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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 119, page id 797435492:0191
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Y, F C F. XVTI.
AV. TV: : CV. CD; e consequentes subduplando, diridendo.
QHC AR. RV:: RV. R D:: RV. CR. Vel AR. RHI:: RH. CR:
hioc est HIN (RX). NC:: KH. CR; quare C R X K ~ = K H
XN O, eA aNtCI XZ 9 = CZ 9 -- CX 9= X69.- CX9 =
NC9 ). RH9 - 2 AC X RH: = RX9- CR 9. ]. 2CR
XR X = N Cg.J. RHI9 - RX 9 - CR g. SuratuE K S = KX,
discurtumque limilem aunibendo liquebit Fore EC = Z Z. _ ideo
DZ = CZ. unde CE --DC (DZ - CZ) =C
-CZ=
Ey = XO = 2 KHI = TV. quare manitestum eAt cArVaS TI.
VEesse Fyperbolas, quarum axis LV, Foci C, D.
IV. Tertio demum, sic angulus C A F. semirectus (vel C A = Fig. 192
CF) erit cum punctum Z ad parabolam; quae iridem ita determina-
tur. Fiac angulus AC P Cenirectus, _ ab iplarum AF, C P in-
tersectione R duCatUE R I ad C F Parattela; erit TVertex, atque C
Focus Parabolae. id quod ex bene nota sectionis hujus proprietare con-
sat; qua scilicet est I A = TR = TC (ob angulos. I AR,
TC R RemirectOS) _ AX =XC = CZ.
V. Manifectum est vero rectam A F sectionestas ad F contingere.
quia nempe perpetuo major est CZ. (vel X(1) ordinata XZ; aderi-
que puncta C exrra curras unagux que jacent hoc est tora AG exIra
illas cadit.
VI. Hilce peaestraris: Esto Circulare speculum MBND, cen F18. 193.
trum habens C; cui exponatur recta quapiam LaC; e huic per-
pendicularis sic recta Ca; quam ad partes avertas (umPEa C A, ad-
aequer.. Sit etiam C F ad C A perpendicularis, ac requalis qua-
dranci diametri BD: connexaque recta A F producatur utcunque.
sumpto jam in recta Fa G puncto quolibetF, ConnectatuT F C, 8
radiationis ab Pin ipla FC limes, seu focus, (it Z; ac per Z du-
catur Z X ad A C. perpendicularis, ipsi A Foccurrensin HI, dico:
fore X HIparem ip(ICL.
Nam (e jam ante monstratis) est F C. CZ:: FMI. MIZ (hoc eA)
: FC = CB. CB - - CZ. tinC exIE B C. CX (AC, CX)::
FC CB. CB--CZ. quare (ducendo in se extrema, ac media)
eric AC X CB - AC XCZ = CZ XFC -C ZX CB. hOC
eA (ipsI C X X F C substimendo A C X CZ, PFOPter a C. CX::
FC. CZ) erIt AC XCB - AC XCZ = ACXCZ -CXX
C. B. transponendoque AC XC B + C L XC B = 2AC. XCZ.
hoc.