Ausszug auss der uralten Messekunst Archimedis vnd deroselben newlich in Latein aussgangener Ergentzung.

KEPLER, Johannes

Published by Hans Blanck, Linz, 1616

About this Item

KEPLER ON MEASURING WINE BARRELS. First edition, a considerably revised, rearranged and augmented version of Kepler's Nova Stereometria published the year before, a work which is "generally regarded as one of the significant works in the prehistory of the calculus" (Gingerich in DSB). "Desiring to outfit his new household with the produce of a particularly good wine harvest, Kepler installed some casks in his house. When he discovered that the wine merchant measured only the diagonal length of the barrels, ignoring their shape, Kepler set about computing their actual volumes. Abandoning the classical Archimedean procedures, he adopted a less rigorous but productive scheme in which he considered that the figures were composed of an infinite number of thin circular laminae or other cross sections. Captivated by the task, he extended it to other shapes, including the torus" (DSB). The Messekunst is not a simple translation of the Nova stereometria. The material is substantially reorganized, the Theorem-proof structure of the earlier work replaced by a more informal approach (that structure had proved unsuitable for a practical audience and sales of the Nova stereometria were disappointing). Most importantly, the Messekunst contains material not present in Nova stereometria: first, the solution to the difficult problem of finding the volume of wine in a partly empty barrel, which had been mentioned but not solved at the end of the earlier work; second, the explanation of the effectiveness of the 'gauging rod' used by Austrian wine merchants to measure the volume of their barrels, which had prompted Kepler's work on 'doliometry' in the first place; and finally, the Anhang (Appendix), on weights and measures from antiquity to Kepler's time, is present only in the Messekunst, as is the German/Latin glossary "that established the beginnings of German mathematical terminology" (Baron, p. 110). This copy of the Messekunst has the printed gauge slip on K1, not recorded by Caspar; it duplicates the figure printed within the text. The Messekunst is significantly rarer than the Nova stereometria in commerce: RBH lists three other copies of the former at auction in the last half-century, and nine of the latter. Kepler (1571-1630) became interested in stereometry as a result of a serendipitous event that took place in November 1613 in Linz, where Kepler was then living. Kepler purchased some barrels to lay in a supply of wine for his family and had them delivered to his house. When the wine dealer came to the house to measure the volume of wine the barrels contained, he used the standard gauger's technique which in effect meant approximating the barrel by a cylinder of the same height as the barrel but with cross-sectional area equal to the average of the area of the ends of the barrel and that of its middle bulge. Thus, the approximate formula for the volume of the barrel was V = ½ x height x (end-diameter2 + bulge-diameter2) V0, where V0 was the known volume of a cylinder of unit height and diameter. To simplify the calculation a gauging rod was used. This was a rod marked with a quadratic scale (i.e., 1 at the first mark, 4 at the second, 9 at the third, etc.); by laying it across the end of the barrel, then inserting it through the bung hole in the middle of the bulge, and reading off the numbers on the scale, the gauger could then calculate an approximation to the volume of wine in the barrel by using the above formula. Kepler was more than sceptical about the accuracy of this method of volume determination, especially how it could work for barrels of any shape and size, and he immediately decided to try to find a better mathematical method, and one that would also deal with the case of partly empty barrels, for which the gauger had no solution. By December 17, 1613 Kepler believed that he had reached his goal. He had composed a short six-page manuscript with about ten theorems, and with a dedication to Prince Maximilian of Liechtenstein. Seller Inventory # 5003

Bibliographic Details

Title: Ausszug auss der uralten Messekunst ...

Publisher: Hans Blanck, Linz

Publication Date: 1616