arithmetica universalis.

rZ§

Produc CD ad Q^, Ut fit DQ = EF; Sc per Problema-„ , ^ . ta Geomk .

Q. age qn parallelam ad. Denique trica.a b &£ f ad ad Sc oyj demitte perpen-dicula ba, fn ; 8c a c ad ab & fn per-pendicula CK, CL. Et CUm fit BC-CDvel ak, erit bk (- ab - ak) = ab-bc,adeoque BKq = ABq - 2 ab xbc + BQq.

Aufer hoc de Bcq, Sc reflabit 2 ab xbc

~~ AB <7, pro quadrato de ck. Eft itaque ab x 2 BC^ab — CKq ,^ eodem argumento erit fn x 2FC — fn=cl#, atque adeo +

ab -

2BC,

Sc + fn = 2FC. Quamobrem, fi pro AB, ck, fn,

cl, fcribas a, y r b y c y Sr. c -y y . erit ^ + \a = bc, & -— 2 ~~-+ i^fc. De fc aufer bc, Sc reflabit ef=- -— 2 —~- + \b— y ^- —{a.

-j- 7 2- 7 ia 1

J a m fi puntfla, ubi- fn produdta fecat rebtam ad Sc circulum gem,dotentur literis h, g, Sc m ; Sc in hg produ&a capiatur hr=ab;

fit hn ( = dqj= es) =gf, addendo fh utrinque, erit fn - gh ;ade °que AB - FN (=hr—gh) = gr ; Sc AB-FN + 2EF, lioc eft a-b+=x R5I . & ^a- ~ b + ef = ]: rm. Quare, cum fupra fuerit ef —yy - -\a y fi hoc fcribatur, pro ef, habebitur a rm =

2

. Dic ergo rm d y Sc erit d

cc — 2 cy -hyy

yy_

a

Duc

0r ^nes terminos in a Sc b, Sc orietur abd—acc-iacy+ayy-byy.•^After utrinque acc—iacy y Sc reflabit abd—acc+zacy-ayy-byy.divide Der a—h. Sz orietur — cy ~ —yy. Et, extradla radice

V-

'aabil — ahbil -B.abccaa — 2 ab -f bb

Quae conclufiones fic abbreviari pof-

1 * " -v

„ nt * Pone c. b : : d. e\ dein a-b. a :: c.f\ 8 c erit fe-fc- ify-yy^1Ve y~f ± y/ff +fe —fc. Invento five kc vel AD, cape. AD =/

v 'ff+fe-fc ; ad d erige perpendiculum dc ( = bc) = ~ \ ab ;

^ centro c, intervallo cb vel cd, defcribe circulum bde; nam, lc tr anfiens per datum pundum b, tanget reftam.ADun D, ScClr culum GEM in L. Q. E. F.

* iir * c circulus etiam defcribi poteft, qui duos datos circulos Scam politione datam continget. Sint enim circuli dati rt, sv ;° rilm centra b, f ; Sc redta politione data pcu Centro f, radio

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