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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 676, page id 851387705:0696
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ap. .
FUCd; CIM LINea Tecta UE AD, (propter aequalia Puncta;) Parallelosram
um: uc BBA (proprer rectas aequales;) vel cirea hoc constructum Prisma, vel
Cstindrus, (propter aequalia plana;) sic Scries Aqualium scu Nullanorum:
Cd.
BaL, TdP, 2.
ENDP-
(Duta Ut P, P, P, eC.) cujus Index o:
eltque isitur ad seriem cocidem maximo
aequalium, hoc est, illam iptam, ut 2 ad
O F T;) Cineque Dictancia, uE Od, L d, 2 d,
ecc. quarum maxima, D: erit Peries mo-
mentorum infinita, uE OaP, TdP, 2dP;
3aP, _c. u(que ad DP; Scries Primano-
rum, cujus Index c: Adeoque simul omnium momenta, (per F hujuS;) ut Z N DP
:NPX Z D. Adeoque diltantia Centri Gravitatis, = D. per 24 C ap. 4
Trem: Cum Priangulum ABB (proprer rectas, Bali BB parallelas, distantiis
à vertice proportionales,) Et superticies Coni Prramidisre (PrOPIEr PerimetTOS
planorum similium bali varallelorum, distanciis à vertice proporrionales;) Ft C0.
nocides (vel Pyramidocides) Parabolicum, super Parabola B AB constructum
(cujus parallela plana, propter ordinarim applicatas in Parabola in Cubduplicata
ratione diamerrorum interceptarum, lunt in diametrorum ratione, lire diltanciarum
a verrice; quippe in duplicata ratione ordinarim applicatarum in parabola circa
0
a
∞dp, i
N
quas tiune illa limilia plana;) Sit Series Pri-
ManOrum; DuTa, UE OP, L P, 2 P, 3P, ecc
alque ad P; cujus Index F: adeoque omnium
Tumma, uc ZNP; (nempe, in ratione ad t0-
eidem maximo aegualium; hoc elt, ad Paral-
lelosrammum, Cplindrum, auc Priima, Cupex
eadem bale, aeque alcumm; ut F ad 2, peF F
hujus:) Sintque in distantiis, ut Od, Ta 2 d, 3 du Ccc. quarum maxima D: Lrunt
Nomenta, uE Odp, Tdp, 4. d p, 9d p, etc. Ulque ad DP; Series Secundanorum:
cnjus Index 2. Adeoque (per F hujus) simul omnia, ut ZNDP = ZNP X ZD
Adeoque, Distantia Centri Graritaris a verrice eAt ZD. Per 24 C ap. q
Trem; Cum Pramis vel Conus, circa Triangulum ABB, (propter diametros
Circulorum, vel latera similium Planorum, in ratione distantiarum a verrice:
Odp, Fd
dp, 27 dp,
ANDP=
adeoque eorum plana, in distanciarum ratio
ne duplicata,) lic intinita series Secundano.
rum; (DUTa UC Op, TP, 4P, OP, Ecc. ulque
ad P;) cujus Index 2; _ omnium summa,
ut ZNP; (hoc est, Prramis seu Conus, ad
circum leriprum Prilina vel Cylindrum, uc L
ad 3;) Per F hujus: Sineque, distantix ut
Od, Fdu 2 d, 3 du c. u sque ad D: FrunE momenta, ut Od p, Z d P, 8 d p, 27 a p
ec. ulque ad DP; Series Fertianorum: cujus Index 3. Adeoque (per E hujus)
simul omnia, ut EN DP = SNPXZD. Adeoque, Distancia Cenrri Graricatis 2
vertice, ZD. ver 24 C ap. 4.
Similiter omnino, de Complemento Parabola dicendum: quae series est Secun-
danorum. Complementum aurem Semi parabola, appello, id quod cum semi. Da-
rabola complet paralleloerammum circum seriptum; (cujus diameter, est parabolae
Tansens in vertice; et ordinatim applicaca, Parallela diametro parabolae;) quod
utrinque cirea eandem sui diametrum duplicacum, appello, C omplementum P arabola
(Puta, quod cominetur incer duas lineas Parabolicas conrexas AB, AB, A8. 128
quas in communi verrice A, cangat AD, complementi diameter; batinque huic
ordinatim applicatam BB; cui parallelae incellixuncur rectae tixuram complentes. )
Elujusque ordinacim, axplicatae ad diametros suas; Tunt ut diametri intercepiae in
Parabola, ad Tuas ordinarim applicacas. Adeoque, in duplicata ratione Diametro.
rum, sire Distanciarum d verrice. Cum itaque sic (ut Pyramis) Series Secunda-
norum: Momenca, lunt Series Tertianorum: Adeoque simul omnia, ut L N DP
=NPxSD: EL Centri eraricaris a verrice, distantia; ED. II, de Cono e Py.
ramide, oltentum. Elt. uvel
De Calculo Centri Cravitatis.
Fix. 127, Centri Cravicaris a plano per Verricem; per 24 Cap. 4. Fa quam habet pro-
128, 129. polirio. Er quidem, ubi per praeced. Centrum Craruacis ell in Diamerro vel AXC,
Com.
datur propterea ipsum Diametri vel Axis Punctum.