492 GEOMETRIA

Caput x. in D, et compleatur parallelogrammum acdi ; eritque ac-#,

" & area quaefita agec (= j-am^acdp-acdi) = idp.

13. Exempl. 3. Sit age CifTois, ad circulum adq_, diametroAQ^defcriptum, pertinens, Agatur dce diametro normalis, etCurvis occurrens in d et e. Et nominatis Ac-L, ce=>', Sl AQj= a ’

propter cd, ca, ce continue proportionales, erit cE,fivej,=

LL

*/ az

z ' five-1 =fl 7

ac dividendo per #, fit y = — — z — . Eft itaque jst

\Zaz~ 1 — i

— 2>J— J

ct inde — A==; aequatio tertiae fpeciei quarti ordinis pofterioris

Catalogi. Collatifque terminisfit d— 1, e=-i, & f=a. Adeo-que z (= -) =x, s/ax-xx ~v, &

z’’

3-f- ixv - t . Quare eft ac =cd=^, et inde AEvn-r, adeoqtie3ACDH-4AADC ( - zr- 2xv = 0— areae cifloidali acega. Velquod perinde eft, 3 fegment-adha - areae adega, five 4 feg'ment. ADHA=areae ahdega.a 14. Exempl. 4. Efto r E

Prima Conchoides Veterum, centro g, afymptoto al, et intervalloLEdefcripta; age gap axem ejus, ac demitte ec ordinatim ap'

plicatam: dicftifque KC-z, ce=)>

Gh—b 8 c, AP —<7; propter proportio-nales ac : ce-al::gc:ce, erit cEfive y — h -~ \/c z — z l (y'). Jam ut ejus

area pec exhinc inveniatur, partesapplicatae ce, feorfim confklerand®lunt. Et quidem fi illa ce ita di-

/ f\

a

R

c __-

e (y?'

\\ \

k.

\ 7 T \\

y.X

\xL \\

vidatur in d, ut fit CD— y/c z -z% acde =—\Zc z -z z erit cd ordinatim

Z

applicata circuli centro a et intervallo ap defcripti: adeoque parsareae pdc innotefcet, et reflabit pars altera dped invenienda.

Cbm

* — _ . EE X CG » - b -p Z /'"Inurf?

(v) Propter el : eg zz ac:cg, erit eg zz —--, hoc eft ec zzcX - -- ^