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# Title: Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio (shelfmark Leibn. Marg. 84:2)
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PR OP. 49.
De Sectionibus Conicis.
bus nempe Diametri interceptae sunc Ordinacim- ap.
plicatarum biguadratis, vel Curdelolidis, eC, propor
tionales:) diei poterit Paraboloides Bignadraricale, vel
Surdesolidale, eC: (nomine nempe rationi aptatO.)
Lacus rectum ejusmodi Paraboloidibus conveni-
ens appello rectam imasinariam; cujus, in Biqua-
dracicalibus. Cubus in diametrum interceptum ductus
aquatur biquadrato Ordina im- applicatae; in lurce
Colidalibus, Biquadrarum in diametrum interceptam
ductum aequatur Surdesolido Ordinacim. applicata:
(e similirer in aliis Paraboloidibus, respectu semper
habito ad gradtum P’araboloideos.) IIE (E (prout SIa-
dus Poltularerit) pa =- d13, vel p5 =- a14, e TC de
INCCPS.
Habene aurem ex haec Paraboloidea Diametros in- parsun
vicem parallelas; carumqi Ordinatim- applicatas pa.
rallelas Tangenti in (suxe cnjusibet) diametri ver
tice.
Recta vero AF (diametri continuatio inter verti-
cem _ tangentem intercepta) est, in Paraboloide Bi-
quadraticali tripla, in Curdesolidali quadrupla, dia-
MCTMInLCrCEPTa PA; (e Timilicer in aliis:) HOC eA.
continuata diameter PF (applicationis puncto et
Tansentis concurtu intercepta, eM ad Diametri in-
cercepta Pa, in Biguadeaticali quadrupla, in Surdelo
lidali quincuplas ee sIc deinceps.
Demonsracio pari modo procedet acq; in Paraboloide Cu-
bicali; auc etiam ipsa Parabola.
Adeo ue jam Paraboloidis Cubicalis, Bignadraricalis, Cur-
desolidalis, auralius cuinlrie, doctrina, non minus cognita ha-
bearur. quam ix ius Parabule
Si eamen, post pecimen hoc exhibicum, operae precium cen-
Febicurrem hane Fulius prolequi, pocerie illud a quolibet Facil
lime fieri cui tancum suppecic otito