Gravesande, Willem Jacob 's
,
Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1
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intellige evaneſcentes, & </
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">demonſtrationes nulli Mathematicæ demon-
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ſtrationi firmitate cedent.</
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<
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<
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<
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xml:space
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reveraque æquales eſſe, ergo in demonſtratione quacunque in qua
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portionem curvæ bB infinite exiguam ponimus, quia hanc evane-
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ſcentem intelligimus, tuto lineas ut fb, & </
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<
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<
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<
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xml:space
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">Demonſtrationes hæ diſtingui debent a demonſtrationibus in qui-
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bus error, licet inſenſibilis, datur, qualis eſt demonſtratio n. </
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<
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<
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">ex qua deducimus ſonum, ſive majorem ſive minorem, eâdem ſemper
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velocitate per eundem aërem moveri; </
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<
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">quod Mathematice verum non
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eſt, ſed differentia velocitatum, quando datur, ita exigua eſt, ut
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nulla arte percipi poſſit, quare differentiam in Phyſicis negligimus; </
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eodem modo ac in praxi geometriæ, ubi montis altitudinem conſi-
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deramus, hanc non pro mutata habebimus, quamvis arenula adjecta
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ſit. </
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infinitè exiguis, ſed de quantitatibus finitis; </
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non modo exprimi poteſt ratio inter arenulæ diametrum & </
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altitudinem, ſed & </
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ſi velis diſtantiam ſtellæ fixæ cujuſcunque a Tellure.</
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<
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">In hiſce demonſtrationibus in quibus pro æqualibus habemus quan-
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titates, quæ tali inſenſibili quantitate differunt, error in demonſtra-
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tione ſenſibilis non erit, & </
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">ideò, ubi de rebus ipſis agitur, de qui-
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bus ſenſibus dijudicamus, demonſtrationes hæ a Mathematicis jure
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admittuntur; </
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ut demonſtravimus, demonſtrationes quæ infinitè exiguas, aut eva-
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neſcentes, quantitates pro fundamento habent.</
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