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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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PrOD. XIV.
De Centro Cravitatis.
aurem Addenda illa vel Auterenda (per 27 Cap. 3.) in ea ratione qux componL. L IB. 3
tur ex ratione Ponderum Bm, n; _ ratione rectarum as, ec, f8, hoc est (proV.
cer Timilia eriangula las, mec, nfe) rectarum ah, em, fn: Adeoque in ea ra-
rione qua ponderarent eadem Pondera circa axem = C Z. libranda; per 13 Cap. 3
Adeoque (per T2 FI. 5.) in eadem ratione est summa Auterendorum pondera
cionibus Bm; ad Addendum Ponderationi n (vel summam addendorum, si plura
elenE;) qua estet ponderum l, m, circa axem = C Z ponderatio; ad ponderatio.
nes ponderisn, circa eundem axem. Adeoque cum sint Ponderationes lx (prop
ter ZCS vel = C Z axem Aquilibrii ex hrpocheli) inricem aequales; criam Ad
denda Auterendis sunt aqualia: 2deoque perinde simul valene, acque A nihil vel
adderetur rel auterretuT, per B CaP. P. (Quodque de Auterendis Addenditre pon-
derationi linistrortum dictum ett, perinde elt acque S de Addendis Auterendisre
ponderationi dexirortum diceretur: quippe idem ralet, plus ad dextram, acque,
minus ad sinistram.) Cum itaque; applicaris ponderibus l, m, n, ad puncta d, e, 
ENet AC. B planum Aquilibrii per axem, ur supra oltentum elt, (adeoque simul
omnium ponderatio, nulli in urramris partem aequipolleret;) et C centrum Aqui-
librii: Fxic similiter, idem C, cencrum aequitibrii; ponderibus ut nune applicatis
ad puncta d, c, 8
ER isicur idem C punctum, aequilibrii Centrum, axis aequilibrii ZC5, quo.
cunque sic constituatur crrare. Quod demonstrandum lulcepimus.
SCTTOF TV M.
Kempli gratia. Si incelligantur Bon
dera L. = +P. M = 3P. N = 3I
Diltancia vero CD = + 6D. CF = f 1D
CF = - 3D. Erit Ponderum ad librx
XCS puncta D, E, F, applicatorum pon.
derario respectu axis C; ut P x + 6D
+6a C  3dC = daC =6e+
F6DP. 3Px + D = F 3DP. 3Px - 3D = =9DP. Adeoque simul omnium
ut F6DP. F 3DP =9DP = ZODP. (arque hoc, ex constructione; poni-
cur enim C, cencrum A quilibrii.)
Et similiter (diminuris in eadem ratione omnium ponderationibus, propter ob
liquationem librae, puta in ratione d ad D) corundem ponderum ad librx =C Z
puncta a en f, applicandorum ponderaciones, erunt uc + 6a P F 3a l = 9 a l=
FOaP.
Forundem vero Ponderum a Plano
per Axem XCS vel =CZ. dictantia;
Duta rectae DL, E. M, F N; vel ab em
Fn; linc ut + 6D, = 3D, = 5D; EF
P
3P
3F
+6D + 3D = 5D
+6DP FODF = I5DP = LODP
tis proporrionales (puca in ratione s’ad +6s P f 9s P = 25 8P = +OS P
D) ad, ec fe; ut + 6d, +
Adeoque corundem Ponderationes ad axem Z CS, vel = C Z; uc f 6DP L ODF
=F5DP = F ODP: (Idque, ex hypochesi; supponitr enim Z C. S, axis aequi-
librii.)
Acque (his proporcionales) ponderationes auterendae f 6s P F 9S P = 15 SP =
+05P
Flis icaqpue rice subductis (addicitre respectire) a ponderationibus prius poticis,
tanquam in d e, f, punctis; prodibit AEquilibrium, sive =Od P ZOSP:
DC
Verbi gratia; Si ponamus d ad s, ut 3 ad F; vel, ut F ad 3; L. X - F 6d P L 3 dF
0aP, Tubductis F6dF F 6sP = 25SP
manebun L 4 qP + oa = 4a l = F0aF
St ponamus d ad s, ut 3 ad 2, vel, ut L
ad Z. LX f 6aP = 3 a L - 3 a l, lubductis
F65P = 9s P = 25sP, ABC estus + 4d
ponaetabat prius vel linultrorium: Lola l1.
bra, vel in neutram parcem, rel in opposi.
hoc  + 2aP + 3dP- 5de:
+ 6a P + 3aP  9aP = =0dP
= 2aP = Za L caP = Z0dP
+ 4aP = 0dP - + aP = +0aF
+6dP + 3 aP = 3aF
4aF - 6gD L 1OdF
F2aP - 3 aP + + aP = + 0dP
cum ponderet: non tamen dettruicur, tumul omnium aequilibrium.
PtCt.
D
L
sDP F 3DD = gDP = =ODP
+6aP = 20 a P; manebuat + 24 P - 3 at
+ TaP = +0dF
Adeoque; Veur ea Porrio quae dextroctuu