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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 120, page id 797435492:0358
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tt e dre dode d
Prop. 3.
Dacus i Consteltus A BC p. Secetur a plano (puta rrianeulo
GrF) quod quidem planum secabit axem coni in punctoq supra verri-
sem produerumm e in communi incer lectione cum saperficie coni habe-
Dic Lineam hyporbolica R SF ducantur a verrice coni A rectX AY, A L,
a piincto odemiuearur perpendiculum q2 laceri coni A p producto e à
punEto A perpendiculum AZ planogrE.
Dico sapersicres conica terminata à linea hyperbolica, r st  rectis
rA, A, ita se haber ad ficuram hyperbolicam cavam gr 5t q ut perpen-
dicuium A L. ad perpendiculum qX.
Recta enim gr, circumlata, quiescente termino q per lineas rst, t_, Ar
generarrres superficies, nempe lorporbolicam cavam gr, st, ec duo rri-
ane_la gt R, qar, dux una cum suporficie sonica terminata à lineis
rst, tA, Ar, comprehendunt Solidum gr s, F Ar. Hloc vero solidum
aequale est prramidi cujus altitado est x qualis perpendiculo gX, nam
intinitae prramidesq arV, qAVV, exhauriun Tolidum gr StAr.
Si vero alirer contemplari volumus, hoc Polidum gr st Ar porestcon-
Ciderariranquam ficura conica ArSF gr habens pro base ficuram hy-
perbolicam cavam gr St 4. ex pro altitudine perpendiculum A Z. FrgO
reciprocando bases alcitndinibus, ut AZ ad qX, ita superficies, rSt Ar
ad figura hyperbolicam cavam gr 5tg.
Prop. 4.
Datus liE Conus rectus A Bh e secetur a plano HF P C, Per avem
intra verricem, a puncto FI ubi planum secat axem coni, demittatur HIR
perpendiculum laceri cuilibet coni ec a verrice A perpendiculum A. L. pla-
nOHFFC.
Dico; Superficies conicaterminata a lineis FF C G A AF ira se
habebit ad planum HI FE C. ut perpendiculum AL. ad perpendiculum
TIR.
xobatu co ee ca sete atueo B UUDetior.
lhaccllentia
E18. 1780
618. 279