Rabdologiae seu numerationis per virgulas libri duo: cum appendice de expeditissimo multiplicationis promptuario. Quibus accessit & arithmeticae localis liber unus. Leiden: Petrus Rammasenius, 1628 [NAPIER'S BONE OR RODS, THE 1ST CALCULATING MACHINES] by Napier, John [Baron Merchiston; Laird of Merchiston] - 1628

Leiden: Petrus Rammasenius, 1628. 3rd Edition. THIRD EDITION OF THE INVENTION & DESCRIPTION OF NAPIER'S BONES, THE 1st CALCULATING MACHINES & THE "PRECURSORS OF SEVENTEENTH-CENTURY AND MODERN CALCULATING MACHINES AND COMPUTERS" (Printing and the Mind of Man 116). Napier's invention, essentially a system of rods, offered a mechanical means for facilitating computation. Note that this work "also contains the first printed reference to the decimal point," an act that then made common its usage (Computer History Portal). The first edition was published in 1617, but this, the third edition is considerably more rare. This specific volume was a part of the Tomash collection on the history of computing.

John Napier (1550-1617) was born in Scotland into a prominent family of Scottish lairds. At thirteen, he attended St. Andrews University, though there is no record of his having graduated. In addition to running his family estates and actively participating in the Scottish reform movement, Napier worked on his avocation - mathematics, physics, and astronomy. Though he genuinely considered his scientific pursuits "hobbies," Napier is the person responsible for the invention of logarithms. In 1614 and after 25 years of work, Napier published his work on the subject, defining logarithms as a ratio of two distances in a geometric form, as opposed to the current definition of logarithms as exponents.

Following the publication of his work on logarithms, Napier sought a way to simplify calculations by some mechanical means. "Looking to ease his own difficulties in calculating logarithmic tables and impatient with the tedious and error-prone process of working with large numbers, Napier invented several mechanical methods of simplifying and speeding up multiplication, the most famous being special rods, later known as Napier's bones [or rods]" (ibid). "These rods, which in essence constitute a mechanical multiplication table, had a considerable vogue for many years after his death (Dictionary of Scientific Biography, IX, 610).

Napier's mechanical calculator, his bones, employed rods with numbers marked off on them. "What Napier did... is that he made slips (columns) with all possible 9 columns of squares of the gelosia grid, and thus he can put aside manual drawing of a grid and writing in squares. These slips are written on the surface of ten rods, later on called Napier's rods (the best sets were made of ivory so that they looked like bones - hence Napier's bones) (CH).

They function as follows: "A grid of squares, divided into parts by a diagonal, must be cross-ruled, as the number of squares depends on the number of digits in factors, e.g. if we want to multiply 3-digital to 3-digital factor, then the grid must be 3x3 squares. To the upper side and right side of the grid must be written the 2 factors, and intermediate products are written in the squares in such manner, that the diagonal divides the units from the tens. The units of the partial product (the digit from the right by the digit from the upper) are written on one side and the tens on the other, so that when a multiple consists of two figures they are separated by the diagonal. To get the final product, the numbers along the diagonals are added and the result is written to the left of grid (senior digital positions) and below the grid (junior digital positions).

PMM 116; DSB, IX, 610; Tomash & Williams N10; Hoogendoorn p.684 Napier 1; Norman 1574; Dibner 107 (1st edition). CONDITION & DETAILS: 12mo (144 x 80mm.), [2], 12, [139 pp]. 9 folding plates (woodcut and letterpress). Contemporary vellum, very slightly soiled. Tightly bound & housed in a handsome linen cloth box. The lower part of the title page has been repaired by a conservator. The missing area supplied in facsimile and is all but invisible to the eye. Pinpoint hole to B7, a few folding plates with slight marginal tears (one professionally repaired). Handsome wide margins; lightly toned within; clean. Very good condition.