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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 118, page id 797435492:0190
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I E C T. XVII.
ad ipsami F. C paralloIX ducantur re AX R F, SV; palam est inderer.
minatum punctum Z inter limires T, V consistere (nam exETa TV
punctum quodlibet L accipiendo, _ inde ducendo L IP ad C P paralle-
lam, eric CL, hoc est L P, major quam L l, unde a C ad rectam L I.
nulla duci recta potest aequalis ipli L I). Tam autem dico, quod
punctum Z ad elliplin existir, cujus axis TV, Focus C. Nam bile-
cetur TV in R; tiat VD = TC; ducatur K H ad C P Paralleta;
Pex HI ducatur H N ad C R parallela. FAque RH:
C. F. I. CV.
FR. L. V S
=RT = RV. EE quoniam AV. AI :: (VS.
TR (hoc est):: CV. CT::) CV. DV; erit per rationis Con-
vectionem AV. TV:: C V. CD. rel, consequentes subduplando.
AV. RV:: CV. CK. diridendOgne AR. R V:: RV. CR; hoc est
AR. RH:: R II. CR. hoc est HN. NO:: KH. CR. quare
RHI X NC = C K x II I =-CRX RX. atqui eA C Z9 = XO9
==RH9us NC9. ]. 2RHX NC. _ C X9 ==CR9-). K Z9
p. 2 CR X RX = CK9. ). R29 .(.2 K H X N C. ergo
RH9 .s NC9 - CR9 = R =9 == CZ9-CX9 =X29.
Adalteras BisegmentI R paEEeS SLIMatuIE R E =X Z, ducaturque EV ad
RHI parallela, secans curram T F Z V in C, _ rectam A HI in v, ac
iptam NEino; erir quoque, simili ex discurtu, ECg =RH9. ]
Vg9- CR9 -KEQ; unde liquet Fore EC =XZ; connexisque
proinde rectis C2, DC, erit D6 =CZ; _ C7. f. CZ = 57 :)
2C == 2 RHI = TV. eroD CC. f. DE (velDZ .f. CZ) =-TV.
unde perspicitur curvam TEZ V esse ollipsin, cujus axis IV; foci
C3D.
TII. Sic autem secundo angulus C A E major semirecto (vel AC
CP) dico puntum Z ad oppolitas hyperbolas, consimili modo
decerminabiles, existere. enimvero Factis (ad utramque rectx C A
paeFH) angulis Pemirectis AC P; _ (ab iptarum C P cum A F
Occursibus) ductis rectis RT, SV ad C F parallelis, punctum X
extra limices TV necessario consicter (etenim ubivis inera I V duet a
TIP ad C P parallela, erir LI SLP, ideoque nulla par ipsi LY
ansulo A LITubrendi porest; id quod extra terminos holcenil pro-
tibet feri) eric jam TV aris, de C focus hyperbolarum. Fiane
enim omnia; qua in casu praecedente; exirque rursus hic RH-
RV. irem ob AV. AT:: C V. DV; ec (inverse componendo)
18. 791.