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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 54, page id 797435492:0270
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SiB. 56.
15. 57
218. 58.
L. E C Y. VY
Corol. Si ZS cangaE hyperbolam DYY; CxIEP M 9. PY 9::
P A. PS.
Nam eAt PMg. DB9:: P Ag. ADq:: P A. AS. ergo per
rationis conrertionem est P Mg. P Z q:: P A. PS.
ZXIII. OuodR reliquis similiter posiris, Sic jamF Y = V PMG
) D B9; erit eriam linea YY Y hyperbola; cujus nempe Cen-
erum A; Semidiameter A F (parallela _ aequalis ipti DB) Semi-
parAmEtOr aUTEM P, SI HAE AF. AD :: AD. P.
Nam ducatur Z K ipsi A P parallela cum A F conveniens in R;
Sirgne F T = 2 F A; CAque A F. P:: (AFg. ADq:: DB9.
ADg:: PMg. APg:: FY9- DB9. APg:: AR9- AFg.
RYg::) LRXEK. KY9:: AF. P. unde constat PropolI
EUIM.
Corol. Ruxsus, Si recta Z S Byperbolam F Y Z FaNBAL, exIt P M 9.
PYg:: P A. PS.
Naim A D est Semidiameter ip(I A F conjugata. unde P A. AS::
P Ag. ADg:: PMg. DB9. ergoP A. PS:: PMg. PM 9
) DBg:: PMg.PY9.
XZIV. Sicrriangulum A D B, rectur habens anguluM ADB.
d curra CCDralis, ut duet ầ quicunque recta F F C ad D B paral-
lela (quae lineas expotitas secet ut vides) sic asprepatum quadrato-
ruM ex F F, F C aequale quadrato ex D B; erit CurVa C C, D Ellip-
sis cujus Temiaxes AD, AC.
ETaM SIE AV = AD. FAtque ADg. DB9 (AC9):: AF 9.
EFg:: ADg - AFg. DB9 - F Fg. HOC CAADg. AC9::
V EX ED. F. C9. unde liquet ProDOCIum.
Nota, TanBat CY ellipsin C CD; eA FFg. EC q:: F A.
F T.
Nam ob AF. AD:: AD. A F, CA A Fg. AD9:: AF. AT.
unde AF g. AD9 -- A F 9:: AF, AT - AF. LIOC CA F P 9
DB9- EFq:: AE. ET. hoc esF Fg. EC9:: AF. ET.
Sit Angulus rectilinens D TH, in cujus latere F D SIGMeTUF pUN-
ctum A. Sic item curra V CC proprietate talis, ut duet a rect â qua-
Piam F FC ad T D perpendiculari (quae lineas TD, TFI, VCC
Iccet punctis F, F, C,) connexaque recta AF, CIC EC = AF.
erit linca V C.C hyperbola.
Nam ducaneur AP ad TH ec V PC ad =D perpendiculares;
Iem
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