302

HISTORY OF

TRACT 19.

that time gradually brought into use; but continued long tobe denoted after the manner of vulgar fractions, by a linedrawn between the numerator and denominator, which lasthowever was soon omitted, and only the numerator set down,with the line below it: thus, it was first then 31i4 ;

afterwards, omitting the line, it became 31 35 , and lastly 31 3S ,or 31.35, or 31 *35: as may be traced in the works of Vieta,and others since his time, gradually into the present century.

Having often heard it remarked, that the word sine , or inLatin and French sinus, is of doubtful origin; and as the va-rious accounts which I have seen of its derivation are verydifferent from one another, it may not be amiss here to em-ploy a few lines on this matter. Some authors say, this is anArabic word, others that it is the single Latin word sinus;and in Montucla ’s “ Histoire des Mathematiques” it is con-jectured to be an abbreviation of two Latin words. Theconjecture is thus expressed by the ingenious and learnedauthor of that excellent history, at p. xxxiii, among the addi-tions and corrections of the first volume: “ A l’occasion dessinus dont on parle dans cette page, comme d’uue inventiondes Arabes, voici une etymologic de ce nom, tout-a-fait lieu-reuse et vraisemblable. Je ladois a M. Godin, de l’AcademieIioyale des Sciences, Dirccteur de l’Ecole de Marine de Cadix.Les sinus sont, comme l’on scait, des moities de cords; et lescordes en Latin se nomment inscripla. Les sinus sont donesetnisses inseriptarum, ce que probablement on ecrivit ainsipour abreger, S. Ins. Delii ensuite s’est fait par abus le motde sinus.” Now, ingenious as this conjecture is, there ap-pears to be little or no probability for the truth of it. For,in the first place, it is not in the least supported by quotationsfrom any of the more early books, to show that it ever was thepractice to write or print the words thus, S. Ins. upon whichthe conjecture is founded. Again, it is said the chords are call-ed in Latin inscript<e; and it is true that they sometimes are so:but I think they arc more frequently called subte?is<e, and thesines seinisses sublcnsarum of the double arcs, which will notabbreviate into the word sinus. This conjecture the learned