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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 637, page id 851387705:0657
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PB
inet
PROP. ZX.
Datis Ponderibus quoclibet; una cum communi Mocus et librx Cen-
Ero (vel perpendiculo per Centrum NOtuS, ejusque Succecanco.
vel motus Axe, aut per hunc plano Perpendiculari;) atque appli
cationum Punctis, aut horum inde Dictanciis:
Vel; Datis saltem summa Ponderum, et simul omnium Ponderatione
ad datas partes:
Punetum Libra data (rel Perpendiculum illud, aut Perpendiculi Suc-
cedlaneum; vel Perpendiculare Planum per AXem; pront ab HOC
aut illo Dictantia data fuerit;) invenire: quo si Suspenderentur
omnia similitex ponderarent; Nempe, caucundem, acque ad datas
DarteS.
Cuod iptum inventum Libra eunctum; est Centrum Aquilibrii:
eltque Onicum. FE Perpendiculum inventum, aut Perpendicali
Succedaneum; est Perpendiculum Rquilibrii, aut Succedaneum hu-
JuS: eAtque item Onicum. Fit invencum Perpendiculare Planum;
es Planum Aquilibrii P expendiculare; eAtque hoc (ex planis plano
huic per Axem parallelis) unicum.
L +OG = TODD
20P
= ErDP L MSDP= AEDP +IrLMS-nt
= rP FsP + cP
p +5
IStO (UE in PFOP. 18.) expoticum C cenerum motus st libix (vel Perpendi-
.culum ver motus centrum, aut perpendiculi Succedaneum, vel Perpendicu- F 18. 77
lare Planum per MOTIS AXem; juxta conditiones ad PFOP. F5. MCMOTALAS:) AL
que expolita Pondera; quorum summa siC, verbi gratia, 20 P: Et simul omnium
Ponderatio, ut 1OGT, vel XO PD, dextrortum.
Vel, exponantur linsula scorsum Pondera, cum suis Diltantiis; unde, per 18
hujus, haec Summa _ Ponderatio collisi postint.
Datur, inquam, Distancia (Per Z5 hujuS) qua Si ad dataS partes HOC 1O-
rum Fondus, vel lumma Fonderum suspendacur, timilices pondcrabic. Nempe
f TOC = = 1OPL
== = = D. HIOC elt; Si Dexerortum (quod innuit signum L.)
in Distancia ; D (puta in puncto E, dictancia CD medio; vel ubivis in ver-
pendiculo, auc perpendiculi succedaneo, per P. cranleunte; rel in perpendicylori
Der F. plano, plano per axem motus parallelo;) Suspendantur simul omnia
Pondera seu lumima ponderum 20 P: Similiter ponderabume, acque jam in Tuis
Tingula suspensa locis; nempe ut f 1OCF, ret F TOPD. Quod erat investi.
Bandum.
Veli Onivertaliter: In distantiis FID, = mD, = nD, Rec. appenta pon-
dera rP, sP, +P, e. Ponderant uc + Ir DP, + msDP, = ntDP, eec. (pet
28 hujus.) Florum Ageregatum, SI per summam Poncerum dividatur; quod pro-
dic (= ErDP =m sDP = nEDE + Ir + ms - n+
P FSP +
p. L s FE D, est Diltantia (DEX.
trortum, auc Sinistrortum, prout nocara signis f aut = praepollent) qua S Tum
ma Ponderum suspendatur, similicer Ponderabunt: per Y5 hujus. Quod crat in.
veltigandum.
Dico porro; Librxe punctum P. sie invencum, A. quilibrii Centrum etse; (Ouod.
que per hoc transic Perpendiculum, rel P’erpendiculi Succedaneum: est Perpen-
diculum Aquilibrii; vel Succedaneum hujus: FF, Perpendiculare planum per F
perpendiculari per axem Plano parallelum; est Perpendiculum Aquilibrii Pla.
nuI.)
Cum enim ita grarant Fibram omnia ilimul Pondera, aque Si ex F. puncto
vel per illud cranseunce Perpendiculo, Planore perpendiculari) dependerent
ommia