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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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5
160.
De Calculo Contri Cravitatis.
Porro, Cum jam exhibuerim, Momenis respectu rectae r à (aue huic parallelae)
uc Axis Mocus seu Librae; Solidorum ex convertione vel semiconversione Semi-
sectorum vel Semiseomentorum BC A, Ba A, BV A, circa A a UE arem ConVer-
Tionis; e Ongularum Semignadrancalium, illis correspondentium, aciem haben-
tium Aa: Eadem opera etiam extribuimus, Momenta respectu A a ut Aris Mocus
seu Litrae, Solidorum ex convertione rel Semiconvertione corundem Semilecto.
rum vel Semisesmentorum BC. A, Ba A, BV A, circa r a (vel huic parallelam
ut axem Convertionis. Fr Ongularum Semiquadrancalium illis correspondentium.
aciem habentium ra, vel huie parallelam. (Ouod e Solidis ex quaris alia con-
versione impertecta, non minus quam ex Semiconvertione orris; Ongulisque aliis
quam Semiquadrantalibus; mutatis murandis, accommodabitur.)
Ouippe idem omnino momencum erit; sive sic A a Axis Convertionis, et T a
axis Libra; sive ra axis Convertionis, ec A a axis Librae. (Pr similiter in unsu-
lis; idem momentum exie, sive Acies Ingulae lic A0, ec Aris Librae ra; sive Acies
Ongulx Fa, _ Axis Lihrae A a, e similicer alibi.
Cum enim, (verbi gratia,) rectae BV momencum respectu Aa, sic BV X Z BV,
(proxcer iplius cencrum graritacis in lui medio,) hoc elt, =BV9: AEque tancun
dem etiam sic Priansulum, in Ongula Semiquacrantali (cujus Acies A a,) cidem
BV insistens, (uc dudum oltentum est:) Eric hujus Friansuli momentum respe.
etu ra rectae (propter V a distanciam) ZBV qX Va. Sed et in Onsula Semiqua-
drancali cujus aeies 2a, eidem BV. insiltet parallelogrammum cujus alcicudo
(proxier ansulum Semiquadrancalem) aequalis erit ip( V a distancix; cujus ita-
que magnicudo erit B V X V a: Cumque hujus Cencrum graricacis sit in media sur
longicudine (per 2 hujus,) adeoque illius distancia ab Aa, seu perpendiculari
plano huic inlistente, sic ZBV; erir ejuldem Parallelosrammis respectu axis Li
bra Aa, momentum, EBVXBVX V a = EBV qXYo ue prius. Cumque idem
obtineat, de lingulis rectis ipsi B V parallelis, Semilectores vel Semilementa BC A
BaA, BV A, complentibus: Idem de torius Onsula Momenco obtinebit: Nempe
idem omnino esse Momentum, Ongulxe (suver eodem plano, ) sive Sit A a acies, 
aaxis libex; Ere ra acies, e axis libra A a.
Acque idem plane obtinet de Solidis convertione, vel semiconvertione de
seriptis: Ouippe haec cum magnituline, cum ee momento, nihil aliud ab Ungulis
Semiquadrantalibus correspondentibus disterune quam quod sinc ad illas in ravione
Pad , vel : P ad R: ut Lupra ostensum est. Adeoque tum facti ex conrertione
BV circa A a momentum respectu r a, tum ejusdem convertione circa ra mo-
vertione, utrobique,
V9n V p: Faclique ex lemicon-
VouVa p. Pr sie rbique.
Est itaque Semiquadrantalis Ongulae super BC A Sectore, aciem hrabencis ra
momencum respectu rectae (planire perpendicularis) A a Cu SC.) 5V R3-F
S2 R= Solidique ejusdem integra conrertione circa r a facti momentum (respectu
ipliuS A ∞) 5V R2 P = 3S= RP; e Semilolidi SV R = X f r6 S2 R L
Adeoque, proprer Ingulae magnicudinem (rel momentum Sectoris BC A re
spectu r a) Za R + 3s R2 (per prOP. praeced. S I.) exic iltius Ongula Cencri gra-
vitaris ab Aa. distancia 82R + 35
T4. R =- 30
122 + 85 12a = 8s
8 R F 3B
72a = 85 ~. Fademque est
distancia ab Aa (recta planove pervendiculari) Golidi convertione (persecta
vel imperfecta) BC. A cirea r a deseripei.
Ingulaque Semiguadramalis super eodem BC A Sectore aciem habentis F A
momencum respectu iptius A a CA (uE SC) 5V R: = 5s2 R2; Solidique cor-
relpondentis, ZV R2 P - 8s2 RF: e Semilolidi, 5V R2P = 6S RP. Adeoque
propier Ongula magnicudinem, Za R2 = = s R, Der S L. PrOP. PrXced.) distantia
Cencri graricaris istius Ongulae (adeoque et Solidi seu semisolidi corresponden.
2is) ab Aa, est
BVR -
3
124 - 85
R - 3B
12a =8.
Es, Speciacim, qua coti Semicireulo insistie semiquadrantalis Ingule aciem ha-
DenEIS
cf. V.