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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 84, page id 1066518432:0112
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84 DE V TRTBOS EF MIOPTBOS CORPOROM. L TD. L.
curra, ex cujus principio F proticilcatur mobile e analogx currr
ARG baliS C1O quadrantem habet sibi insistentem, quemadmodum
basis CD suum quadrantem KID, idcircO tempUS per FR, hoc est
EFR = NY. VA. aNG. ION, aEquO adCO FFE A = NV. VA. anG. MON.
Es CrGO EBF A ad FFF A, ut N. VA. ang. HCD ad N. VA. ang.
MCNhoc eA, licut angulus rectus ICD ad angulum rectum MCN,
atque adco in ratione aequalitatis; erso sequali tempore omnes ar-
CUS BA, FA, ZA eEC. DCTCUErenEuE, atque adeo curra provote
tionis nostrae BF A est ilochrona. Ouod crat demonstrandum.
GOK OL L A R L u n I.
173. Si OA Fuerit radius osculi seu curraturae ilochronae in ver-
tice A, erit generaliter N = V (OA. O A: 0O. A2). Sumto enim ar-
culo AX indefinite parro vertici contiguo, ductisque Cx CentrOO
acculo ZV, X per Y ordinata Y Y curvam AR sccante in Z. Jam
quia (secundum hypochesin) AZ = N. YZ, vel AXE =NN. Y7
(Secundum hypothesin) =NVNV. dupl. arexe AVγa = 2NNV. AY. Aa,
ec quia AY CA aGGTCGatUM SINLUm VerTOrUM aECULOTM AX _ X Y
instar aequalium accipiendtorum, quorum CeNEra TUNE O et O, Ret
AY - AX = AX CXY.
20A 20A atque aded 2AY = AX2. 0O: OA. O A, 2c
proinde substitutione Facta, Proveniet AZ2 =NN. AX3. OO. A2:
OA. OA, ex qua facile clicitur NN = OA. OA: OO. A2, 8
N = Y (OA. OA: OO. A2).
OR OE L A R F u M TI.
274. Si jam minimus ilochrona arculus XA vertici. A adjacens
consideretur instar arcus circularis radii aA a pondere A flO OA
appenso descripei; erit tempus, quo arculus X A vel tota curra BR A
delcribi potest, semissis unius oscillationis penduli OA. Onde, quia
(5. 172.) TXA = NV. VA. an8. rectum, erit AT LA, Teu duratio dua-
rum penduli cujusque oscillationum minimarum, quod deincepsdi-
Catur T, erit inquam Y = IV. VA. 4 rectos scu nominando periphe-
riam D, cujus ractius Y crit T = pNV. vA, vel substicuendo ralorem
iphus N articulo praecedenti detinitum, reperictur T = DY (A. OA.
AO: OO. Aa). Oui est canon valde generalis, in quo oa signiticat
lonsicudinem penduli, AO ponderis minimam diltanEIaM a CeH.
ExO