Gravesande, Willem Jacob 's
,
Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1
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PHYSICES ELEMENTA
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<
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xml:space
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">Jugum Bilancis figuram habet quæ in AB repræſentatur, in ipſis locis A & </
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B excavatur, ut hoc in fig. </
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<
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fig. 5.</
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craſſitiei.</
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<
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xml:space
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">Propter figuram irregularem, admodum difficilis foret computatio; </
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<
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ſervato jugi pondere, mutatam concepi figuram; </
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<
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xml:space
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à centro, & </
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<
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">admotis aliis, poſuique figuram illam eſſe, quæ repræſentatur in
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fig. </
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<
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<
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">, in qua tota longitudo illa eſt, quæ in Bilance inter puncta ſuſpen-
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ſionis datur; </
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<
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xml:space
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">ex qua mutatione exiguus tantum error in computatione dari
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poteſt.</
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<
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</
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<
s
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xml:space
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">Hujus figuræ ſuperficies, cum jugum ejuſdem ſit craſſitudinis ubique, re-
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præſentare poteſt jugi pondus in omnibus partibus. </
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<
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xml:space
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">Figura hæc AB conſt@t
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ex parallelogrammo & </
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<
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illam quæ in fig. </
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<
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<
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">exhibetur, qua adſumtâ computationem inibo.</
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<
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<
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<
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xml:space
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">Hunc uſum computatio hæc habere poterit, quod inde patebit, cum
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demonſtratis circa percuffionem experimenta noſtra congruere. </
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<
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xml:space
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">Fundamentum
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autem ipſius computationis habetur in n. </
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</
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<
s
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xml:space
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">Ante omnia ſingula puncta ſuperficiei ADEB, pondus jugi repræſentan-
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fig. 7.</
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tis, per quadrata diſtantiarum ſuarum a centro motus reſpective multiplicari
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debent. </
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<
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xml:space
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">Hoc ſine errore ſenſibili fiet, ſi loco diſtantiarum a centro, di-
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ſtantiæ a lineâ CF uſurpentur, quo computatio facilior evadit.</
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</
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<
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<
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xml:space
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">Si nunc operatio pro parallelogrammo inſtituatur, ſingulæ lineæ parallelæ & </
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æquales lineæ DA, per quadratum ſuæ diſtantiæ à CF multiplicandæ ſunt,
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id eſt, ſingula hæc quadrata per eandem quantitatem AB aut CG multiplica-
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ri debent, id eſt, ſumma quadratorum per CG multiplicanda eſt; </
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<
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tem quadratorum eſt pyramis, cujus baſis eſt quadratum AC & </
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<
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dem AC, quæ pyramis valet {1/3} AC
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. </
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<
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{1/3} CG x AC x AC
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ſummam productorum ſingulorum punctorum paralle-
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logrammi DC, multiplicatorum per quadrata diſtantiarum ſuarum a
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CG.</
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<
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">Similis ſumma pro ſingulis punctis trianguli DCG æqualis eſt, {1/12} GF
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x AC x AC
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. </
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<
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<
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lud explicare inutiliter laborarem. </
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<
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milem ſummam pro integra figura ADFEB; </
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<
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<
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+ {1/6} GF x AC x AC
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, = b x AC
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; </
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<
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AC.</
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<
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<
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<
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dendo acquiſita, qua globus in lancem Mincurrit, & </
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hujus altitudinis proportionalis eſt , poterit √ a deſignare.</
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<
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<
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xml:space
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<
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ſtantiæ AC, & </
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<
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in experimento motorum, reſpectivè multiplicatorum per quadrata diſtantia-
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rum ſuarum a centro motus, habemus velocitatem puncti A poſt ictum .</
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<
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<
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">Partem hujus ſummæ jam determinavimus, quoad jugum nempe, quod ſu-
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pereſt habemus multiplicando pondera lancium L & </
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</
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<
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<
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quaſi darentur in ipſis punctis ſupenſionis A & </
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<
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