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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 129, page id 797435492:0371
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V
E E CF. ZII
in puncto M, ductisque rectis M P Z ad BD, _MO Y ad AD
parallelis, Politoque rectam M T tansere CurVaM AMB, CIETP.
EM:: OY. PX; CrUNE fIGUTX ADR E, DBLO Sibimet aequa- F18. 201.
leso
Valet hoc converlum. NNempC (I fBuTK ADR F, DBL C X
quentur, _ MT CUTTaI A M B tanSAE, Crit YP. PM:: X.
PX.
Noc. Omnium hactenus Propolitorum Faecundissimum est hoc
Theorema; Peaecedentium quippe complura vel in eo continentur, gue
ab eo facile consectantur. Nlam posito lineam A M B indeterminatam
esse natura, Si ipCarum F Z R, C: Z L allerutra pro tuo arbitratu de-
terminetur, exinde resultabit Theorema quoddam ejusmodi, qualia
superius exhibentur aliquammulta. Si c. e. linea Ca Y L ponatur recta
cum ixCa B D Temi- rectum constitmens angulum (quo casu concipiun-
tur puneta D, C coincidere) proveniet inde prima Lectionis XI. Si
OFI sic recta ad D B Parallela, emerset Lectionis ejusdem. RUr- Fi8. 202.
suS(I F MI = P X (vel lincx AM B, F XK snt exdem) conseque-
turhine decima ejuldem. Fxhrinc porro liquet adsumpro cuilibet spa-
cioinfinita; genere diversa spatia aequalia Facile designariveluri ( spa-
rium D C: L. B Ponatur circuli quadrans, cujus centrum D; e curra
AM B Cic parabola, Cujus axis AD, CMErCE CUEVA F XR HXC PrO-
prietas, ut (BI dicatuE DB = Y; AP = = X; P X = y; _ k (vel
DB.
2AD Cit parabolae semiparameter) (it -  = ke k x J. x yy. Sin
AM B Bonatur hyperbola, procreabitur alterius generis curra PXR.
hisautemm expenlis a Bncliar meam inculo, qui non hoc Fheorema ((I-
cut ex ea quae subsequuntur, quorum fere ratio consimilis est, _ sup.
par uuS) primo loco poluerim, e ex eo (nec non e reliquis mOX
subjiciendis) quod fieri posse video, reliqua deduxerim. Veruncamen
hujusmodi Phrysiam sapientiam juxta mecum plerisque Familiarem au-
cumo, liceras has cractantibus.
Lheot. V
Fi
comprenemu) i scet eusra LLLI CL caCtuca, ic  Cuera L16. 203.
A MB libere sumatur punCtuM MI, dUCALUFD M Z, SIE DO =-DN,
ducatur Y ad D B perdendicularis, sit D I ad D M perpendicula-
ris, recta M T curram A M B contingat; (I, his inquam suppositIS, (IC
TD. DM:: DMX GY. DX G, eriT spatIUM DCL. B spatiI ED R
duplu
Theor.
Sic spatium quodxiam A D B (rectis D A, DB, _ curra A MB