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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 122, page id 797435492:0198
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E. E C F. ZVTII.
CZ. FC:: CZ. C A; adeoque CZ XC A = FC XC X). qua
proprer (elidendo FC) CA CMXC. R + C L XC R = CZ X
C A = CM X CX; transponendoque C M X C R -f CM X
CZ = C. Z XC A - CZ XCR. HOC est CM X RX =CL X
A R. quare (ad analogismum redigendo) est A R. CM:: RZ.
CZ. hoc eAt CR. C E:: RX. CZ. hOC est RX. XH:: RX.
CZ; unde XH = CZ: Quod F. D.
II. Fxhinc (_ ex iis quae circa sectiones conicas nuperrie sUNE
ostenta) liquido consectatur, si C R major fuerit quam C F (vel
quod eodem recidit, AR major quam C B) quod punctorum om-
nium Pin recta P A C imagines absolutae (quales Z) ad ellipsin con-
Sistent, Cujus Focns C, cujulque penitus dererminande modum Patis
Facilem tunc octendimus. item (i C. R = C P, quod imagines iltxe ad
parabolam erune; e denique, si CR  DC F, quod exdem inhy-
perbolis oppolicisreperientur; quarum etiam sectionum Focus com-
munis est punctum C, ex quarum axes delignandi modum reliquaque
circa iplas praelertim advertenda declararimus. (Nempe, S recta
C P cum ipsa C A semirectos constiruant angulos; e hx rectam R F.
interlecent ad punctaS, indéque demittantur ad A C perpendiculares
ST, SV, erume T, V aristerraini, rectaque C. P. semi parameter exir)
unde patet torius recta E A C ad infinitum prorenx absoluram ima-
ginem (quin ec illam, quae ad oculum in cenrro C politum refertur)
aliquam esle dictarum conicarum, pro suo reculiari litu hanc vel illan
respectire.
TII. Adnorari porro deber in isto calu, sectionis ellipticae (quineriatm
ec parabolicae) TF Z. parrem anricam T P ad concaras circuli parres
IDE spoctare; licuri postica PY ad convenas M BN perrinet. in
hoc aurem alrero tora hyperbola Z. V Z, nec non hyperbolae P T P ParS
(intra P CF) P E F Y ad partem circuli conrexam reterri debent
(nempe si centro C, interrallo CP deleriptuis circulus rectam F C
secet punctis R, R; hyperbola Z V Z reCtaM INTETCEPEAI R R REPEX-
Cuncabir, ipsiusque PC quod reliquum est hinc inde procensum pars
TF R Y reteret) pars autem superior F T P ad caram cirelili partem
E DE spectat. II. Semper autem (cum hic, cum ubique) incellisatur
ad urrasque proxoliti circuli partes ejuldem generis retractionem efficis
seu ejuldem speciei medio ractios incidere.
Vio   oc alita, Giil ut. DCu AGua COMLETUENdA AaHI.
buit,
E15. X9.