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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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PFOP XXVIII. DeCalculo Contri Cravitatis.
omnes Z. Y, Teu NI F, ad coridem maximo aequales; hoc est (proprer seriei Indi
cem S,) uE F ad S-L F (per prOP. F. hujus.) Oux quidem P’arabola seu ParL
bolocides est Figura Spiralis dupla; Curraque illius, hujus currae aequalis; Fan
genlque illius cum Parabola seu Parabolocidis Ordinacim applicara in puncto con-
cactus, eundem angulum tacit quem lacit Lansens Spiralis cum hujus radio respe.
ctivo.
Si vero, vice versa, quaeratur quaenam Figura Spiralis expoliia Paraboloeidi
conveniat; puca cujuis Fxponens Lit . Fric =
5 L = Cut ex dictis pacet; )
ergo p = =  =, e p5 = 5 + +, et p8 = 5 = +, _5 = -, qui Index eric
Seriei radiorum M Z in Spirali quaelica; cujus recta cerminalisM F Pucura est Pa
rabolocidis bali aequalis; angulusque circulationis calis ur Sectoris ArCUS COnter.
minus eam habear rationem ad expositae Parabolx vel Parabolocidis altitudinem,
quam habet S + Y ad E. Duod ex modo demonstracis fucile colligieur.
Superest, ut Centra gravicatis exguiramus. Quod eodem modo siet acque in
Propositione Draecedente factum est. Potito enim, ut illic, P pro peripheria primi
circuli; cujus pars intinitelima st T; radius R; limiliumque scctorum radii ut
eunque crescentes, n; quibus relpondeanr in eadem ratione t: Prunc similes Secto. L1B. 2c0.
res quilibet En t, sen=; corumque ab M distancia Centrorum gravitatis re-
sectire MR = 2n; adeoque d PMP, Coruncem distancia R S. = 2p, ab FHIC
distantia RX =
lnempe, in caratione ad R MI qua est Sinus Rectus illie,
hic Co. tinus seu sinus complementi, ansuli PMR, ad Racium: ) FL PrOPterCa,
singulorum respectire momenta re spectu recta PMP, 2R
spectu rectae F. M C, 2 s
MX n3 X Z
n5 n 5Z
3R 3  = i1 XC
3R 3 =: Vet, (nexlecto Z, ob caulas 2d
SE. BTOP. Praced. Madticas, ) illie, ; hic, n . Acque hoe quidlem univer.
taliver, quacunque ratione creseane radii M P, quos n dieimus ulque ad eorum
maximum N, qui sIE M P cerminalis.
Et proprecea; Siereleant M T, seun, in ralione angulorum PM P ariutinericee
proporcionalium, quosa dicimus; erit n = = R, (hoc est, in cadtem ratione ad
A radium circuli primi, qua est a ad P; hoc est, angulus expoticus P Nt F, 2d
quacuor rectos; seu istius anguli Arcus in Circuli primi peripheria, ad veriphe.
riam incegram; ) adeoque 2 F ae 87
a3X RF
n5+
2R 272 ic
dic 38.
a35RY
1, 32
nEa F
3 s 
3∞3. Dui est calus, spiralis Archimedea, capice praecedence expotiens. lo,
Si vero creseane M. P seu n, in angulorum a racione duplienca, cripliceala, ali-
alve mulciplicata; exien = . B, vel m , _, et sie porro prouc racionis, mul.
riplicacae eradus postulareric: Adeoque
nXF. ca X RY
3R 3~; V
n2Z. aERY
2R 280
et lic Porro, prout res postulaverit.
ut
ee
aR
2 ∞4 3 e
n3 5T
3R
aesRZ
3
5∞53
aSRTI NXZ ~ a XRY
383 3H 383
Si crelcane M F seu m, in angulorum a racione subduplieata, tubiriplicaca,
XX XXX 3
A raulsryllo inis: dscaliatve