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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 46, page id 1066518432:0074
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46 DF V ERIDUS ET MIOTTBUS CORBORUM. LIB. I.
ms = an, d S = an: M, dC d5 = aman - anam
ma3 vel quia ds = adX: n, exit
da =mnan-annam: mm =-mmam -nnam: nm = - aadm: mm, ex-
50 uc Cupra (5. 103.) invenictur dy = ada: Y (2a∞ + dex) aequatio
Catenariae, juxe eadem prorsus est cum Velaria. Sin vero grarium
directiones in puncto ad distantiam finitam PONantUE COnVergerE,
Catenaria crit Byperbola aequilatera, cujus demonstratio brevitatis
gratia aliis relinquenda est, quanquam caeteroquin non lonsa (IE,
sed Ferme una linea et absque calculo potest pertci.
PROPOSTTTOZTTT. PROBLEMA
207. Inventa curva manente, in quam velum, linteum, aut quod
vis aliud corpus ptexile a potentiis applicatis arcuatur, assienare me-
diam directionem potentiarum e impressionem earum, juxta banc me-
diam directionem.
Fi5. 30. Sit ACD inrenta curra cerminis suis tigillo seu linex inflexili
ACD alligata, quaeritur media directio omnium potentiarum eb,
ab ecc. currae applicatarum, ec quantitas impulsus, seu imprestio.
nis, quae secundum mediam directionem CB in tigillum DCA CXC.
ri dcbet.
SolutiO. PeT TErMInOS CUEVX A, D duCEX SINE TANGONECS CUEVR
AB, DB conrenientes in puncto B, in quarum alteruEra, uE AB,
capiatur legmentum AF, quod sit ad reliquam tangentem totam DB,
ut tenacitas currae in A ad tenacitatem ejus in D, quae tenacitates
ex Cuperius (5. 93.) demonstratis BabenEUE. PeT DUNCTa A eF D
agantur perpendiculares AC, DMI, recta DA, _ per F ac B cidem
AD aequidistantes FC, BP. perpendicularibus occurrentes in C et
F. Diridatu AD in C, UE SIE AC: DC ==DF: AC, eE in peFPCM.
diculari linex AD per punctum C Cursum ducta sumatur portio
CII = AO F DB, ec in parallela cidem AD per punctum II ducta
Tumatur TTI =BE = FC, e jungatur denique IC, ejusque conti-
nuatio CB erit media directio quaelita, impullus vero ex omnibus
currae applicatis potentiis resultans, secundum hanc mediam dire-
etionem, erit ad tenacitatem fili in A vel D, sIcuF IC eA ad AF
vel ad DB.
Demonstr. Lea L NO altam a Potentiis eb, ab eC. CUrVX
AeD applicatis imprestionem subire potest, quam quae resultat ex
Potentiis, quibus in directionibus tansentium currae AB, DB urge
tur, Seu ex tenacitatibus currae in A et D, quandoquidem in his
tar