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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 793, page id 851387705:0813
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PFOD. XIX. DeCalculo Centri Cravitatis
Trem Omnes s, (corundem arcuum Sinus recti,) Tune iptum Frilineum rB0 F 1
B R (per S 2. PrOP. 17.) ErSO Omn. = 25 R 2: = = ZB R 3.
269.
irem Omnia Sh (ad bB F spectancia) 1B R, C peC BA. prOP. 18.) ELCO Omn. 270.
aSBR: = = 8B= R 2.
ErgO; Omn. Za R 2 - = 5 R = - = sB R: (hoc cAt, Ungulae bBF, aciem Ha-
benes bB, momencum respectu ra; seu aciem habencis r a, momentum respectu
DB;) 30. 2 R 2 - Z B R 3 = BB2 R 2 = 8a2 R 2 = B R3 f 35 2 R =; SCU (DTOPEEE
a = 3 ∞ - a, _ B = 2 R = V,) =ER E P2 = 8a R = D + 3a  R  = 2 R a + V R
=3s2R2
Onod quidem, 3a2 R - 3 B R3 = 8b2 R= momentum, per Dnoulae BPr, aciem
habencis bB, magnicudinem z a 2 R = B R (per SH. prOP. 17.) divitum; exti.
bec ejuldem cencri graricaris dictantiam d ra, Z R -
d FA, 3R + -
+ Sh= R2
402 -- 8B R: adeoque 2
4 a 2 - 8B p: ejusque relpectu T A momencum, da: R - 3b X
Idemque Za 2 R = - 3 B R3 - d B R momentum, per Vngulae BBr, aciem ha-
benuis ra, magnicudinem 3 a R2 - 3 5 R = = = sh R (per S L. prOP. 27.) divisum;
exhibet hujus dictantiam centri graricacis a BB, ; c- f. 3 a. s R = aish - 6b t - 15. A
a F57 + a - 3 as R + a SB - 6B R2 - B: R
6aR = 65 R = 25B
60R = 65R = 25B
Adeoque ejusdem Ongula bBr (aciem habentis ra) momentum respectu F+.
a2 X2 - 3 asR =  a sB R + 3 b R = 3b2 R2. Idemque eAt, aciem tabentis
Fr, momencum respectu ra
Ouod quidem 3a= R = = 3 as R 2 - + a 5B R + 2 B R  = 5h2 R 2 momencum.
per Ongulae bBr, aciem habentis PY, magnicudinem, Za2R = a5 R + BR= (Per
S H. prOP. 27.) dirisum; exhibet ejusdem Distancam Cencri gravicatis d 7 a
R = 2e 5B
4 a 2 = 8a5 + 8B X; adeoque d F A, ZR -
2R +
E = 2 a sB
442 - 8a5 = 8BR; ejuL.
que respectu T A, momencum, 3a = X 2 - 3 a5 R 2 f ZB R 3  + a sB R = 3 B2 R2
Idenque cHt, aciem habentis F A, momencum respectu F=
Acque hOc demum 3a = R = = Z a 5 R 2- f ZB R 3 f + a s B R = SB= R2 WOMCH.
cum, per Ungula bBr aciem habentis T A, magnicudinem, Z a R = -35 R? L Lsh R
(PeT GF. PrOP. 17.) dirilum; exhibet ejuldem distanciam Cencri gravitaris d Yr,
a-
TOB R B R - 5a5R + ast
TOR - 105R + 25b iadeoque, d bB, a 20B R - B R - 5asR + asto
10a R- 1OSR + 25h ejuF.
ques relpectu bB, momencum, 3a2 R2 - 2b R3 + 5b. R2; idem quod aciem hy
bentis bB, momentum respectu Y A, modo repertum.
Ouaeque de Ingulis bBr tric dicta sunc; eadem omnino Ongulis ABR con-
veniune; subltituris a pro a VprOB, T A prO Ta Aa Pro PT, d vice verta.
Ouippe AbK porrio, limiliter adjacet rectis Y A, Ae, acque rb B rectis ar, 2I.
Solidorum aurem, sire semisolidorum, respondencium magnicudo, ad maenicu.
dinem Ongula correspondentis; eorumque momentum ad momencum hujus, (respe-
au ejusdem plani ad convertionis axem aciemque Ongulae, recti;) elt ut X vel 38
ad P. Distantiaque a planis ad conversionis axem, actemre Ongulae, rectis, uirO-
bique eadem respectire.
Dende
: Si ex Ongularum ABBamomentis, SF tradiris; auterantur respectira
Onculacum Bb Ba momenta: habencur respectira Momenca Ongularum ABB:
e quae hinc dependene.
Est aurem Ongula BbBa, aciem habentis b B vel Aa, (propter magnicudinem
Ea= B, Der ST. PrOP. X7. Centrique gravitatis, in media longicudine Dolii, per
PrOD. 2. distanciam a ra, Z B; adeoque d Y A, 2 R = ZB:) Momentum respectu
ra, +a= B2; respectu PA, a  B R = = a= B2: IIIudque : a 2 p2 (ob distantias et
alicidines recipiocaras,) momentum etiam, aciem habenuis ra, relpectube vel
Hhhhh