Legendre's Elements of Geometry

In the year 1794, André Marie Legrendre (1752 - 1833) published his Eléments de géométrie. In its preface, Legrendre says he tried to produce a geometry that will testify to the l’esprit of Euclid. The book became an immediate success in Europe and eventually went through 20 additions.  The first American translation appeared in 1819, a work by John Farrar (1779 – 1853), Hollis Professor of Mathematics and Natural Philosophy (Science) at Harvard. This is the title page of Farrar’s translation of Legendre's Elements, the second edition (1825). Farrar went on to translate five French mathematical classics of this time. The style and format of these books transformed American mathematics teaching, and they became models for the new mathematical textbooks employed in the U.S military academies.


The image above (click to enlarge) is of pages 106 and 107 of Legendre’s Elements of Geometry and discuss the construction and properties of planes. Note the use of the symbol for line segment. This is one of the first applications of this symbol in an American textbook.

Legendre's Elements of Geometry 

Leonhard Zubler's Nova Instrumentum Geometricum

Leonhard Zubler wrote Nova Instrumentum Geometricum in 1607. Zubler (d. 1611) was a Swiss goldsmith and instrument maker. He is credited with introducing the use of the plane table into modern surveying. This book demonstrates and promotes the use of his instruments in techniques of triangulation. Many of the situations depicted concern warfare. Note the two surveyors flanking the title page, proudly holding their measuring instruments.


The image above is page 23 of Zubler’s Instrumentum and demonstrates a triangulation technique for obtaining the distance to a fortress.


Leonhard Zubler's Nova Instrumentum Geometricum 

Desargues' Sundials

Girard Desargues (1591—1650) was a French mathematician and engineer best known for his contributions to projective geometry. He published materials on many technical and engineering topics. In 1640, he published a tract on dialing-constructing sun dials. This is the title page of the 1659 English language translation of this work.


Desargues' Sundials

Kepler's Logarithms

This is the title page of Johannes Kepler’s (1571—1630) Chilias Logarithmoria, 1624, logarithmic tables he constructed by geometric procedures. Kepler also gave a proof of why logarithms worked and then used them extensively in his calculations of the Rudolphine astronomical tables.


Kepler's Logarithms

Johann Kepler's Uralten Messekunst Archimedes

Johannes Kepler ( 1571—1630 ) was concerned that Austrian wine merchants were cheating their customers by gauging the volume of their barrels incorrectly. To correct the situation, he undertook a study of the volume of wine barrels. He published his findings, Nova Stereometria Doliorum vinarorum, in 1615. Forsaking classical techniques of volume calculation, Kepler produced solids of revolution, dissected them into an infinite number of circular laminae and obtained a volume summation. He applied this technique to consider solids other than wine barrels; in total studying the volumes of 92 different solids. Written in Latin this work was scholarly and had a limited audience. In order to increase his financial returns in 1616, he published a popular German language version of his work, Ausszag aus der Uralten Messekunst Archimedes. The page images are from the Messekunst. Page 27 contains a discussion on the volume of a torus. Page 28 returns to a consideration of the volume of wine barrels.

Johann Kepler's Uralten Messekunst Archimedes