Saturday, December 24, 2011

Boethius's Liber Circuli

Illustration from the 1503 edition of Boethius’s Liber Circuli. Folio 86 discusses the quadrature of a circle.

Saturday, December 17, 2011

Billingsley Euclid

In 1570 Sir Henry Billingsley (d.1606) published the first English-language edition of Euclid's Elements: The elements of geometrie of the most ancient philosopher Euclide of Megara [sic].

The image is Folio 314 of Billingsley's 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

Pages from the original Italian version of the 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.

Among Agnesi's examples was a description of a curve which she called la Versiera. We give here (pp. 380-381) her geometric description of the curve and her derivation of its analytic formula. The figure is given below.

Saturday, December 3, 2011

Leonhard Euler's Integral Calculus

Leonard Euler’s discussion of volume 1 of his Integral Calculus concerning the integration of logarithmic and exponential functions on page 121 of Integral Calculus, vol. 1 (1768). Note that Euler used lx to represent what we write as ln(x).

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