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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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DeCalculo Centri Cravitatis.
Cap. V.
L18. 299. Spiralis ad conterminum Sectorem, ut F ad 3 f F, 3 f 2, ec. (nempe ut L ad sc.
riei indicem unicare auctum, per prOP. 2. hujus;) hoc clt, uc 32d7, 22d5, etc.
Ouod iplum similiter ralerer, li incelligerentur Racii crescentes secundum Se
riem cujus Index siE numeruS TurdUS, PUTa V 2, V 3, Sc. adeoque Index seriei Se-
Etorum, 2V 2, 2 V 3, Ecc. quippe Figura Spiralis ellee ad Sectorem concerminum,
ut L ad 2 V 2 = T, 2V 3 F 2, ecc
TIIud utique ubique obrinet; Ii Radii Cint ut Series cnjus Index sIc S; Sectgrum
Series Indicem habebit 2 S; adeoque summa Sectorum omnium ad maximum tocies
sumprum; hoc est, Figura Spiralis ad Sectorem conterminum; ut, 2 ad 25 f F:
Dex PFOD. L. hujuS.
Ex consequener, Facile altignabitur Spiralis sic constructa, ut Figura Spiralis,
ad Sectorem conterminum, datam habeat (minoris ad majus) rationem. FIto
enim ratio dara, ut L ad D. Ouoniam cst (uc jam oltendimus) Fisura Spira-
lis ad Sectorem conterminum uc L ad 2 S- L F; aegue imperarum ett ut Lic, uE F ad
D; erunc xad 2 5 F X, et Y ad D, cadem ratio; adeoque D =2 5 ] I, 1OC
est D - 1 = 2. 5, e =
dicem habens =
= 5. Si icague Radtit M T, ponanuue ut Secies In.
Qi exit sienra Spicalis ad concerminum Sectorem, ut L ad D,
in ratione daca. Cum enim series Radiorum indicem habeac   ; Series Se-
Etorum habebit Endicem (iltius duplum) D =x; adeoque Sectorum crescenti.
um ageresarum, ad coridem maximo aequalium; hoc est, Hisura Spiralis ad Secto.
rem conterminum; exit uc F ad D; nempe ad Seriei indicem D = F, unicate au-
ctum (Per PTOP. L. hujuS.) QUOd CTaE imPeracum:
Puca; Si ratio data, sit F ad 2; adeoque (DOSitO Z -  2
Erme M. F, Series Sabsecundanorum: hoc ell, in subiduplicata patione angulorum
PM Z
e lire sit. e le ulee tLM Iq
Si ratio data, Tic F ad5; aceoque (BOlitO D = 5) = == 2. ErunEMII,
Series Sccundanorum; leu, in duplicaa ratione anentorum P M P.
D = = 1 S dEI 111I.
Si rario data, sic X ad 3; adeoque =  = L. FxUNEM P, Series Primano-
rum, seu in ixta angutorum P N J raione. Ouxe MA Spiralis Archimedea.
Si ratio data, Fit 2 ad 3; seu Fad 3; adeoque  =LL FruNE MF, Se-
ries Subguarcanorum:; seu in angulorum ratione Subquadruplicata. 10
Si dacaratio, lic r ad 4; adeoque  = 2. Fryne M F, Series Racioum
Duadraticarum Tertianorum; Tou in ansulorum ratione Subduplicata criplicat.
Et similiter alibu quaecunque tuerit ratio data.
Dico aurem, In Ratione Minoris ad Majus: Ouia supponitur Spiralis (a Prin-
cipio orta) radios habere M P, ab 0 continue crescentes; totaque, circum seripto
Sectore concermino. MInOr . L~NA Eit 1.
Si veco peponereur Rauio aualiais, L ad r; adcoque 
=2 = O. EF
Sent M L Seties aeualium (cuijits ihdex o;) ee pro sixura Spirali, prodiret Cit-
culi Sector, (ex Conroturo Paralle logrammo contectus,) cum iplo Sectore (quem
concerminum sipponimus) coincidens.
Sin provoneree Majoricalis rario, puca 2 ad L; seu x ad 3: adeoque
= = Z: FBenLM P ex eis Seriebus utia, quad Reciprocas detinivimus,
CAeF. 2. huju5. ) pura Reciroca Subquarcanorum, cujus Index  ds Adcogye non
inciperenc ML ab 0, crescendo; sed ab Intinico (0= ∞) decrelcendo: Fsset
que concermins declosi non quidem careumleriouis led taterieruo. t
894
200.