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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que non æquari lineæ A c, niſi ad centrum uſque continuetur, illam autem
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finitæ eſſe longitudinis, licet inſinitos gyros peragat.</
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<
s
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">Si nunc concipiamus punctum, quod ex A procedat, & </
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<
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">velocitate quacun-
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que finita moveatur ita, ut hujus directio ad lineas ad C ductas ſemper æqua-
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liter in clinetur, augulos efficiens æquales angulo c AC, perveniet punctum
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">36.</
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hoc ad C tempore finito, in co nempe in quo eadem velocitate rectam Ac
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potuiſſet percurrere; </
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<
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">id eſt finito tempore, velocitate finita, in ſpatio finito, per-
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aget infinitos gyros.</
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<
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<
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">Non omnia infinita eſſe æqualia, evidentiſſime patebit, ſi conſideremus lineam,
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quæ ad partem quamcunque extenditur, in infinitum poſſe produci, talemque
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lineam in finitam eſſe; </
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<
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">minor tamen erit aliâ lineâ, quam partem utram que ver-
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ſus productam concipimus in infinitum, hanc etiam ambarum ſumma ſupe-
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rabit.</
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</
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<
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">Infinita linea continet numerum infinitum pedum, duodecuplum numerum
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pollicum.</
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<
s
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">Infinitorum inæqualitatem etiam detegimus, comparando diverſas curvas
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ſpirales logarhthmicas ſtatim indicatas.</
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<
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& </
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">aliam ſpitalem logarithmiam, ex A exeuntem, & </
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fig. 4.</
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tem, ut duabus revolutionibus pertingat ad F, duabus aliis pertinget ad G;
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<
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">quia duæ requiruntur revolutiones, ut accedendo ad centrum dimidium di-
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ſtantiæ ab hoc percurrat, numerus revolutionum in hac duplus eſt nu-
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meri revolutionum in ſpirali prima, quando æqualiter cum hac prima ADF
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ad centrum accedit; </
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utraque tamen curva niſi poſt infinitas revolutiones ad centrum non accedit.</
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<
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<
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">Quæ de infinito omnium maxime paradoxa demonſtrantur, ideaſque no-
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ſtras in immenſum ſuperant, ſunt quæ ſpectant infinitorum claſſes va rias.</
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<
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">Detur curva ABC parabola, cujus abſciſſa quæqcunque ſit AD ordinata
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huic reſpondens DC.
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fig. 4.</
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<
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inter abſciſſam & </
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</
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">quare ſi abſciſſa quæcunque dicatur x, ordinata reſpondens y, parameter a,
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ſict. cou.
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lib. 3.
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pro. 2.</
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in omnibus parabolæ punctis habemus {.</
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la cum AF, per A parallelâ ad abſciſſas, non congruit, daturque tota infra hanc
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lineam, quæ illam tangit, & </
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<
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<
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">Si augeatur a manente x augetur y, & </
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formatur nova, in qua omnes ordinatæ aliûs curvæ ordinatas reſpondentes
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ſuperant; </
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<
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gentem AF tranſit, minoremque angulum mixtum cum hac efficit. </
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meter autem in infinitum poteſt augeri, & </
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quem cum tangente efficit Parabola.</
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<
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">vertice A, detur alia curva AEG, cujus ordinatæ di-
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cantur z, quarum relatio cum reſpondentibus abſciſſis x exprimatur hac æ-
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quatione bbx = z
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: </
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turque angulus contactus, qui augendo b in infinitum minui poteſt.</
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<
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">Habemus ergo duasclaſſes angulorum decr eſcentium in infinitum; </
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