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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 719, page id 851387705:0739
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PFOD.XV. DeCalculo Centri Cravitatis.
Fes respecta rectae FA, momentum Scctoris B CB A, elt 
23 p., e iplius F18.
BCA, 3a = 25 pr. FC speciacim, corius Semicirculi ADa, momentum sire
respectu ran sire respectu T A, (PTOPtCE a = 3P, _ 5 =0,) est : R2 P.
ERque (per 5 ee S hujus) Trianguli BBC, Cencrum gravicatis in C. V, ejus.
que d C. Cencro distancia ZC V = ZN. Adeoque d ra, R FZ X; proue intra S
prave Cencrum tueric; (nempe  F Z a si lupra; R - Z x si intra Cencrum;)
HIOc est (DrOPIeF N = R - v E supra Centrum, e x = v = P E intra C entruIM,)
uiroque casu, 3 R =32. Adeoque ejuldem à T A distantia, R F Z N = 5 R + 3V.
FIt autem (ut supra, GF,) magnicudo Frianguli BBC = s N; (hoc elt
5R = s2 si Tupra, rel 5u - s R si intra Centrum.)
Ouod ductum in Ceneri graricatis distantiam a 7 a, R + Z _ =3 R - 20; exhi-
bec ejuldem, respecta rectae ran momencum s.X R + 3, 5 ~7 - 3
2v: HOC
230 =750 R + 258, vel =5o + 7 50 R - 20V. prouc lupra inttave
Fuerit.
Idemque ductum in ejuldem d F A distanciam, R = Z ~ = = R f 2V; extribet
ejuldem BBC. Frianguli momentum respectu rectae L A, 5 V R F 35 v; hoc ett
R2 + 50 R =250
Fuerit.
vel
=50 R + 25V
Dront supra intrare Cencrum
Aut etiam (PFOPter Aa AB, AV; hoc est 2 R, c, v; continue proportiona
les: adeoque 2v R = 0 = 5 + v2:) Ilie quidem 5. R = 35 0 X = 25 vet
=55R + 350 R + 25
Deou supra intrare Cencrum tueric hoc Frianeulum.
(Acque hic monendum duxi; quod oppido nocandum velim, ne sic opus idem
ExpIUS RCPetCrC: Hlanc reductionem in sequentibus saepistime occurrere. Nempe.
DFODTEF 22R = 0 = 5 f 2; quocies occurrit c2 vel 2; pro c substicui 2V R
etu pro v, Tubstitui c = 5, hoc elt 22 R = s. Ommino enim expedire comper-
cum habeo, uc unam aliquam Formam de signandi eandem quancitatem adhiberem;
ad quam aequipollentes aliae reducantur quum opus fuerie; ne Cymbolorum rarie
tas contutionem pareret. Ouod memineris relim, ne, in reductionibus a nobis
Tubinde crebro taciendis, aliquando haereas.)
Arque hoc Prianguli Momentum, respectire Subtractum Addicumre, (prOnE
supra Centrum intrare Fuerit,) Momento Sectoris BCBA, (nempe, a R2 L Z5 B
respectu rectae ra _ a R = 3s R respectu rectae F A,) exhibet (ueroque catu)
Momentum Segmenti BB A respectu rectae 28, a R - s R + 5u R + Z5-
eK
FsVR F= s; e semilesmenci BVY A, Za R = Zs R = Z5VR + 353 = = e R=
FE5VR F 3s: Et respectu rectae T A, Momencum Sesmenci BBA, a R =sR
-SVR -
S = e R= = sVR = 35; e semilexmen BV A, ZA R =  5R
F35VR - 3 5 = Z e R = 3SVR - 55
Oua quidem momenta, per magnicudinem scementi BB A = C R L 5V, aue
semiscomenri BV A = Le R = 350, (respectire,) arila: extibent segmenti,
aut semitermenti, distantiam d r a, R +
etam,
3CR F 3 5y: Adeoque illius altitudinem (uPTA CeNIUM C, auF C D sC.
3eR F 359 hoc est
2.S
BaR = 3sR. F 3SV. BE Tupra rectam BB, seu BV,
0.
L
BCL + 350
5ta= 3544350,
Atque