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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 691, page id 851387705:0711
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PrOv. IX. De Calculo Centr  avitath.
proca; (quo calu, curra BB, CA Fyperbola; Cujus ATyMPIOI LUNE A D, AS: uE
DEOp. 02, 95 Rrichm. Intin. demonstrarimus: Adeoque, Tolidum istius conver
lione circa AS deseriptum, cst Forricellii, Solidum Eyperbolicum Aeurum. 
ex hujus apud Forricellium detinitione constat:) Fric elanum illud Magnicudine
Intinitum, (per 7 hujus.) Si tamen, circa As convertum, incelligatur Solidum
deseribere; erir hoc magniudinis finita; rantae scilicet quanta in Propolitione de
Tignatur. Cum enim, luperticies Cylindrica, recta DB deseripta; vel, huic xqua
le Parallelogrammum cujus Balis DB, alticudo aequalis peripheria puncto D de
TexipEx, SE P: acque huic aeque altum Parallelepipedum, super parallelosrammum
A B crectum; (L NP: (cui quidem Parallelepipedo, aequatur Duplum Cytincrr
eodem Parallelogrammo cirea A S converto deseripti: Nam, qua ratione cireulus
racio AD deleriptuIS, xequatur semisti Parallelogrammi cujus Basis elt AD, alti
cudo equalis Peripherix puncto D deseripexe; quod notum est: cadem de Cylincrus
parallelosrammo AB deseriprus, eandem habens alticudinem, aequabitur semissi
Parallelepipea: propier linsula hujus Parallelogramma linsulorum in illo Circu-
lorum, relpectire sumprorum, dupla: ee communem alcitudinem DB:) Sincque
superticies Cylindricae rectis ipli DB parallelis deseriptae; (vel, his aqualia P2.
rallelogramma quorum bales, exdem rectae; alticudines respectiris peripheriis x
quales;) Series aequalium; propter - s.+
= T==O: (vel ctiam; quia
cum peripheria lunt in rarione dillanciarum ab As directa, et rectarum conver-
Parum in carundem diltantiarum ratione reciproca, adeoque cum Parallelopramma
inricem xqualia, cum ex Superticies Cylindrice; per 6 C ap. T. vel 24 F. l. 6. Demper
quod ob minorem balis peripheriam oritur decrementum, aucta in eadem ratione
alcicudine compenlatur; ur superticies Cytindrica, rectis in AD BBs plano ipsI
DB Parallelis deseriptae, sine inricem aequales:) Frune simul omnes illae superti.
cies Cytindrica, live quod ex his incellixitur constari Solidum; = ,, = NP, HOC
cst - =, -NP =NP; aquale scilicet ipli Parallelepipedo, vel Duxlo Cytin-
ori, quod per NP detignarimus. AF vero; proxier Distancias (d plano recta AD
deleripto) Centrorum praritatis harum superticierum Cytindricarum, rectis con-
versis proportionales; adeoque secundum seriem cujus index = L ex constructio-
nC: eFIL Momentorum seu ponderationum series, indicem habens
(nempe qui ex Indice serier superticierum cytindricarum, o; et Indice Periei di-
Stanciarum, = 2; aBGrCBatUT) Adeoque summa momentorum,  
(nemPC, quae SIC ad NPD, ut F ad = r F Z. = 0; qua ratio est infinica;) vel
ENPD; quod per NP (quod est omnium Pondus, ut modo oltensum est) di
vitum: distanciam exhibet, cencro gravicatis debicam, sD, intinitam. Ouod isi.
tur nusquam exit.
Similiter: Si Plani series Indicem habeat -s = - =: (quod est magnicudine F.
Plusquam infinitum; per ProP. 7 hujus.) Prit Solidum hujus Plani convertione factum,
=s  = N P = 2 N P; maxnicudine tinicum. Sedt summa momentorum
-2 NPD = =- NPD, plusquam infinita. Et distanria Centro gravicacis
debita; == D, plusquam intinita. Ouod itaque nusquam exit.
Icem: Si Plani Series indicem habeat == =Z; (cujus itague ordinatim. ap.
plicatae, lunc ordtinatim applicatis in Parabola, reciproce proporrionales:) Planum
hoc est magnicudine Finitum, ( pex 7 hujus. ) Et Solidum conventione la
cum, icem tinicum; nempe -,, = NP = = NP. Eriique hujus Momentum,
SFCF =
e