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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 276, page id 1066518432:0304
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276 DE V FRTBVS. F FT MIOTEBVS: CORBORVH. L. 1B. IL.
positione datum, aequari facto ex magnicudine genitrice in riam
centri ejus graritatis; e rix centri graritatis sunt circumterentia
circulares a centro delcriptx, atque adco radiis luis proportionales.
Propterea magnitudines genitx lunt in compolita ratione magnitu-
dinum. genitricium ec distanciarum centri carum graritatis ab aXc
rotationis. Idcirco erit superticies Cx COnexTIONC CUIEVX AC CirCA
AI ad circulum quemcunque, cujus radtius est RL, in compolita ra-
tione magnitudinis AC superticiei genitricis ad magnicudinem R
circuli genitricem, ee distantiae centri graritatis r illius magnitu
dinis ab axC AT seu rE ad distantiam centri graritatis hujus, (eu sR,
hOc CA, HCHE AC. Er ad R. ER, id es, SICNL 2AC. Ey vel 2AC. OI-
2AB. AT ad R; adeoque si R. = 2AC. CI - 2AB. AI, erit CuPer
Acies genita circulo aequalis.
70. Eodem argumento circulus, cujus ractius R potest duplum
arex hyperbolicae, AMNL, aequatur superficiei ex conrertione AC
circa axem u2c genitxe. Nam dicta superticies erit ad circulum, ut
AC. uEad sR2; vel uE2AC. uE adt R; aequi (num. 4.) AC. HE = AMNL,
ergo superticies ex Curra AC circa n2c est ad circulum radii R =
YZAMNL, UEZAMNL ad ZAMNT, id est in ratione aequalitatis.
8. Sin vero centrum Fuerit graritatis arCX UAC 2f, ducatur pd
Parallela AB, eritque (5. 44.) ud in arcam u AC2f = omnibus mo-
meneis rec- lorum f26 ad aXem V2C appenSOrUM; HOC CA WB. ANI.
AB = OmnibuS 5. C2C, 62C. CF; na (NUM. 3.) CA aFCA UAC2f = AMI.
AB. AEqui 112C, C2C. Cf = : BMI: BM. MIp = = AB. BM. MIm = :AB.
adco VB. AMI. AB = ; AB. AI NM, vel 2UD. AM = ALNM. Scd
(num. 4.) tabuimus etiam AE. AMI = AL. NM, erGO UE. AMI = 21D.
AMI, vel uE = 2. UD, adeoque centrum graritatis CurVX AC dupl0
Lonsius distat a linca 12C, quam centrum graritatis arCX WAC2f.
9. Flinc Colidum Cx rOtatiOnO AGUEX WAC2f circaaxem u2f, lC-
missis est cylindri, cujus altitudo AB, _ baleos radius potest du-
plum arex hrxerbolicae AINM. Nam hoc solidum (5. 47.) Xqua-
Tur Facto CZ area WA C2f in circumterentiam radii vo, Cum p SIE
centrum graritatis areae, hoc est = AB. AM in circumt. radii uB
(Num. 8.) ==AB. AM in circumF. UE. AEqui AC vel AM in cir-
CumF. UE CA CuperF. CZ AC CIrCA H2C (RUM. 7.) = circulo cujus ra-
dius =V2ALMNI; orgo Solidum area WAC 2f Circa V2f POtaEX = CY
lindro, cujus radius potest2AL. MNI, et altitudo cst; AB; adeoque
Drxedictum Colidum dimidium est cslindri, cujus altitudo AB baseoS-
Queradius potest 2AL. HIM.
LC