COINING THE TERM "LOXODROME" AND FORESHADOWING THE DIFFERENTIAL TRIANGLE OF PASCAL

SNELLIUS, WILLEBRORD (SNELL; SNELL van ROYEN).

Tiphys Batavus sive Histiodromice, De navium cursibus, et re navali.

Leiden, Elzevier, 1624.

4to (194 x 150 mm). Bound in a beautiful contemporary full calf binding with gilt centrepieces blindstamped lines and four raised bands and gilt ornamentations to spine. Spine neatly restored. Old owner's names to title-page, one of them crossed out. Occassional very light browning or soiling. An excellent copy. With the book-plate of Paul Heilbronner to inside of front board. (54), 109, (1) + (2), 62 (being tables), (1 - errata), (1) pp. + 3 engraved plates (one being in the text, on p. 101, but full-page). Woodcut illustrations and tables in the text.

Scarce first edition of one of Snell's main works, his important lessons on navigation, in which he coined the term "loxodrome" and foreshadowed the differential triangle of Pascal.

"The idea and figure of what is now called the differential triangle had appeared on several occasions before the time of Pascal, and even as early as 1624. Snell, in his "Tiphys Batavus", had thought of a small speherical surface bounded by a loxodrome, a circle of latitude, and a meridian of longitude as equivalent to a plane right triangle." (C.B. Boyer, The History of the Calculus and its Conceptual Development, p. 152).

"In 1624 Snel published his lessons on navigation in Tiphys batavus (Tiphys was the pilot of the Argo). The work is mainly a study and tabulation of Pedro Nuñez’ so-called rhumb lines (1537), which Snel named "loxodromes". His consideration of a small spherical triangle bounded by a loxodrome, a parallel, and a meridian circle as a plane right triangle foreshadows the differential triangle of Pascal and later mathematicians." (D.S.B.).

Paul Helbronner (1871-1938) was a French topographer, alpinist, and geodosist, who pioneered cartography of the French Alps. Pointe Helbronner in the Mont Blanc massif is named in his honour.

Order-nr.: 50996