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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 892, page id 851387705:0912
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E
De Caiculo Centri Cravitatis. C ap. V.
F.X hujus itaque Nomento, E Tubducatur Nlomentum incegrae Circulacionis
Primae; habetur Momentum Guadrancalis Ouinea, respectu F. M C,
364 - 480 R. P - 292. R. D2 + 125 X
192∞3
Et Sic deinceps quousque libet.
: Et (propter maxnicudinem, S. X P, ) Dillan.
1681 -960 R1 p - 384  P + 250  7
62P
Atque eadem opera decerminarimus, in Solido Scalari, (super tiguram Spiralem
PTM obliquo sicu alcendencem, alcicudinem candem quamlibet habente super
oblique ascendentem tisuram spiralem,) magnicudinem, momentum, acque dictan-
tiam Ceneri graviratis ab erecto luper R. M G plano. Ouippe eadem omnia hic lo-
cum habent respectu erecti in F. M C plani; quxe respectu plani in PMF crecti
Tupra diximus, SC. Denon Ec opus cadem repetere.
1.O Oux M Propositione praecedente, de Spirali Archimedea, cradita TUnE;
Fis. 199, cadtem omnia Spiralibus aliis Facile accommodantur, in quibus Ra-
2.
dii M T, M I, continue crescant, non quidem (ut in illa) in ipso-
rum AML, AML L, anculorum ratione, sed ex in iplorum ratione
Duplicata, Friplicata, Ouadruplicata, aliatre utcunque mulcipli-
Cata: dut etiam in Subtriplicata, hujusce uccunque multiplicata.
Sed _ Maenitudinem quod spectat, iis etiam in quibus crelcant MY,
MT, radii, in corundem AMT, AM T, ratione Subduplicata, Sub
quadruplicata, aliasre urcunque submultiplicata; vel etiam in xa-
tione subduplicatae triplicata, quintuplicata etc. aut subquadrupli-
cata, quintuplicata, septuplicata, ec. aliatre, ex multiplicaris et
submulriplicaris composita; auc eriam alias per numeros turdos de-
bionanda.
Ouod ad HOmentA vOrO, et Centra graritatis, quae dicta sunt, non ita
Facile ad has accommodantur ubi ratio submultiplicata eAt, Icu CX
submulriplicata compositca qua multiplicatae non aequepolleat, rel
Caltem suberiplicata, aut hujusmulciplicatae.
Suncque hae Spirales omnes ex Parabolarum vel Parabolocidium cor-
respondentium convolutione facta; possuntque in Parabolas illas
Scu Parabolocidea crolvi.
C. D. Ia quidem Spiralis Archimedea ex Apolloniana Parabola: Pa nempe.
quae Balem habeat aequalem Spiralis radio cerminali; Axemque a
qualem semissi arcus Sectoris contermini.
Cujus quidem Parabolae semissi, aequatur illa Figura Spiralis. Onde
constat, omnino possibilem esse Figuram Rectilineam, Circulo aequa
lem; ejutre Sectori cuilibet.
FX data vero Alcicudinc istius Parabolae, quae Datae Spirali respondeat;
datur circuli Onadratura.
Rectaque Parabolam tanoens, eundem cum Ordinata angulum Facit
quem Facit, cum spiralis correspondente Radio, rect a Spiralem tan-
SCnS.
H. Unde alia colligitur circuli quadeatura Archimedea (Oualis ee ab aliis
R.
Fic, Curram Parabola, aequalem esse Spiralis Cuira.
L. M. Alix vero Spirales; ex iis Parabolocidibus in quibus Ordinacim applica
EX
e l L. aA
Spiralibus collisi pocerit.