011

### Leibniz - Bernoulli Correspondence

Gottfried Wilhelm Leibniz carried on an active correspondence within the intellectual community of his time. In particular, two of his main correspondents were the brothers Jacob and Johann Bernoulli. Johann began corresponding with Leibniz in 1693.

In this December 1696 letter from Leibniz to Bernoulli, there is a discussion of integration by parts applied to functions having powers of*x*and powers of the logarithm.