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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 337, page id 1066518432:0365
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DE VTRTBUS ET MIOTEBUS CORPORUM. LIB. II. 337
COR OZ L a R Lu n TII.
585. Si relistentia est uniformis, Curra ARC abit in lineam re
ctam ipsi AC parallelam, eritque hoOC CasU AMNSB = CMNSB =
BB. 6II = AC. BR, ac per consequens resistentia medii BR unifor-
mis ad graritatem unitormem se habebit, ut OHI differentia abscis-
Parum BC _ BII arcuum currX AB ec BC descensu e sublequen-
te alcentu descriptorum ad AC asgresacum iplorum arcuum ABC.
C OROLL A R L U M IV.
586. Si curra ABC est cyclois ordinaria, cujus axis vel diameter
circuli generatoris eAt bB et basis ac; femisis differentix quadrato-
rum ex arcubus crcloidis ADB e BF C descensu ex ascentu descri-
PtiS aQUABIEUT AFCX ATRTC.
Nam, quia BB exponitigraritatem unitormem juxta ea, quae 5. 179.
dicta TunE, haec BB erit dupla diametri bB; hinc BB. BC, = 2. bB. BC =
2. BR (rel, quia arcus crcloidis ADB aequat duplam subtensam BK)
= 5. AB, _ BB. BII = 2. bB. BIT = :. BC, ergo BB. GTT = : AB-
:BC==ATRTC. HhOc CR, rectangulum ex lemisse difterentix ar
Cium ADB e BF C descensu e sublequente ascensu in creloide
delcriptorum, in a58resatum ABC corundem arcuum, x quat arcam
ATRIC.
Hloc corollarium coincidit cum propositione ZZZ. L ib. II. Princ.
Phil. Nac. TIlustr. Nertoni, cujus tamen demonstrationem ex aliis
principiis hausit, uc demonstrationem illam inspicienti cuilibet pa-
tebit.
COR OE E A R YU M V.
587. Erso, in calu corollarii TII. hujus, resistentia uniformis in
creloide erit ad graritatem, id est, RB ad BB in Ag. 134. Sicut di-
midia differentia arcuum ADB e BFC ad BB, seu hemicreloidem
aDB, vel sicut disterentia dictorum arcuum ad interram crcloidem,
aBC. FA enim (5. 585.) BR: BB = GTI: AC = BB. GFL: BB. AC
(5. 586.) = (: AB --: BC). AC: BB. AC = ; AB - : BC: BB vel aDB,
=AB -BC: crcloid. aBC.
SCHO-