AR I T H ME T I G A UNIVERSALIS.

I2Z

quales, fic procedendum erit. Demit-D tatur dc perpendicularis ad ac ut ant^, trica.

OBLEMA-TA GeOME-

& agatur dh conftituens angulum dha

ecqualem angulo hae, puta obtufum: dic-B H C E -g _ ^ BD _ AH — Xj §£ p rD —y^

Propter fimilia triangula e ab, bhd, erit bd. dh : : eb. ab ; hoc efty - - <2. AB - y. Aufer hanc de ah, 8 c reflabit bh = x - —•Praeterea in triangulo dhc, propter omnes angulos datos, adeoquedatam rationem laterum,, affume dh ad hc in ratione quavis data,Pota b ad <?; cum dh fit y, erit hc = &hb x-hc = ‘| -onique per i 2. II. Elem.in triangulo bhd, eft bd# - BH# + dh# +2 e Hxhc, hoc eftM = XX - + -ZL -v yy + fi _

Et, ex-

tra&a radice, a=

*/ eeyy — bbyy + bbbb

Ubi cum b fit major e, hoc

e ft ee—bb negativa quantitas, patet iterum curvam efle Ellipfin.

P R O B. XXXVII.

Ih dato angulo , pab, actis utcunque rectis, bd, pd, in data ra-il °ne, hac femp er lege , ut bd fit parallela ap, 62? pd terminetur adpundtum, p, in redici ap datum ;. invenire locum puncti d.

A GE cd parallelam ab, & de perpen-pendicularum ap ; ac dic ap = a,cp —at, & CD=y; fitque bd ad pd in ra-tione d ad e ; 8c erit ac, vel bd, = a - x , &pd = Azflj Sit infuper, propter datum

c ; K — -p angulum dce, ratio cd ad CE,,fift>d/, 8c

erit ce = & ep = x - Atqui propter angulos ad e recftos,

d ’ a

eft CD#-CE# ( = ED q) = pd#-ep#, boc

ffyy eeaa — iceax texxdd dd

XX +

2fxy

d

ffyy

dd'

Ac deletis utrobique - terminifque rite

rlifpofith yy _4- eeaa — 2eeax eexx ~

i

-. Et, extradfa radice, 7 - y +

dd

+ ee

ee *a~ 2 eeax~ddxx+ff

Ubi cum x 8c y in aequatione penultima non

nift