306

HISTORY OF

TRACT 20 .

dently Latin words, and seem to be intended for the Latintranslations of the names by which the Arabians called theselines, or the numbers expressing the lengths of them.

And this conjecture has been confirmed and realised, by areference to Golius’s Lexicon of tbe Arabic and Latin lan-guages. In consequence I find that the Arabic and Latinwriters on trigonometry do both of them use those words inthe same allegorical sense, the latter being the Latin trans-lations of the former, and not the Arabic words corrupted.Thus, the true Arabic word to denote the trigonometricalsine is pronounced Jeib, (reading the vowels in the

French manner), meaning sinus indusii, vestisque, the bosompart of the garment; the versed sine is Sehun, which

is sagitta, the arrow; the arc is which is arcus, the arc;

and the chord is y «, Vitr, that is chorda, the chord.

TRACT XX.

HISTORY OF LOGARITHMS.

The trigonometrical canon, of natural sines, tangents, andsecants, being now brought to a considerable degree of per-fection; the great length and accuracy of the numbers, toge-ther with the increasing delicacy and number of astronomicalproblems, and spherical triangles, to the solution of whichthe canon was applied, urged many persons, conversant inthose matters, to endeavour to discover some means of dimi-nishing tiie great labour and time, requisite for so many mul-tiplications and divisions, in such large numbers as tbe tablesthen consisted of. And their chief aim was, to reduce themultiplications and divisions to additions and subtractions, asmuch as possible.

For this purpose, Nicholas llajuner Ursus Dithmarsus in-vented an ingenious method, which serves for one case in the