Fabri, Honoré, Tractatus physicus de motu locali, 1646

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          <chap id="N15AC3">
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            <p id="N168F9" type="main">
              <s id="N168FB">
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              Theorema
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              44.
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              </s>
            </p>
            <p id="N16907" type="main">
              <s id="N16909">
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              Hinc peteſt dici creſcere velocitatem quolibet inſtanti iuxta rationem ſpatij
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              quod illo inſtanti decurritur
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              ; </s>
              <s id="N16914">quod certè verum eſt, dum intelligatur legi­
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              timus horum verborum ſenſus; </s>
              <s id="N1691A">quidquid reclamet Saluiatus apud
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              Galil. dialogo 3. modò aſſumatur progreſſio incrementi in ſingulis in­
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              ſtantibus, in quibus reuerà fit; cur enim potiùs in vno quàm in alio? </s>
              <s id="N16924">
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              quippe ſi comparetur velocitas vnius inſtantis cum velocitate alterius; </s>
              <s id="N16929">
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              haud dubiè erit eadem vtriuſque ratio, quæ ſpatiorum; </s>
              <s id="N1692E">ſi enim vno in­
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              ſtanti percurritur vnum ſpatium cum vno velocitatis gradu; </s>
              <s id="N16934">certè in­
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              ſtanti æquali acquiritur duplum ſpatium cum duobus velocitatis gradi­
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              bus, nec obeſt, quod obiicit Galileus tunc motus eſſe æquabiles; </s>
              <s id="N1693C">quia
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              motus qui fit in inſtanti debet conſiderari vt æquabilis; </s>
              <s id="N16942">appello enim
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              inſtans totum illud tempus, quo ſimul acquiritur aliquid impetus, ali­
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              quid enim ſimul acquiri neceſſe eſt; </s>
              <s id="N1694A">nec demum obſtat quod dicit, dari
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              non poſſe motum inſtantaneum, quod multi haud dubiè negabunt; </s>
              <s id="N16950">ego
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              in Metaphyſica explicabo quonam pacto dari poſſit motus inſtanta­
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              neus, qui reuerà datur actu, non potentiâ; </s>
              <s id="N16958">quia quacunque duratione
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              data poteſt dari minor; igitur quocunque dato motu poteſt dari minor. </s>
            </p>
            <p id="N1695E" type="main">
              <s id="N16960">
                <emph type="center"/>
                <emph type="italics"/>
              Scholium.
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                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1696C" type="main">
              <s id="N1696E">Obſeruabis primò hanc ſpatiorum rationem, quæ eſt eadem cum ra­
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              tione velocitatum aſſumendam tantùm eſſe in iis ſpatiis, quæ acquirun­
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              tur ſingulis inſtantibus; </s>
              <s id="N16976">ſi enim accipiantur partes temporis maiores, quæ
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              conflentur ex multis inſtantibus; </s>
              <s id="N1697C">haud dubiè maior erit ratio ſpatio­
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              rum, quàm velocitatum.v.g.ſi primo inſtanti acquiratur primo ſpatium,
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              ſecundo, 2.tertio, 3.quarto 4.igitur ſi
                <expan abbr="cõparetur">comparetur</expan>
              velocitas primi inſtantis
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              cum velocitate quarti æqualis erit, vt ratio ſpatiorum, id eſt, vt 1. ad 4.
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              At verò ſi accipiatur pars temporis conſtans duobus inſtantibus, hæc 4.
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              inſtantia conflabunt tantùm 2. partes temporis æquales; </s>
              <s id="N1698E">in prima ac­
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              quirentur 3.ſpatia, in ſecunda 7.vt patet: </s>
              <s id="N16994">ſed quia velocitas primæ par­
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              tis temporis non eſt æquabilis, nec etiam velocitas ſecundæ; </s>
              <s id="N1699A">addantur
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              velocitates primi & ſecundi inſtantis, itemque ſeorſim velocitates tertij,
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              & quarti; </s>
              <s id="N169A2">certè ratio collectorum erit vt ratio ſpatiorum; ſi enim velo­
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              citas ſecundi inſtantis comparetur cum velocitate quarti eſt tantùm
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              1/2 cum tamen primum ſpatium ſit ad ſecundum in ratione 3/7. </s>
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            <p id="N169AA" type="main">
              <s id="N169AC">Secundò, ſi comparentur ſpatia cum temporibus eſt alia ratio v.g.ſpa­
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              tium acquiſitum vno inſtanti ſe habet ad ſpatium acquiſitum in duobus
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              inſtantibus, vt 1, ad 3.in tribus vt 1.ad 6.in 4. vt 1. ad 10. </s>
            </p>
            <p id="N169B3" type="main">
              <s id="N169B5">Tertiò obſeruabis, non poſſe ſenſu percipi inſtans, imò neque tempo­
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              ris partem ex mille inſtantibus conflatam; </s>
              <s id="N169BB">nec etiam ſpatium quod ac­
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              quiritur primo inſtanti; </s>
              <s id="N169C1">adhibenda ſunt tamen inſtantia neceſſariò ad
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              explicandam proportionem huius accelerationis, quæ fit in ſingulis in­
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              ſtantibus; vt verò rem iſtam reuocemus ad ſenſibilem praxim, aſſume­
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              mus proportionem aliam ſenſibilem, quæ proximè ad veram accedit, nec
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              ferè ſenſibiliter fallere poteſt, de qua infrà. </s>
            </p>
          </chap>
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