Saturday 29 January 2011

Nova Stereometria

Here is a very detailed collection of images from the Posner collection of books at the Carnegie Mellon University .

"The Posner Memorial Collection of six hundred twenty-two titles includes landmark titles of the history of western science, beautifully produced books on decorative arts and fine sets of literature. Mr. Henry Posner, Sr. formed the collection from 1924 to 1973, starting with literature and decorative arts and, after 1950, focusing on the history of science. When possible, books are in electronic format with text and images and accompanied by a Collector's File of Mr. Posner's records."

One of the books in the collection is a very rare book by Johannes Kepler. Kepler was a brilliant mathematician and mathematical physicist who is chiefly remembered for discovering the three laws of planetary motion that bear his name. However, Kepler also did important work in optics, close packing of spheres, logarithms and solid geometry.

One of his lesser known works was prompted by a problem he had encountered whilst buying wine after his second wedding celebration in 1613. Kepler noted that the vintner measured the capacity of the wine barrel by putting a stick into the bung hole and measuring the distance to the bottom of the barrel. It struck Kepler that the crude `dipstick' method of estimating the volume of the barrel wouldn't take into account the curvature of the barrel and would thus give an inaccurate estimate of the volume. 

Prompted by this observation Kepler made a careful study of the general problem of accurately estimating the volume of wine barrels and other solids of revolution. Kepler's solution was to divide the barrel into a large number of slices and estimate the total barrel volume by summing the volumes of the individual slices. Kepler's work was published in 1615 as Nova Stereometria Doliorum Vinariorum, which roughly translates to `New Measurements of Wine Barrels'.

The Nova Stereometria is a rarity and has never been translated into English. However, although it's technical content is little known to non-specialists it has become a sought after commodity amongst book collectors; a mint condition copy of Kepler's book in its original binding will sell for upwards of $30,000.

Keplers work was an important precursor to the calculus.

Here is the title page of the Posner copy of Nova Stereometria.