ARITHMETICA universalis.

rrz

EF(2#.).EG + GF (AG + GF) feU AF. PnostEMA.

. TA GeoME»

2ay 4- 2 aa / v

Quare — (= af = ab + bf) trica.

aa —yy

- x + \/aa-yy. Jam, multipli-cando per \/aa—yy , fit 2 ay + laa

— aa - yy + x \/ 'aa-yy, feu lay+aa +yy-xs/aa-yy : & quadrando

Part£ s divifas per v/#+y, ac ordinando, prodit jy 3 + 3<2vy

+ 3 *«« + a

+ XX

y — 0 ,

MV — CtXX *

aliter.

In bc cape hinc in-de bi, 8 t ck aequalescf ; Sc age kf, hi, hc,.VEL ac df ; quarum hc acN df occurrant ipfis af&ik in m&n:& inhc demitte normalem

-IbCF -^EGF - GFD = AMH - MHI - CIL ;

. Eritque angulus k. — -7^^^ — y^ — nnin — «inx — ,

°que triangula re&angula kbf, fbn, hli 8c ilc fimilia. Dicer S° Fc -a, Hi —a, 8c ic=jy; & erit bn (2 a-y.). bk (y): : lc. lh : :Cl ?(-^y.) Hi*? (xx.) adeoque 2 axx-yxx=y\ Ex qua aequatione facilet fligitur hanc curvam effe Ciffoidem Veterum, ad circulum cu-centrum lit a ac radius ah, pertinentem.

ita

P R O B. XXXV.

& datc 2 longitudinis reBa ed, angulum datum , ead, fub tendens,foveatur , ut termini ejus, d 6s? e, anguli iftius latera , ad ae,

petim contingant ; proponatur Curvam fcg determinare , quamutn quodvis c, in reBa, ijld, ed, datum, defer ibit.

A Dato puncto c age cb parallelam ea ;

8c dic ab - x, bc —y, ce -a, cd -b :8 l propter fimilia triangula dcb, dea, erit

ec. ab : : cd. bd. hoc eft a. x : : b. bd = —•

a

d at Bhg d Praeterea demiffo perpendiculo ch, propter

a ngulum VAE vel dbc, adeoque datam rationem laterum

R 2 trianguli