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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 526, page id 851387705:0546
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F1B.5
D E C NCF OIVL
∞4
reliquis, nivore proporcionales; ) nemve  = 16 B:Si haec alicudo in balio
magnicudinem 5D D = F∞ ducatur; habetur s D ~ dictae porcionis prismaris
(ailineo BCC insisteniis) magniudo: (aqualio quidetu momenio supra in
VentO. 1
15 e
33. Ejuasdem vero porcionis prisnaris (erilineo BCC insistentis) Momeneum,
his pallibus inveltioamus. Si luper Pemicirculum F BC Ag. F. erigatur semieslin-
dei porcio, qualis LCC ZZ F3. 5. alticudinem habens in F nullam, in C vero
CiC =C. F: Semicirculus basis est Z DX; hic in altieudinem super centro grarita-
tis plani, hoc est in ED, ductus, dac 1 D P magnicudinem expolicae porcionis
Semicylindri.
34. Flujus rero portionis Semiexlindri, cencrum gravicatis distat à plano in F
tangente, recta F 3 ==3D (uc supra 557;) quae distancia in magnicudinem
6 D P ducta, dat Les Z D momencum expolica porrionis Semicylindri respectu
rangentis in L, hoc elt F A Hig. F. 1e
35. Fx hac veroSemieylindri portione, auteramus primo eam istius partem
quae quadranci FYZ tig. 5. insistir, (hoc est, quadranti F Cib fig. X. Vel 7.) eu-
jus magnicudinem primo, deinde momencum, sic invelligamus.
36. Ouactrantis F YZ Hi8. 5. cenrum Bravicais, d recia YZ, distat Z ; ad.
eoque ab F A diltabir : D  =7; quae distancia (cum sie alcicudini suver idem
Pravicacis cencrum aequalis) ducta in balis magnicudinem S D P, dac porcionis tivic
p
quadranci insistencis magnicudinem, sD P = + D, vel 3
90
4, ∞ D2
37. Si autem incellisatur haec porrio (quactranri K YZ fig. 5. insistens) plano
Y2C0 abscindi, ee sic Cuper reliquam parcem replicari, ue cum ca compleat Cy-
lindrum quadrantalem: F’acta hac replicatione, tanto ulera Y constiruetur ictius
replicatae partis centrum sraritaris, quanto prius cira conlticutum crat: uc patet.
38. Momencum veco hujus Cxtindri quadrancalis, sie habetur; Cenorum eravi.
catis quadrantis YZ C. fig. 5. distat ab AF,  ∞ F=D, (quod modo oltentum
Cst i 26;) quae itaque esE distancia ceneri gravicatis quacrantalis Cylindri (super
YZC constituri) a plano e F A: Oux quidem distancia in quactrantalis Cylindri
magnicudinem is D P ducta, dac  D + s D P ejuldem momencum respectu
rectae FA.
39. Hinc rero si auteramus momencum porcionis ance seplicacionem, lactam,
1 D P (uE supra  34.) manebit a D = 1i0 D. P, sive 26 3 D, aug
84
mentum momenti ob promorum gravicacis centrum parcis replicata. Ouod qui-
dem momenii auxmentn, per 3
dirisum, dac 26D -39
AD ∞ replicacae parris maenicudinem,
96
72F = 7 Z D, mencuram promotionis cencri eravitgiis:, Cujus
CB CLIS.
24 ~ = 32 7 D est ceneri pravicaris parris lreplieata distancia )
itaque Temistis 26D = 37
15F
medio: Dux quidem _ ex ; D auteratur, quod restac =
vel
15P = 32∞
L 2
2D
3P = q. D =3 D, est ejusdem centri distancia a plano a F. A. Aique Haec
denum dillantiu, in J E.  a P p maenuudinem ducto, dix 5 P  32. 2, D
sire 136 D P =  D, expotia porcionis quadranti F YZ insistentis momentum,
respectu rectae FA. Duod  35. proponitur inquirendum.
40. Hoc ixitux momentum, ex 2 D X momenco corius portionis semieslindri,
ablacum,