Musschenbroek, Petrus van
,
Physicae experimentales, et geometricae de magnete, tuborum capillarium vitreorumque speculorum attractione, magnitudine terrae, cohaerentia corporum firmorum dissertationes: ut et ephemerides meteorologicae ultraiectinae
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CORPORUM FIRMORUM.
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ctum H a pariete recedendo fibram ſuam tendit, elongatque ut ac-
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quirat extenſionem 1H 2H, hoc modo omnes fibræ inter B & </
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<
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xml:space
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tenduntur, extrahuntur, elongantur, maxime ſupremæ 1B 2B,
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minus mediæ 1H 2H, omnium minime, quæ ſunt proximæ pun-
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cto A. </
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<
s
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xml:space
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">proinde fibræ intermediæ 1H 2H minus reſiſtunt potentiæ
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Q, quam 1B 2B propter duas rationes, 1°. </
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<
s
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xml:space
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">Quia B A C vectis eſt
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incurvus, cujus unum crus eſt B A, adeoque vi eâdem applicatâ di-
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verſis punctis 2B, 2H, erit momentum in 2B, ad id in 2H, uti
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A B eſt ad A H; </
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<
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xml:space
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">hoc eſtuti diſtantia â puncto? </
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<
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xml:space
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">A: </
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<
s
xml:id
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xml:space
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">quare momentum
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Cohærentiæ in B, ad illud in H, erit uti diſtantia AB, ad AH,
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quemadmodum ex natura vectis ſequitur. </
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<
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">2°. </
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<
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xml:space
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">Quoniam ambæ
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fibræ 1B 2B, & </
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<
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xml:space
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">1H 2H ſimul tenduntur a potentia Q, minus ta-
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men 1H 2H, quam 1B 2B: </
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<
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xml:space
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">ſupponamus vires retrotrahentes fi-
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brarum tenſarum eſſe in ratione extenſionum, ita ut fibra tenſa & </
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<
s
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elongata aliquouſque a pondere uno, duplo plus elongetur a pon-
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deribus duobus, triplo plus â tribus, & </
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<
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xml:space
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">ſic porro: </
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<
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xml:id
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xml:space
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">tum erunt vires
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retrotrahentes, uti ſunt tenſiones, ſive elongationes, hoc eſt erit
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vis in H, ad eam in B, uti 1H 2H, ad 1B 2B. </
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<
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xml:space
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">ſed ſunt A1 H
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2H. </
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<
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xml:space
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">& </
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<
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xml:space
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">A 1B 2B duo Triangula ſimilia, & </
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<
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xml:id
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xml:space
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">1H 2H, ad 1B 2B
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;</
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<
s
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xml:space
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">: A 1H ad A 1B. </
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<
s
xml:id
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xml:space
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">quare erunt vires fibrarum retrotrahentes in
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1H & </
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<
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xml:space
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">1B, uti A 1H ad A 1B ſed ob rationem vectis modo da-
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tam. </
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<
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xml:space
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">erant momenta virium in H&</
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<
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xml:space
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">B, uti A 1H ad A 1B. </
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<
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xml:space
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">qua-
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re ob duas rationes ſimul, erunt vires in H ad eas in B, in ra-
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tione compoſita ex AH ad AB, & </
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<
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xml:space
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">ex AH ad AB, hoc
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eſt in ratione duplicata diſtantiæ AH ad AB, a centro mo-
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tus A.</
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</
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<
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xml:space
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">Quæcunque demonſtravimus de viribus duorum punctorum H & </
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B conveniunt viribus omnium punctorum inter A & </
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<
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xml:space
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">B, ideoque
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omnes vires in unam ſummam addendæ ſunt, ut habeatur tota
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vis reſpectiva Cohærentiæ. </
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<
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xml:space
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">Hæc ſumma ſequenti modo cognoſce-
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tur: </
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<
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">capiatur NR æqualis AB, in quâ fiat NP æqualis A H: </
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<
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de ut NP
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ad NR
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. </
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<
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xml:space
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">ita ſit quæcunque PQ ad RS, quæ ad angulos
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rectos inſiſtant ipſi NR, per puncta NQS deſcribatur parabola A-
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polloniana, cujus vertex ſit in N, & </
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<
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">compleatur rectangulum NR
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ST. </
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<
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">Tum ſi R S exponat vim Cohærentiæ puncti B, PQ exponet
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eam puncti H, omnesque parallelæ ad RS utrimque terminatæ </
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