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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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101
PFOD. XTII. De Calculo Centri  aouat
Trem; Figura Sinuum Rectorum, ejulre Seomenti, Momentum re- X
spectu rectae cui adjacent sinus illi: Veh Semiguadrantalis VH
sula (unde et de aliis Ongulis hiet judicium pro alticudinum ea-
tiOnC,) Fisnex Sinuum Rectorum, ejusre Segmenti aciem habens
rectam illam cui adjacent. (Nempe, Semissis dumma Ouadrarorum
corundem sinuum.) Adeoque, Centri graricaris Plani distantia
ab ipla cui adjacet recta.
Item; Alujus Ongula Momentum, respectu ejusdem adjacentis rectae,
aciei sux. (Nempe, Friens Cummae Cuborum corundem Sinuum.)
Adeoque, Centri graritatis inde dictantia. (Intellioe: Si prius co5-
noscatur, cum ordinatim applicatarum illarum summa, hoc est,
ipsum Semicirculi Sesmentum; cum summa quadratorum carun-
dem ordinatim applicatarum: Duorum utrumque methodis jam no.
tis coenolcunur: atque hic intra docentur.)
VIECa AXCM XS, recta ec (in eodem plano
 constirura) conrertatur; cujus medio
Puncto Y intiltens perpendicularis TC, axi
occurrar in C: Ab excremis aurem punctis i, 1,
perpendiculares ad axem ducaneur cd, Fd; ac.
queu d T medio, TD.
Si sIc ETF axi Parallela: Manifectum eAt,
cum TC, TD, eandem esse rectam, tum dD d,
cTc, (Parallelas parallelis terminatas,) rectas
aequales; adeoque conltare propolicum.
Sin Parallelâ non HI; OCCurraE Axi in A:
Eritque (propter parallelas, ec limilia trian-
Gula,) cPE ad dDd; ut AT ad AD; hoc
elt, (propter limilia criangula,) ut CT, ad TD.
Adeoque tactum ab extremis, EE in FD; aequabitur facto a mediis, d d in CF.
Ft (provcer, Similes Peripherias, radiis suis proportionales,) Factum ex et in
xipheriam racio D I descripeam, ad factum ex dd in limilem peripheriam de-
Teripcam ractio CT, vel qui luic xqualis Cc. AdCoque (Der PrOP. PrXCCd.) Su-
perticies curra quae a conversa et (cujus centrum graritacis elt l, ejusque ab axc
distantia FD) deseribitur; aequalis erit currxe superficiei Cylindri, quae recta da
vel huic aequali deseribatur, in distancia ab axe quae sit ipsi C Y aequalis. Quod
crat demonstrandum.
Nempe; qua ratione CP longior est quam DY, eadem brerior est d d quam LL.
Dico autem; modo ne Avem secet; quonium (uc ad prop. praeced. dictum cAt)
hoc calu, duarum curvarum disserentia, aequalis ester illa Superticies Cy lindrica.
Trem; ne sit ad axem ad aneulos rectos: quoniam, hoc calu, non Curram sed
Planam supertieiem describeret conrerta recta; cui in Curra superticie Cylindrica
nihil responderet. Nec, de illa procederet demonstratio.
Ouodque de una converta recta dictum est;
Dluribus limiliter accommodabitur; ductis, a lin-
sularum punctis mediis, ad axem, respectiris re-
etis. Ouippe s in omnibus cadem (Ic, vel aqua-
lis, recta FC; ejusdem Superticiei Cylindrica
sesmentis aequâles crunt quae a et rectis desert
bentur: Sin minus; diversarum.
Puta; Si circa Semiperipheriam (arcumre ad.
huc minorem) circumponatur, ex rectis contlata
cer linea; quarum lingularum puncta media
P, T, sinc in F L peripheria; adeoque TC
TC, invicem aequales: rectis autem LI, FL aeque
altae dd, dd, aris portiones; atque his aquales
55, 5d; quarum ab axc distancia d d sit aequalis
2.
C.
B
19.