Fabri, Honoré, Tractatus physicus de motu locali, 1646

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            <p id="N17547" type="main">
              <s id="N17577">
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              1000000. quæ omnia ſunt inſenſibilia, neque maiorem habent diffi­
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              cultatem, quàm in motu perpendiculari, de quo ſuprà; etiam conceſſis
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              vltrò omnibus experimétis propoſitis. </s>
              <s id="N17584">Igitur ſuppoſitâ progreſſione ſpa­
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              tiorum arithmetica in inſtantibus, tàm propè accedit ad aliam, quàm
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              Galileus ponit, ſiue in perpendiculari deorſum, ſiue in quadrante fune­
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              penduli; </s>
              <s id="N1758E">aſſumptis ſcilicet partibus temporis ſenſibilibus, vt differentia
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              diſcernit non poſſit; </s>
              <s id="N17594">immò nec duplum differentiæ, nec centuplum, nec
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              millecuplum; </s>
              <s id="N1759A">ſed de his ſatis quæ ex dictis ſuprà facilè intelligi poſſunt:
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              quare veniemus iam ad rationes. </s>
            </p>
            <p id="N175A0" type="main">
              <s id="N175A2">Prima ratio, quam affert Galileus eſt; </s>
              <s id="N175A6">quia cum natura in ſuis opera­
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              tionibus adhibeat ſimpliciſſima media; </s>
              <s id="N175AC">& cum acceleratio motus natu­
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              ralis non poſſit fieri iuxta faciliorem, vel ſimpliciorem progreſſionem,
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              quàm ſit-ea quæ fit per quadrata; </s>
              <s id="N175B4">non eſt dubium, quin iuxta illam pro­
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              greſſio motus naturaliter accelerati fieri debeat; præſertim cùm omni­
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              bus experimentis conſentiat, & in ea omnia phænomena explicari
                <lb/>
              poſſint. </s>
            </p>
            <p id="N175BE" type="main">
              <s id="N175C0">Reſp. Primò progreſſionem arithmeticam ſimplicem iuxta hos nu­
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              meros 1.2.3.4. longè ſimpliciorem eſſe alia quæ fit iuxta illos 1.3.5.7.vt
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              nemo non iudicabit. </s>
              <s id="N175C7">Secundò
                <expan abbr="cũ">cum</expan>
              accidit duas hypotheſes conuenire cum
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              omnibus experimentis ſeu phænomonis, debet eſſe aliqua ratio, cur ad­
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              hibeatur vna potiùs quàm alia; </s>
              <s id="N175D3">ſed nulla eſt ratio, cur Galileus adhibeat
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              ſuam, vti videbimus; </s>
              <s id="N175D9">nos verò ratione demonſtratiuâ probamus noſtram; </s>
              <s id="N175DD">
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              igitur noſtra eſt præferenda pro theorica rei veritate; quia verò alia in
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              temporibus ſenſibilibus proximè ad verum accedit eam adhibendam eſſe
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              decernemus infrà ad praxim, & communem iſtorum motuum men­
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              ſuram. </s>
            </p>
            <p id="N175E8" type="main">
              <s id="N175EA">Secunda ratio eſt; </s>
              <s id="N175ED">quia, ſi accipiatur ſubduplum maximæ, & minimæ
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              velocitatis; ſitque ex his quaſi conflata velocitas motus æquabilis, hoc
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              motu æquabili æquali tempore pèrcurretur ſpatium idem, quod antè
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              motu naturaliter accelerato v.g. ſint numeri datæ progreſſionis 1.3.5.7.
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              9.11. certè ſumma terminorum ſeu totum ſpatium erit 36. accipiatur
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              ſubduplum primi 1/2 & ſexti 5. 1/2 habebitur velocitas vt 6. igitur cum
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              velocitate vt 6. æquali tempore percurretur ſpatium 36. quod rectè de­
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              monſtrauit Galileus. </s>
            </p>
            <p id="N17602" type="main">
              <s id="N17604">Reſpondeo non minùs noſtram hypotheſim cum hoc ipſo ſtare, quàm
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              ſtet hypotheſis Galilei: </s>
              <s id="N1760A">ſint enim 6. inſtantia, & ſingulis ſua tribuantur
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              ſpatiola more dicto 1 2 3 4 5 6. ſumma ſpatiorum eſt 21. aſſumatur ſub­
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              duplum velocitatis primi inſtantis 1/2, & ſubduplum ſexti inſtantis, ſcili­
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              cet 3. conflatum ex vtroque 3 1/3; </s>
              <s id="N17614">ducatur in 6.id eſt in numerum termi­
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              norum, vel inſtantium; ſumma erit 21. igitur quod tribuit Galileus ſuæ
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              progreſſioni, etiam noſtræ competit. </s>
            </p>
            <p id="N1761C" type="main">
              <s id="N1761E">Tertia ratio petitur ex matheſi ſit enim linea AE diuiſa in quatuor
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              partes æquales, quæ nobis repreſentent 4. partes temporis æquales; </s>
              <s id="N17624">
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              haud dubiè, cùm acquirantur temporibus æqualibus æqualia velocitatis
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              momenta; </s>
              <s id="N1762B">haud dubiè, inquam, his 4. temporibus AB, BC, CD, DE, ac-</s>
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