Full text: Musschenbroek, Petrus: Physicae experimentales, et geometricae de magnete, tuborum capillarium vitreorumque speculorum attractione, magnitudine terrae, cohaerentia corporum firmorum dissertationes

CORPORUM FIRMORUM. tudo data a k = e, latitudo e o = f. altitudo a e = x pondus p
= p.

Tum erit momentum parallelopipedi A E F D ex gravitate, =
{1/2} a b d d, & momentum ponderis ſibiannexi = o d: Cohærentia vero
= a a b. præterea erit momentum ex gravitate parallelopipedi, a e o k,
= {1/2} e e f x. & momentum ponderis P appenſi = e p. Cohærentia
= x x f. proponitur vero {1/2} a b d d + d o, a a b: : {1/2} e e f x + e p. x x f
idcirco {1/2} a b d d f x x + d f o x x = {1/2} a a b e e f x + a a b e p tranſpoſito-
que {1/2} a a b e e f x. fit {1/2} a b d d f x x + d f o x x - {1/2} a a b e e f x = a a b e p. factaque diviſione per {1/2} a b d d f + d f o
fit x x - {{1/2} a a b e e f x/{1/2} a b d d f + d f o} = {a a b e p/{1/2} a b d d f + d f o}
additiſque {{1/16} a 4 b b e 4 f f/{1/16} a a b b d 4 f f+{1/4} a b d 3 f o + {1/4} d d o o f f}. erit x x - {{1/2} a a b e e f x/{1/2} a b d d f + d f o} + {{1/16} a 4 b b e 4 f f/{1/16} a a b b d 4 f f + {1/4} a b d 3 f o + {1/4} d d o o f f}
= {a a b e p/{1/2} a b d d f + d f o. } + {{1/16} a 4 b b e 4 f f/{1/16} a a b b d 4 f f + {1/4} a b d 3 f o + {1/4} d d f f o}
atque utrimque extrahendo radicem
x - {{1/4} a a b e e f/{1/4} a b d d f + {1/2} d f o} = {a a b e p/{1/2} a b d d f + d f o. } + {{1/16} a 4 b b e 4 f f/{1/16} a a b b d 4 f f + {1/4} a b d 3 f o + {1/4} d d f f o o}
tranſpoſitisque - {{1/4} a a b e e f/{1/4} a b d d f + {1/2} d f o} habetur ſola quantitas
x = {{1/4} a a b e e f/{1/4} a b d d f + {1/2} d f o} + {a a b e p/{1/2} a b d d f + {1/2} d f o}. + {{1/16} a 4 b b e 4 f f/{1/16} a a b b d 4 f f + {1/4} a b d 3 f o + {1/4} d d f f o o. }.

513. PROPOSITIO XXXV.

Tab. XXV. fig. 2. Dato parallelopipedo A B C D, in quo gravita-
tis momentum, una cum momento ponderis dati H pendentis ex D,
ad Cohærentiam ſuam habeat quamlibet rationem; ad rectam da-
tam I K, applicare aliud parallelopipedum, æquale A B C D, in

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