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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quæ deinde porrigitur in filum longitudinis tredecim millium
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pedum.</
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<
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<
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xml:space
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mus ſubtilitatem & </
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longo tempore fere nihil ſui ponderis amittunt & </
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<
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">ſpatium
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fatis magnum particulis odoriferis continuo implent, qui
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computum de tali ſubtilitate inire voluerit in illarum nume-
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ro quid portenti facile reperiet.</
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<
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<
s
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">Ope microſcopiorum objecta quæ viſum fugiunt magna
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<
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">30.</
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videntur, dantur animalcula per optima microſcopia vix vi-
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ſibilia, habent tamen partes omnes ad vitam neceſſarias, ſan-
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guinem, & </
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<
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quanta ſit quis non videt?</
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">In finitum vocant quidam illud, quo non datur majus, & </
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<
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">negant materiam,
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eſſe diviſibilem in infinitum, quod, hac Infiniti data definitione, libenter
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concedimus. </
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non poſſe dividi, nullumque diviſionis dari limitem, defendimus.</
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">31.</
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merum ſuperante, in quantitate finita contineri, ex conſideratione progreſſionis
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geometricæ decreſcentis deducitur.</
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<
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<
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nullumque dari continuationis limitem quis non videt? </
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xml:space
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minorum ſummam nunquam excedere unitatem; </
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<
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">imo exacte unitati æquari
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demonſtramus, ſi revera in infinitum continuatam concipiamus progreſſio-
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nem.</
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">hujus dimidium AB eſt primus terminus {1/2}; </
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fig 1.</
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midium reliqui eſt terminus ſecundus {1/4}; </
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do DE in duas partes æquales habetur terminus ſequens; </
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">& </
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<
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in infinitum continuari poteſt ſeries, ſemperque defectus ſummæ termino-
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rum ſeriei AB, BC, CD, &</
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ſeriei æqualis erit quantumvis hæc continuetur. </
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terminorum eſt finitus denominator fractionis, ultimum terminum exprimen-
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tis, eſt numerus finitus, & </
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ab integra unitate deficit.</
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nator ultimi termini omnem numerum finitum ſuperabit, partemque lineæ
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AE exprimet omni parte finita minorem, ideoque differentia ſumman </
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