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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MECHANIQUE.
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<
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LEVIERS.</
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s
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xml:space
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">Le point A ainſi tiré par les puiſſances D & </
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<
s
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">E,
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doit en recevoir une impreſſion ſuivant quelque
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ligne AG qui ſoit la diagonale d’un parallelogramme
<
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RS fait ſous des parties de leurs lignes de direction
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AS & </
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>
<
s
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xml:space
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">AR qui ſoient entr’elles, (Lemm. </
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<
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xml:space
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">3.) </
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<
s
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xml:space
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ces mêmes puiſſances; </
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>
<
s
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xml:space
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">& </
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<
s
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xml:space
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">la force de cette impreſſion
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doit être à chacune des puiſſances D & </
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<
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xml:space
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">E, comme
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(Lem. </
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<
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<
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<
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">AG à chacune des lignes AS & </
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<
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">AR,
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ou SG qui lui eſt égale; </
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<
s
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xml:space
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">c’eſt-à-dire, (Lem. </
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<
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">5.) </
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<
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">comme
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le ſinus de l’angle ASG, à chacun des ſinus des angles
<
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AGS, ou GAR qui lui eſt égal, & </
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<
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xml:space
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">GAS; </
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<
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xml:space
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">& </
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<
s
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xml:space
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">par conſé-
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quent les puiſſances D & </
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<
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xml:space
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">E ſont entr’elles, commeles ſi-
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nus GAR & </
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<
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">Elles ſont auſſi (hyp.) </
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<
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xml:space
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">entr’elles, com-
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me les ſinus des angles RAB & </
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<
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xml:space
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<
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xml:space
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<
s
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xml:space
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">par conſé-
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quent les ſinus de GAR & </
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<
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xml:space
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">de RAB, de même que
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ceux de GAS & </
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<
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xml:space
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">SAB ſont égaux entr’eux: </
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<
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xml:space
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">donc les an-
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gles GAR & </
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<
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xml:space
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">RAB, auſſi-bien que GAS & </
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<
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xml:space
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">SAB, ſont
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auſſi égaux, ou, du moins, complemens l’un de l’autre à
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deux droits. </
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<
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xml:space
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">D’où il ſuit que AG eſt en ligne droite avec
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AB; </
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<
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xml:space
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<
s
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xml:space
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">par conſéquent le point fixe B dulevier AB ſou-
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tient, lui ſeul, l’impreſſion toute entiére que le point A
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reçoit du concours d’action des puiſſances D & </
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<
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xml:space
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<
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point demeurant ainſi en repos, ces puiſſances doivent
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auſſi par conſéquent demeurer en équilibre. </
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<
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faloit démontrer.</
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<
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I.</
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<
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<
s
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xml:space
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">On voit de-là qu’une même puiſſance peut ainſi
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faire ſucceſſivement équilibre avec pluſieurs autres,
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quelques grandes, ou quelques petites qu’on les ſuppo-
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ſe, pourvu qu’elle ſoit à chacune d’elles en raiſon </
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>
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