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# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 113, page id 797435492:0347
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L R CT. ZII.
C 2 Pecans in Y, hyperbolam in R) _ connectatur C. R; erir spatium
ACIY a sectoris hyperbolici F C K daplum.
Nam est C. Ig. C Ag:: ASg. C Ag:: F M9. C Fg:: C A9
=CFg. C Fg. componendoque, C I9 .]. C A9. C A9:: F18, 169.
C Ag. C. F g. hoc elt (ex hpperbola nacura) IR g. C A9:: C A9.
CFg. velIR. C F:: C F. IY. itaque spatium A CIY a sectoris
F C R duplum esse perspicuum cA e praecedente.
ZI. CoroIl. TIinC (I PolOF, Chorda C B, Sacirta C A descripta SIF
Conchois AVV, cui occurraE Y F M producta in V; exit MV = F Y;
adeoque spatium AM V spatio A F Y aquatur.
ZII. Unde spatiorum ejulmodi Conchoidalium dimonsiones innotelcunt.
XIII. Nescio, an operae sit hoc adjicere Corollarium.
ZIII. Sit reCtA A E rectae RS perpendicularis, _ C F =C A;
linrque dux (Cibiet inver(x) Conchoides AZ Z, E YY ad eundem
polum E, communemgne reculam RS delcripex, ab P. vero ducatur
utcunque recta P YZ (lineas incerlecans, ur vides) sic eriam hyperbole F18. 170.
aquilatera PRK, cujus centrum C, semiaxis C F; dud ique IR
ad AF. Parallela, connectatur CR, erit sparium quadrilineum
AFOTEPA (reCtIS AF, YZ, _ conchis FOY, APZ compre
hensum) xequale quadruplo sectori Fyporbolico F C R.
Nam RICOntrO F per C ducatur arous circularis C X; e dictis Faci-
le colligetur spatium A P L IC eequari duplo sectori Byperholico F CR
una cum sectore circulari C F. X. item sparium F OYIC xquari duplo
sectori F CK, dempto sectore C FX.
Ita quoque Facile colligas. DucantuE Z F, YC ad CS parallela;
e prorratiantur GYL, L IHI. ac ob IY =IZ, eAFZ. 1 GY=
2 C. I. de trapezium FC YZ = rectans. P. CL II = 2C C x CI.
exsOPaTEF.
Adnocari porest Silubet, ductâ A T ad CS parallela, prorracta-
que FZ T, SiPOnaTIE N = 2 trianB. C F I - 2 lect. ECR; FOre
(PaC. EZ T -)  F OXF = 2II.
Nempe N -) . C XI = SPaT. AZT. ∞ II - C ZI = spat.
EOXF.
ZIV. Adjiciemus etiam hisce cognatam Cissoidalis sparii dimentio-
neM.
iE demotion L CCusus Cemu L) Quem cansal recla
AH; eique consruens Cissois AZ Z cujus scilicet haec proprietas est,
e 21. 1.