Varignon, Pierre
,
Projet d' une nouvelle mechanique : avec Un examen de l' opinion de M. Borelli sur les propriétez des poids suspendus par des cordes
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<
s
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POULIES.</
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de démontrer</
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que{ # {x. R :: a. b. \\ R. y :: d. c.} # Donc {x. y :: ad. bc. \\ & \\ x. x + y :: ad. ad + bc. # }Donc
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# {z. R :: e. f. \\ R. x :: b. a.} # Donc z. x :: eb. fa.
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<
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<
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<
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">Donc z. </
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<
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<
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adeb. </
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<
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xml:space
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">adeb + aadf + abcf. </
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<
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">Or R. </
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<
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<
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</
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<
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<
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<
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">adeeb + aadef + aebcf. </
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<
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xml:space
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diviſant les deux terniers termes de cette derniére
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proportion, par ae, l’on aura R. </
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<
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<
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<
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xml:space
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adf + bcf. </
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<
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<
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XVII.</
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<
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">D’où il ſuit que dans cet uſage des poulies, lors
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que les parties de corde, qui touchent celles de l’é-
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charpe LH, ſont paralleles, la puiſſance R eſt au
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poids D, comme l’unité au double du nombre des
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poulies ſuſpenduës; </
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<
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">mais que dans tout autre cas,
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elle lui eſt toujours en plus grande raiſon; </
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">& </
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<
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xml:space
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">même,
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cette raiſon augmente, quoi qu’en proportion diffé-
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rente, à meſure que les angles A, C & </
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<
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moins aigus, ou plus obtus.</
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<
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">On voit aſſez que tous ces Corollaires avec une infinité
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d’autres qu’on pourroit encore tirer de cette propoſition, dé-
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pendent abſolument de ſon univerſalité, & </
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<
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">que ſans cela
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il ſeroit impoſſible de réſoudre une infinité de Problêmes
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qu’on peut faire ſur cette matiére. </
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