1x6 N E W T O N I

CafutXIV. be, ut & perpendiculum df a pundlo qucefito d ; di£tifque ae=<%ac = b, eb = c, af = x, Sc fd =y, erit ad q = xx+yy; Fc=b-XVcd q (=fc< 7 +fd(?) -bb- 2 bx+xx+yy ; EF-.V-S,ac bd q (- ef <7 + eb + fd quad.) -xx- lax + ad+ cc + icy +yy. Jam cum fit ad ad cd in dat&

- jn / xx+ yy. Cum etiam fit ad ad bd in data ra-tione, fit ifta ratio ^ ad /, 8c erit bd =xx +yy. Adeoque eft e S ? x +J ey Z (- C Dq) -bb — ibx + xx + yy ; Scffxx+Jpl svq) . = xx - 2 ax + aa +cc + 2 cy + yy. In quibus fi, ab-breviandi caufa, pro feribatur p, Sc q pra emerget

bb- 2 bx+ j xx +■ - d yy - o, Sc aa + cc- 2 ax+ 2 cy+ ^ xx + -j yy-o •Per priorem efi — ^xx + ^yy. Quare in pofteriori pro

aa + cc — iax +

-jxx + ~yy feribe Sc orietur 2 Jt } t~ hb i +

2 cy - o. Iterum, abbreviandi caufa, feribe m pro a - Sc 2 Cfipro b -~ — aa — cc \ Sc erit 2 mx + 2 cn — 2 cy ; terminifque per 2 c di-vifis, y + n -y. Quamobrem in aequatione bb- 2 bx + -jxx +^yy-Qy pr oyy feribe quadratum de y + n y Sc habebitur 2 b$+ ~xx + xx + x + - v. Ubi denu6.fi, abbreviandi

d dcc ac cl

caufa, -f feribatur pro ^ 7 pro b - Sc ~ pro bb +

habebitur xx—zsx—tb. Et, extracta radice, x—s+_ Vss- tb. In*"vento x, aequatio ~ + n —y dabit y ; Sc ex datis x Sc y, hoc e$af Sc FD, determinatur pundtum qusefitum D..

i P R O. B» XXVIII.

ReStarn , dc, data longitudinis in datam Conicam JeSUonem , da c? 'fic injeribere , ut ea per pundlum, g, pojitione datum tranjeat .

IT af axis Curvae, 8c a punctis, d, g Sc c, ad hunc de"mitte normales dh, ge, Sc cb. Jam-ad determinandam pod"

tione^