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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 104, page id 797435492:0326
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L E C F. XI.
AF. C aquarur Circulari seemento ADB demonstrationem, ne longius
erager, obmirram.
XXXIV. Sint duo sirculi AIMO, AKNH sele contingentes ad A;
communique diametro A H C, urcunque perpendicularis ducatur rect a
DN M: habebic scementum AIM D ad sesmentum AKND mino.
rem rationem, quaM rECtA DMI ad rectam D N.
Nam lic A R ad AC perpendicularis, ac ip(I A HI aequalis; e
connectatur HR, cui occurrat recta M D in Z; ducaturque recta
GXS; tum ad axem A C parametrum AS per N descripta con-
cipiatur Elipsis ALNCI; haec Cuni Pacis manifestum) intra arcum
AR H TOta cader. Fs autem SCOM. A IMD. sCOM. ALND: 3
DM. DN. erso Ccom. AIM B. (CGM. ARND =3DM. DH
XXXV. Sic EIlipLIS YEZT, cujus axes conjusati YZ, FT; sit item
i8= 154. recta DC axi majori YZ Parallela; e per D, F, C cransear circulus
DECV centrum habens K, in elliplis aze minore L. Y sicum; dico
circuli partemM DOFPC inera ellipLIS DarFCM DMENC jacere.
Nam (iCF Lad FV perpendicularis, _ in haC TUTATIW FS = FV; _
connectatur V S, cui DC producta occurrat in X; ee connexa I X
ipsi EI occurrat in R. _E Cum (IEC D 9 =- F C3 X C, V==- F C, X6X
liguer ipsam FR esse ellipsis, axi F Tcongruam, parametrum; unde
constat Propolitum.
XXXVI. Sic circuli, cujus centrum L, segmencum DFC, e sumpto
in ejus axe CF. puncto quopiam F, siC curra DMFC talis, ut ducta
vtcunque recta RMS ad C, F. paraNeli, sIE RS. RM:: G F. GF
exIFDMEC ellipsIS, hoc modo dererminata: FIaE F G. F C :: C,L.
OH; _ Per H erigatuE YHL ad DC. parallela, CIEquC HY par ipE L F:
exunEHT, HIE ellipsis semiaxes.
Demonstratum habetur à Creg. a S. Vincentio, L. IV. PxOP. 154.
Corol. Elinc leBM. DEC. DMEC:: FC. FC.
ZXXVII. Sint dux circuloru pOrtIONES DFC, DOFC. quarum
communis subrensa DC, _ axis CFF; portio major DF C ad porrio
DEm DOFC majorem rarionem haber ea, quam habet axis C F. ad
AXCI GF.
Nam sinE L circuli DSFC, _ R circuli DOFC CCNTTA, _E Hat FO.
FCi::GL. CH, _ Hac ZHIZ ad HII perpendicularis, _ sIE HI X
qualis ips LP. cum semiaxibus HT, HIE descripta concipiatur ellipsIS
XDMECZ; e mox praedictis liquer elliplin DMFC circulO DOFC
circumduci. F.s autem circulare segmentum DFC ad sexmentum el
lipriCum DMFC, ut CF ad CGF; quare segA DFC ad seom circula-
reDOFC. racionem haber majorem, quam GF ad CF: Ouod. F. B.
LPer.
EiB. 154.
F18 155.