Gravesande, Willem Jacob 's
,
Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1
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181 - 210
211 - 240
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361 - 390
391 - 420
421 - 450
451 - 480
481 - 510
511 - 540
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MATHEMATICA. LIB. I CAP. IV.
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& </
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<
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">lineam AE inter evaneſcet, id eſt erunt æquales quantitates hæ. </
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<
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<
s
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">Infiniti ideam non habemus; </
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<
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xml:space
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">ideo ideis non aſſequimur, quæ de infinito de-
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monſtramus; </
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<
s
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xml:space
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">quæ tamen ex indubitatis principiis immediate ſequuntur, cer-
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ta ſunt, &</
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<
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<
s
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xml:space
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">Innumera circa Materiæ diviſibilitatem captum noſtrum ſuperantia eviden-
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tiſſime demonſtrantur, inter hæc notatu maximedigna ſunt, quæ ſpectant cur-
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vam ſpiralem logarithmicam dictam.</
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<
head
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style
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it
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">De Spirali logaritbmicâ, & bujus menſurâ.</
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<
s
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xml:space
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">Hujus curvæ proprietas eſt, quod cum omnibus lineis ad centrum curvæ
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ductis angulos efficiat inter ſe æquales.</
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<
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<
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">Sit centrum C: </
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<
s
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xml:space
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">in A angulus curvæ, id eſt tangentis ad curvam, cum radio
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<
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">TAB. I.
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fig. 2.</
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AC, nempe BAC, æqualis eſt angulo EDC, quem tangens, in puncto alio
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quocunque D, cum linea DC efficit.</
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<
s
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xml:space
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">Si angulus hic fuerit rectus, ſpiralis in circulum ſe convertet, ſi autem
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fuerit acutus, ad centrum continuo accederefacile patet: </
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<
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xml:space
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infinitos gyros ad hoc pervenire poterit.</
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<
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<
s
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xml:space
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">Ponamus revolutionem primam, poſito curvæ initio in A, terminari in F,
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puncto medio inter A & </
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">centrum C. </
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<
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">In hoc caſu angulus BAC paululum
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excedet 80. </
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<
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">Secunda revolutio ad FC illam habet relationem, quam
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prima ad AC; </
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<
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">C, quod
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ad gyros ſequentes etiam applicari debet; </
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xml:space
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">& </
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<
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in integra revolutione quacunque, accedendo ad centrum, percurrit dimidi-
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um diſtantiæ ſuæ a centro in principio revolutionis. </
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<
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am a centro quantumvis exiguam pervenerit, non unicâ revolutione ad hoc per-
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venire poterit; </
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<
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xml:space
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">auctoque numero revolutionum, quantum quis voluerit, non-
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dum ultimam attinget; </
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<
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rabit.</
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<
s
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">Ad centrum tamen curvam pertingere, ibique terminari, etiam conſtat. </
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tio curvæ ABEG; </
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<
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fig. 3.</
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batur circuli portio GL, ſecans lineam C A in L.</
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<
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">Concipiamus LA diviſam in partes æquales, ſed exiguas, AD, DI, IL,
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per quarum ſeparationes concipiamus circulorum portiones, centro C de-
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ſcriptas, ſecantes curvam in B & </
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<
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">ductiſque radiis BC, EC, formentur
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triangula rectangula ADB, BFE, EHG, in quibus propter exiguas AD,
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DI, IL, hypotenuſæ, licet portiones curvæ, pro rectis haberi poſſunt; </
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<
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rus enim partium in AL in infinitum poteſt concipi auctus, manentibus, quæ
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huc uſque ſunt expoſita, ut & </
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<
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<
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<
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præterea ex natura Curvæ angulos habent æquales BAD, EBF, GEH. </
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<
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etiam æqualia, propter latera homologa æqualia AD, BF, EH, quod ex æ-
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qualitate partium AD, DI, IL, ſ quitur.</
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<
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">Ex A ducatur linea A c, cum C A angulum efficiens CA c, æqualem an-
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gulo CAB; </
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<
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lares C c, L g, I e, D b, ſecantes A c in punctis c, g, e, b; </
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<
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& </
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<
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">eb parallelis ad AC, formantur triangula AD b, bfe, ebg, ſimilia & </
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qualia inter ſe, ut & </
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<
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quet.</
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<
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">Idcirco hypotenuſæ A b, be, eg, æquales ſunt hypotenuſis AB, BE, EG, id
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eſt, linea A g æqualis eſt curvæ portioni AG.</
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<
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">Hinc patet quomodo portio quæcunque curvæ menſuranda ſit, curvam-
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