96 N E W T O -N I

CaputXIV- pofitis linearum nominibus, erit ab. bd ::bd, be. a.x::x.^’

•Et ba - be (a - = ea. Nec non ea. ad :: ad. ab, adeoque

ea x ab (aa-xx) — xv>q. Et lic ratiocinando circa triangulumacd, invenietur iteriim ad q — bb-cc-rzcx-xx. Unde obtine-

, aa — bb-\-cc

bitur, ut ante, x— ———.

P R O B. III.

'Trianguli redi'anguli , abc, perimetro & area datis , invenire hypo -

tenufam bc.

IV' STO perimeter a, area SS, bc = ,t, 8 c ac =y;

' eritque ab - s/xx-yy ; unde rurfus perimeter(bc + ac + ab) eft x+y+\/xx—yy, 85 area Qacx ab)^eft ^y\/xx—yy. Adeoque x+y+\/xx—yy = a, 85\yVxx—yy — bb.

Harum aequationum pofterior dat V 7 xx-yy - quare fcribov 7 ^-

pro v 7 xx-yy in aequatione priori, ut afTymmetria tollatur; 85

prodit x +y + — = a; live multiplicando per y, 85 ordinando,

y — ay — xy - zbb. Porro ex partibus aequationis prioris auferox+y, 8c reftat s/xx-yy- a-x-y, cujus partes quadrando, ut affym-metria rurfus tollatur, prodit xx-yy - aa-iax-iay+xx+ixy+yyiquae in ordinem redafta 85 per 2 divifa fit yy - ay-xy-^ax — \aci‘

Denique ponendo aequalitatem inter duos valores ipfius yy, habeo

2,bb

ay-xy-zbb - ay-xy+ax-^aa, quae redudta fit Ia- — — x.

! Idem aliter.

\

Eflo a perimeter = a , area - bb, 85 bc = x, eritque ac + aB- 2 a—x. Jam cum fit xx (bc q) - ac^+ab^, 85 4 bb — 2AcxAB>erit xx + /\.bb-xcq+ ab<? + 2Acx ab = quadrato ex ac + ab = quadratoex za-x-^.aa-^.ax+xx. Hoc cHl xx +At-bb-^aa-^ax+xx \ quLL

reducta fit a - - - x.

a 1

7

PROB-