Fabri, Honoré, Tractatus physicus de motu locali, 1646

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          <chap id="N15AC3">
            <p id="N173E1" type="main">
              <s id="N173E7">
                <pb pagenum="102" xlink:href="026/01/134.jpg"/>
              8 primis acquiritur ſpatium YS æquale GH; quod debet diuidi in ſpa­
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              tiola 36, quæ reſpondent 8. temporibus, ſeu terminis huius progreſſio­
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              nis, quibus æqualia ſunt 144. in GL, cuius YS eſt 1/4, ſed ſi in 8. primis
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              acquiruntur 36. in 8. vltimis acquirentur 100. igitur S 6. eſt 100. igitur
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              Y6. eſt 136. igitur eſt ad GL vt 136. ad 144.ſeu 17.ad 18.igitur Y6.eſt
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              ſpatium totale minus vero (1/18). </s>
            </p>
            <p id="N173FA" type="main">
              <s id="N173FC">Deinde diuidatur adhuc tempus AF in partes 32. æquales, 16. pri­
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              mis acquiritur ZR æquale GH, quod debet diuidi in ſpatiola 136.quæ
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              reſpondent 16. temporibus quibus æqualia ſunt 544. in tota GL, cuius
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              ZR eſt 1/4 ſed ſi in 16. primis temporibus acquiruntur 136. in vltimis
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              16. acquiruntur 392. igitur R 7. eſt 392. & ZR 136. igitur Z 7.528.
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              igitur Z 7. eſt ad GL, vt 528. ad 544. ſeu vt 33. ad 34. igitur Z 7 eſt
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              ſpatium minus verò (1/34) </s>
            </p>
            <p id="N1740B" type="main">
              <s id="N1740D">Denique ſi diuidatur tempus AF in partes 64.ſpatium acquiſitum erit
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              minus vero, aſſumpto ſcilicet tota HL (1/66), ſi diuidatur in 128. partes, erit
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              minus (1/130) ſi diuidatur in 256. partes, erit minus (1/258) ſed temporis par­
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              tes 2.AE. EF minimè ſenſibilium diuidi poſſunt in infinita ferè inſtan­
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              tia; ſint tantùm ex.g. </s>
              <s id="N17419">1000000. igitur ſpatium tunc acquiſitum erit mi­
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              nus ſuppoſito vero HL (1/1000002), quæ ſi deſit tantùm ſpatio KL vt ſit 1/4
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              totius GL, quis hoc diſcernat? </s>
              <s id="N17420">igitur etiam ſuppoſita progreſſione arith­
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              metica, quæ fiat in finitis inſtantibus; </s>
              <s id="N17426">ſi obſeruetur acuratiſſimè ſpatium,
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              quod percurritur in vna parte temporis ſenſibili v. g. ſpatium GH in
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              parte temporis AE; </s>
              <s id="N17432">ſpatium, quod acquiretur in tempore ſecundo æqua­
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              li tàm propè accedet ad ſpatium HL, id eſt ad triplum prioris GH, vt
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              nullus mortalium diſcernere poſſit; igitur cum hoc experimento tàm
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              poteſt ſtare noſtra hypotheſis, quàm alia Galilei, igitur neutra ex eo tan­
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              tùm euinci poteſt. </s>
            </p>
            <p id="N1743E" type="main">
              <s id="N17440">Hinc obiter obſerua progreſſionem differentiarum; </s>
              <s id="N17444">quippe ſi ſint
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              tantùm 2. partes temporis, differentia eſt 1/4; </s>
              <s id="N1744A">ſi 4.1/6 ſi 8. (1/10); ſi 16.(1/18); ſi 32.
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              (1/34); </s>
              <s id="N17450">ſi 64.(1/66) nam primò denominator fractionis ſuperat tantùm binario
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              numerum partium temporis; ſecundò differentiæ denominatorum ſunt
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              in progreſſione geometrica dupla numerorum 2. 4. 8. 16. 32. 64.
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              128. &c. </s>
            </p>
            <p id="N1745A" type="main">
              <s id="N1745C">Eodem modo ſoluendum eſt ſecundum experimentum rotati globi in
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              plano decliui; </s>
              <s id="N17462">præſertim cum globus ab incurſu aſperiorum partium
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              tùm globi, tùm plani ſaltuatim deſcendat; </s>
              <s id="N17468">quod dubium eſſe non poteſt,
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              & quò decliuius erit, faciliùs reſiliet a plano, vt patet; ſed de motu in
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              planis inclinatis fusè agemus infrà libro integro. </s>
            </p>
            <p id="N17470" type="main">
              <s id="N17472">Quod ſpectat ad tertium experimentum; </s>
              <s id="N17476">multa in eo ſupponuntur
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              vel falſa, vel ſaltem dubia: vel ea quæ cum noſtra hypotheſi optimè con­
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              ueniant. </s>
              <s id="N1747E">Primum eſt, quando dicuntur omnes vibrationes eiuſdem fune­
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              penduli, ſiue maiores, ſiue minores eſſe æquediuturnæ, quod manifeſtis
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              experimentis repugnat; </s>
              <s id="N17486">quippe vibratio maior plùs temporis; </s>
              <s id="N1748A">minor ve­
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              rò minùs in ſuo deſcenſu ponit; </s>
              <s id="N17490">dimittantur enim duo funependula æ­
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              qualia; </s>
              <s id="N17496">alterum quidem ex altitudine 90.graduum, alterum ex altitudine </s>
            </p>
          </chap>
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