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# Title: [Johannis Wallisii SS. Th. D. Geometriae Professoris Saviliani Oxoniae, Tractatus Duo] Johannis Wallisii SS. Th. D. Geometriæ Professoris Saviliani Oxoniæ, Tractatus Duo (shelfmark Leibn. Marg. 103)
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Mlomentum
solidi circa
L respe-
= 3R= P+3A = P, HOC CAZ= P -+ R =
ex convertione Semleycloidis circa recta C F, UE PIIUIS.
86. Simiter, cum (per 578) racio omnium 2 Z arichmerice
proporcionalium, in respectira Triangula o FP, ad correspon
dences omnes z Y in eadem Priangula, sIE UE A3 ad 2 RE P; hOC
eAt, 3 P3 _ 2 R= P ad 2 R = P, LIVC, VC 5 P= = 2 R ad 2 A
vel = P=-4 R 2 ad 4 R3; (hoc est, uC AF9= CF9 ad CF9:) A-
deoque noncuplum illius ad duplum hujus, 9eA2 ad 4R= P; hOC
eCt, uE 3 P= = LBR P ad 4R= P, CiVC VC:
FPd  36R dd BR=; (hOC eA
UE O A F 9 - 9 C. F 9ad 2 C F9:) Si adjongiur raciO5 ad 2,
Sive 20 R ad 3 R=: HAbCTOEITCTUM FaTIO Z P Z =36 R = +20R2
P~ = 16 R, ad 8 R =: FIOC el9 A F9- 4 C F 9 ad 2
C F 9. Quod supra (530) suscepimus demonstrandum.
87. Oliensum est supra (5 46;) Momentum solidi ex conver-
tione (vel semiconrerti One) Zemicrcloidis circa A F (A9. Y.) ce
Et C F ex Spectu recta C F, ad momentum solidi annularis ex convectione,
vel semiconrertione) semicirculi C D F circa candem A F re-
spectu ejusdem C F rectae; esse, uc 7 ad 3, acque insuper ut de-
euplum momenti Colidorum ex cali conrertione lriangulorum vFip
in diltanciis 2 Z Tuspentorum, ad triplum momenei eorundem (0-
lidorum in distanciis 2 Y respectire uspentorum. Cujus racions
investigationem sic aggredimor. Omnes 2 Z (aequales arcubus in
semicirculo arirhmerice proporrionalibus) in respectira solida
ex sic convertis criangulis vF P, ad omnes 2 Y (arcuum illorum
Tinus rectos) in eadem respectire Tolida; HOc eA (PrOPTeEVD
ubique aequales) omnes illae 2 J. in quadraca alricudinum F X (hOC
es, Tinuum vertorum residuorum arcuum,) ad omnes illas 2 Y in
eadem respectire guadrata; Tune, uc momenta omnium circulo-
rum (vel cylindrulorum) Z E (aequalibus interrallis Tum PEOruM)
convertone erilinei resticuri C A F A9, 7. CIECA A F FactOruM,
Tuspentorum in distantiis  = (trianguli F A a) hoc eAt ZZ (cri-
linei resticuri;) ad momenta eorundem circulorum (vel extin-
deulorum) suspentorum in diltanciis sE (bilinei F a n;) HOC eA,
uemomentum Colidi ex convertione Trilinei recticuri C AF (cir-
ca A F) respectu rectae C F, ad duplum momenti annuli ex cimile
convertione C. b F semicirculi, respectu C F rectae. (Dico, ad
duplum momenei annuli; propter, cum magnieudinem solidi ex
conversione Parallelogrammi in crisineo, ad magnicudinem solidi.
DF
YCLOTDC
Cirea C F
respatit.
decta =LL.
18.