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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 627, page id 851387705:0647
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De Libra.
lari, acque ab SC recta (quae illius est, atque circuli libratiore deseripeiu ad pla
num illud recti, communis sectio) Diltancia: Sive (quod eodem recidit, proprer
punctorum, live d recta, sire a plano, distantius, rectis perpendicularibus men lurar;
Solitas) quod rectae Bu BC in circusi plano perpendiculares, ad SC rectam, sune
etiam ad illud per axem planum perpendiculares: Constat ex, DeF. 4. F. L IX. Duoc
etiam aftirmatum erato
ruist srcts. dC a. iu Demonstrati.
iiCISE CLIIE
e
:ELILCS
sccliet C
1e0
Fadem, alias demonstrabimus, ex PFOB, 2 L. Cap. 2. pro varia moins Obliquirace.
Nam (constructis ur prius, ductisque continsenribus BP, Br, bL, uc, in Schemare;) L18. 69
Duncti B, quocunque onercoravani (et quidem sive in recto ad horizonrem plano
sive urcunque Obliquo) per areum BBB moti; eadem est obliguitas mocis, in Ep(iS
B, B, B, puctis, alque B L, B+, bc Concinsentum; (per F5. Cap. 2.) quarum in-
elinationum ad horizontem ansuli (si planum st erectum) sunC L BC, TBI, CDC:
et his aequales; anguli SOB, SCB, SCB; (ett mique TBO, SCiBis Interque re
EtusZ _r SBn, cnmSC.B, Timpro communi BC, complent reCtuM, Per 10
EL. 3. ec 32 FI. L. es Similirer cum cBC, cum SC.b, sumpro communi cbC: ) quo-
rum Sinus recti sune, BC, Bu, BC: Flisisicur proporrionalia sunc A qualium pon-
derum momenta in punctis B, B, b, in crecto planO, DeF RF, Cap. 2. lAdeoque
Inaequalium, in ratione quae ex illa et Ponderum ratione Componitur; per FO Cap.
2.) Fademque plano Obliguo accommodanda, ut priuIS, PCF 26. C ap. 2. Oua
erant probanda
Ouodque de una Tuubra ostensum est; de pluribus similiter ollendetur. Pura, A
ad Libra C B, punctum s; et, Librae Cb, punctum b; appensa sint xqualia POD
dera: ponderabuns (per jam dicta ) in racione distanciarum sO, b c, exeteris pari
bus, (Adeoque, s Pondera tinc incequalia; in rationibus ex Dictanciarum e Ponde.
rum rationibus compolica, per FCap. 2.). Ouod itidem erat propolicum.
Denigue; quod de Axibus inaqualiter inclinatis, aftirmatur; adeoque, Mocuum
Planis inxqualiter Decliribus: Conltac Cx PrOP, 24, 255 26, C, aB. 2. Duod ulrimo
demonstrandum erat.
dC+
0
Forandum incerim bsc erit; non ita haec inehisenda este, quati, F ad Libram
N AB appentum pondus in B, Ponderi in A, aquiponderei; illud in B, huic
in a cederet, seu minus ponderaret. Ouanquam enim illud in B, minus ponderet
quam in B; non camen destruitur agnilibrium, quoniam et in cadem ratione (prop-
ter eandem obliquiratemt) minus ponderet hoc in a quam in A. Quodqué de
Aquilibrio dicitur; Pariter de de momentis inaegualibus obcinebit. Puta, qua ra-
tione pondus in B, praepondetat ponderi in A; eadem de illud in B praepondera-
bic huie in a. Nam ueriusque momencum proporrionaliter minuitur, ob candem
motuum obliguitarem ratione Perpendiculorum ad terea Centrum; quae Ponce
rum moventium Directiones sunt, e supponuntur inricem parallela.
AE Vero: Si loco Ponderis in A, a, a, (elljus Directio supponitur eadem cum di-
rectione ponideris in B, B, b; ucraque scilicet deortum ad rerrxe cenrrum; adeo
que de proptex Tansentes parallelas, Declivicates aequales: () Substicuacur, verti
scatia, Vis humana; quae non minus applicari pocerit secundum directionm av
quam a V perpendicutum; (adeoque ejuldem crirmomenti in quocunque libra
licu; dum incerim illud Ponderis a B ad B mori minuitur: ) Minuerur continuo
ratio Retistencia ponderis (d B ad B, B, noti) ad aquale momentum Virium in
A, an a. Adeoque Vis in an tacilitis movebie potidus in B, quam ris eadem ju A3
pondubidem in B. Dux ex propoticione sequenle apextius constabunt.
lLep =TII.
(1P 1O1