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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)
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PxOP. VII. DeCalculo Contri Cravitatis.
LROP. LI.
Si intelligatur ex Rectis Planitre, secundum aliguam ex Reciprocis (in
def. 2. hujus definitis, Indicem habentibus Negatirum) seriem insi-
nitam, (ab 5 ip(a feriei orisine inchoatam, et dato terminatam,) Fi-
dura conslari:
Etabebit haec, ad Verticem, laticudinem Infinicam:
Finitam tamen, G, ex parte Verticis, intelligatur vel tantillum Plano pa
rallelo abscindi; (adeoque sigura faltem truncata magnitudinis erie
Finica:)
Aream rero; quae sic ad Parallelogrammum, vel solidum Prismaticum, D.
super aequali Baseaque altum: uL Z, ad Indioem Dnitate, auctum:
Adeoque rel magnicudine Finitam; E Index sic major quam --- =;
(DuTa = 2 = 3, = 2, 8C.)
Vel Intinitam; si Index sit ----F:
Vel Plusquam Intinicam; si sic Index minor quam = F; (puta, -- 27
3,etC.)
5.
t
Ouaeque sunc magnicudinis intinita, (auc plusquam Intinicx,) Cen- II.
erum Graritatis non habent.
Duae sune tnicx magnicudinis, siquod habent Cenerum Graritatis, in L. L.
ea habene a rereice distantia, qua uta dividitur Diameter vel AXiS,
ut pars ad Basin, sic ad partem quae est ad Verricem: ut +, ad Indicem se-
riei Onitate auctum.
Habene aucem Centrum Gravicatis hujusmodi Fisurae (magnicudinis
sinitae) si sint Incegra, (hoc est, utringue Circa Diametrum rel
Axem similiter polica;) Nempe, in Axis illo puncto, quod, ita ut
dictum eA, distar.
Eix dimidiatis vero (vel quae trarum instar (unE) qua habent, quaeque
non habent, in Propoluione sequente dicetur.
Ouau exemplis facile explicantur.
Deque his Figuris Fruncatis, auc alias Mulctacis, vel Aexresatis; idem
judicandum est acque de illispropositionis Praecedentis.
AEque tae Fieurae interminabiles (plana, Solidaeros) ad. Par aboloeidium
genera spectant, vel adharum Tolida.
IpIx autem Linea Curva, ad quarum conrexas adjacent interminabiles
hujulmo di Pieura Planx; ad = syperbolarum seu Ly perbolocidium senus
reterendae lunt.
Sed et ouxe ad Fyperboloeictium harum (ea TOIA CKCEPtA QUX CA VerA HY-
perbola Apolloniana) Concavas adjacent Fisurae plance, (concara et
FCCtIS tErMInaLX) tum quam magnicudinem habent hinc determina.
bitur; tum ex Centrum graritatis datum exit.
Ncelligatur, ad Diametrum vel Axem AD, hujusmodi Figura plana solicave
construi, asBD; cujus Basis DB; d huie paralelae rectae aue superticies pla.
K.
L.
1
d
D
F18.
na (tixuram complences) ordinatim applicarae, lecundum seriem ex Reciprocis il 129,
lis quamlibet.
Erit, propter Teriei Directae terminum primum o, leriei reciprocae primus termi-
nusco intinitus: puta 2 = ∞. (Nam, ubi quanciras quaelibet dividitur; si diri-
dens Tro, quociens erit co: quippe nulla quancitas tinita, pro quoriente polita,
diridentem o mulciplicans, rellicuer dividendam.) Adeogue Recta Verricis A S
erit incerminabilis: Sive sigurae lacirudo, in Vertice, infinira.
Cum vero Seriei directae terminus post primum quiliber quancitarem habiear Fini. C.
can; seriei reciproex reliqui omnes termini sune tiniti; adeoque ligura intra
verticem