. Trigonometria. F and CG being equal andparallel, by the Propofition, the angles EC Aand P G A arc equal, by the 29 of the tirft, andEGA and P A G are equal by the 5 of thefirft, and therefore the triangles B A F andFAG arc like, and their fides proportional,by the fourth of the fixt Book of Snclid, andtherefore A B . A F:: A F. A G ; and feeing that the Radius A B is but an pnit by fuppofition, A 3 is the fide, and A G the fquare thereof, Confeftarj. 1 Therefore the fubtenfe of an arch being given, the fubtenfe of an arch comoofed of the archgiven, andof half his complement to a femicircle i
. Trigonometria. F and CG being equal andparallel, by the Propofition, the angles EC Aand P G A arc equal, by the 29 of the tirft, andEGA and P A G are equal by the 5 of thefirft, and therefore the triangles B A F andFAG arc like, and their fides proportional,by the fourth of the fixt Book of Snclid, andtherefore A B . A F:: A F. A G ; and feeing that the Radius A B is but an pnit by fuppofition, A 3 is the fide, and A G the fquare thereof, Confeftarj. 1 Therefore the fubtenfe of an arch being given, the fubtenfe of an arch comoofed of the archgiven, andof half his complement to a femicircle is given alfo. Forbythis Propofition AGequal to A C and E F is alfo equal to the fquare of A F, the fubtenfe of the arch E D F, andB A the half complement of p p F to a Semicircle, and the Root is AY, the fubtenfe;fought, M h verfed fine U a ri§nt Hne in a Semicircle perpendicular to the right Sine of the famei?ch- Thus (in i\w firft Piagram of this Chapter) Fip fs th? verfed Sjne of the arch C D, being 8 l per=. a Trigonometria Britannica. Perpendicular to the right Sine C F; and H F (for the fame reafon) isdtt^^flg^tbealff^ £ right Sine of its complement are equal to the ^A™l*tbefirft Di*granof thk Cbapter)¥D the verfed fine of C D and AF are equal to AD therefore the Radius and fine complement of an arch being givenu the verfed fine of thata,chS given , for the right Sine of the complement being deduced from the Radius,;thef^^lf^^cdanccf^J^]^^! a quadrant; or being added to the; Radius,^iSarcVate is the verfed fine of an arch greater then a quadrant. Thus A F deducted fromA D, letvef F D, the verfed fine of C D, or being added to H A, equal to A D, their aggregateitHF the verfed fine of HB C- . . The right Sine and verfed Sine of an arch are together equal in power to the fubtenfc of the fame arch. ^ - ^ anncXfid Diagram the rignt sine C F, and the verfed SineEF, with the fubtenfc E C, do make a right angled Trian-gle, and therefore the fquare of C F and E F are together
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Keywords: ., bookcentury1600, bookdecade1650, bookidtrigonometri, bookyear1658
