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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
# Folio 687, page id 851387705:0707
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PFOD. VTII. DeCaui Citr suatis.
SC+OL TV M.
N praecedentium aliquor propolicionibus; in figuris Parabolicis omnibus, es
Parabolocidicis, corumque Solidis, Centra graricaris determinarimus. Neque
hoc tantum in Figuris incegris: Scd et (quod neleio an alii nobis priores sece
rinc) in Firuris Dimidiatis; uc Semi parabolis, Semi parabolocidibus, dc. etiam
in figuris Reciprocis (quorquot habent) Dimidiaris: Arque in horum omnium
Semi solidis; auc eriam, solidorum porcionibus quibutris, duobus per adem pla.
nis, interjectis.
De FieuriS autem RCcipEOCIS (uE ADBB5,) speciacim monendum est; VTE
tae natura lua sine ucrinque in intinitum concinuabiles, (sunt utique AD, AS.
ad curram B B, ATyMPTOIX;) nos tamen hie eas consideramus ut Bale BD termi-
natas, ad Diamecrum ordinatim Dolica (sicur _ Parabolas alia sque tiguras indeti.
nice concinuabiles, Base pro arburio claudimus;) led ad Partes B s indetinite con.
FinuataS,
Cumque harum aliquas magnicudine simpliciler Entinicas ostendimus (nempe,
cum Index seriei eAt = L; quo catu BBcurra, cll vera Ilyperbola, cujus ACymp
tOca TUnE AD, AS;) Alias vero rel Finitas, rel plusquam Intinitas: Tunt qui-
dem hae tigura ad ea(dem curras utra que terminata. Ouippe, (I A DB BS, Ter-
minata basi BD, interminata rero ad partes Bs, Sie Pinira; Cadem ex parre BS ter-
minata, et interminata ex parte BD, eric Plusquam infinira: e Contra. OuX Vero
ad veram Flyperbolam ponitur (seriei indicem = + habens) utraris parte cermi.
verur, (modo ne ucrague,) Cst paricer Intiniia: Argue haec 1ol2. Quod prop. 105.
Arichm. Intin. Ostendimus.
Conttat aurem, ex his Figuris Reciprocis; (quae inter Geometria miranda cen-
Tentur;) Piguras lonsicudine Enfinicas (Planas Solicatre) Magnicudine l’initas
esse polle. Nempe, li ADBBS ex parce BS incerminara, seriei Indicem habeat
nesatirum quidem, sed majorem quam- +.
Fademque Figura, (longicudine infinita, Sed finica magnicudine,) si verinque ad
AD diametrum similiter ponatur; habebir (in ipsa AD) Centrum pravicaris.
Eadem rero figura dimidiaca AD BB s, indicem habens negatirum led majorem
quam = =; utuc magnicudine finica GE, centrum tamen Craricatis non habebit;
nili ee major lic Index quam -=. Ne quidem quae ex duabus hujulmodi dimidiaris
veringue ad infinitam AS similiter POLciS ConHatur. Diltabit utique ab A verlus
P, diltantia Calcem intinica, vel daca quaris majore.
Sin major sic Index quam - 5, Cencrum Cravicatis habebii, tum dimicliara illa
Figura, tum et ex duabus ucrinque ad AS potiris constata.
trem; Figura istiusmodi plana, magnitudine Finica esse pocest; (nempe cum
Index major est quam = F;) ee Solida camen, quae hujus convertione tic, magni-
cudine Intinita: (Nempe, S non e major sic Index quam-
Ouippe, I FC-
ries Rectarum, planum complencium, indicem habeat = Z; series PlanOrum, quX
harum convertione circa ADtiunt, Solidum complencium, (propier Plana inra-
tione duplicata rectarum in illis similiter posirarum,) Judicem habebic .,
eriique proxcerea magnicudinis intinita. Sin series Rectarum In.
dicem habeat minorem quam -3; series Planorum habetrie indicem minorem
quam =+; adeoque Solidum erit magnicudinis plusquam intinicx. Ouae omnia,
Ex lupra demonstratis constant.
Contra vero; Istiusmodi Figura Plana, non modo maenicudine finica quaevis;
Sed ec intinira, modo Index major sic quam = 2; circa As converta: Solidum
exhibet maxnicudine sinicum: Et quidem, modo Index major sit quam =+; quod
Cencrum habeat Cravicalis. Quod ex prop. leg. patebic.