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HISTORY OJF

TRACT 1?.

sagitta tlie arrow, by which name the versed sine, which re-presents it, was sometimes called; also, that the tangens wasso called from its office, being a line touching the circle, andsecerns from its cutting the same: I therefore, imagined that thesinus was so called, either from its resemblance to the breastor bosom, or from its being a line drawn within the bosom('sinus) of the arc, or from its being that part of the string(chorda) of a bow (arcus) which is drawn near the breast(sinus) in the act of shooting. And perhaps Vitalis’s defini-tion, above-quoted, has some allusion to the same similitude.

Also Vieta seems to allude to the same thing, in callingsinus an allegorical word, in page 417 of his works, as pub-lished by Scbooten, where, with his usual judgment andprecision, he treats of the propriety of the terms used intrigonometry for certain lines drawn in and about the circle ;of which, as it verv well deserves, I shall here extract theprincipal part, to show the opinion and arguments of so greata man on those names. “ Arabes autem semisses inscriptasdtiplo, numcris prtesertim cestimatas, vocaverunt allegoriceSinus, atque ideo ipsam semi-diametrum, quae maxima estsemissium inscriptarnm, Sinum Totum. Et de iis sua me-thodo canones exiverunt qui circumferuntur, supputantepreesertim Regiomontuno bene juste et accurate, in iis etiamparticulis qualium semidiameter adsumitur 10,000,000.

“ Ex canonibus deinde sinuum derivaverunt recentiorescanonem semissium circumscriptarum, quern dixere Ftecun-dum; et canonem eductarum e centre, quem dixere Foccun-dissinium et Beneficum, hypotenusis addictum. Atque a debsemisses circumscriptas, numeris prsesertim sestimatas, voca-verunt F<zcu?idos, Sinus numcrosve videlicet; quanquam nihilvetat Fci’cundi nomen substantive accipi. Ilypotenusas autemBeneficas, vel etiam simpliciter Hypotenusas: quoniam hy-potenusa in primfi. serie sinus totius nomen rctinet. Itaquene novitate verborum res adumbretur, et alioqui sua artifici-bus, eo nomine dibita, preeripiatur gloria, prseposita inCanone Mathematico canonicis numeris inscriptio, candideadmonet primam seriem esse Canonem Sinuum. In secunda