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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 (shelfmarks Leibn. Marg. 84:1, Stück 2; Leibn. Marg. 84:1)
# Folio 43, page id 826605435:0063
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isa
DE CrCLOIDE.
circuli radiorum Z S ad coridem circulos radii C F, hoc est, uF
hemisphaerium ad circumleriprum Cylindrum: hoc est, uc 2 ad
3, uE prius:) Adeoque omnia criangula 2.58 (quadratorum di-
midia) portionem complentia, hoc est ipla porrio cplindrica, ad
eundem rectae C P cubum, uc T ad 3. Fc consequencer, Bilineum
FC Y AB. FT. ad eundem C F quadeaEuM, UE X 2d 3: FCBili-
neum ACv fg. 20. (Prioris duplum) ad idem quadracum, uE
2 ad 3. Hloc est, ZDL, Sive Z R2.
24. Pc simile de parcibus sec judicium. Cum enim eriangula
2 58 Hg. FL. Sinc ad invicem uc circuli in hemisphaerio; erit por-
cionis Ceementum ZSou, ad cocam porionem, ue respectirum he-
misphaerii seomentum plano abscissum, ad cocum hemisphaeriums
adeoque magnicudinis nocx: Cui Forrionis segmento Z.Son, (I ad -
datur pri(ma Z SsCZC, habetUF seGMeNEU 1S5CZC; ad eoque _
ipliuS Fario ad D cubum diameeri circuli genicoris; hoc ett, racio
seomenti CZ Y, cum ad corum bilineum F C X, cum ad quadra-
CU reCtX C F. (Bilinei aurem istius FC X, lacicudo maxima,
sive maxima alcicudo ratione basIS F C, es R = Z C F, quae oui-
dem illic concingit, ubi sUMNEuF C Z = CF N = = D 1 2; hoc
et, ubi C 2 ad C. F eA, uc sinus rectus gradtuum 45, ad Ra-
dium: quod camen ad praesens negorium cogniru non viderue
necellariu.) Porest aurem idem eciam sic colligi. C um 20 Pa.
rallelooramma, sinc ubique rectarum 2 S momentis, respectu
rectae Cn, proporcionalia, (UE DAECES) PrUIHEK SSCZC segmen
Ea, CunC inceF CC, cum ad eocam xoFC Porcionem, uc momenca pla-
nOTuM KSZC respectu rectae nC, cum incer se, cum ad momeneum
N F C quadrantis respectu ejusdem x C, (quam 567 e sc99.
exhibendam docuimus;) eadem igitur ex racio planorum C Y Z
Eequidem, cum omnium rectarum 25, illa maximum, respectu
Cx rectae, Forciatur momentum qua grad. 45 subrendic; ea
Timiliter quae huic correspondee erie omnium Z Y MaXIMA,
adeoque bilinei C F Y verricem designabic.
25. Cum isicur habeamus (A8. 20.) cum Trilineum CZ A F
2R P = 8R Per  9; cum Bilineum C ADL Z R, Per ~ 13:
FOruM ABBTESACUM 2 Z P = =E R 2, aequatur Facto ex omnibus
barciculis curva C A fi3. 8. in suns respectire distmins Z Y.
TC
FIB. 1C