Fabri, Honoré, Tractatus physicus de motu locali, 1646

Table of figures

< >
< >
page |< < of 491 > >|
    <archimedes>
      <text>
        <body>
          <chap id="N22A20">
            <p id="N24655" type="main">
              <s id="N2465F">
                <pb pagenum="327" xlink:href="026/01/361.jpg"/>
              ponit; </s>
              <s id="N24668">atqui ſuprà demonſtrauimus aſcenſum minorem eſſe deſcenſu, non
                <lb/>
              tantùm propter reſiſtentiam aëris, vt vult ipſe Galileus; ſed propter prin­
                <lb/>
              cipium intrinſecum deſtructiuum impetus acquiſiti in deſcenſu, de quo
                <lb/>
              ſuprà. </s>
            </p>
            <p id="N24672" type="main">
              <s id="N24674">
                <emph type="center"/>
                <emph type="italics"/>
              Corollarium
                <emph.end type="italics"/>
              5.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N24681" type="main">
              <s id="N24683">Quintò equidem, ſi AG demittatur ex AR, affixo clauo in P, non
                <lb/>
              modò ſegmentum PG aſcendet in PR, verùm etiam altiùs aſcendet ver­
                <lb/>
              ſus A; immò gyri plures erunt, ſi clauus affigatur propiùs ad punctum
                <lb/>
              G, qui certè gyri quò minores erunt, eò citiùs conficientur. </s>
            </p>
            <p id="N2468D" type="main">
              <s id="N2468F">
                <emph type="center"/>
                <emph type="italics"/>
              Corollarium
                <emph.end type="italics"/>
              6.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N2469C" type="main">
              <s id="N2469E">Poteſt determinari numerus iſtorum gyrorum; </s>
              <s id="N246A2">ſit enim primò clauus
                <lb/>
              in P, ſint que APG æquales; </s>
              <s id="N246A8">ſi AG poſt deſcenſum KG aſcenderet in
                <lb/>
              AD; </s>
              <s id="N246AE">certè ſegmentum PG aſcenderet per ſemicircumferentiam GR
                <lb/>
              A, in PA, ratio eſt, quia pendulum G deſcendent ex K; </s>
              <s id="N246B4">ſed ex hypotheſi
                <lb/>
              Galilei ſi deſcenderet ex Y aſcenderet in R; </s>
              <s id="N246BA">igitur cùm aſcendet cum illo
                <lb/>
              impetu acquiſito in deſcenſu KG, aſcenderet in D ex hypotheſi Galilei;
                <lb/>
              ſed arcus GD eſt æqualis GRA. </s>
            </p>
            <p id="N246C2" type="main">
              <s id="N246C4">Obſeruabis primò iuxta noſtram hypotheſim, qua diximus pendulum
                <lb/>
              AG poſt deſcenſum per KG non aſcendere in D, vix poſſe cognoſci
                <lb/>
              affixo clauo, ad quod punctum circuli GRA ex G pendulum peruentu­
                <lb/>
              rum ſit; </s>
              <s id="N246CE">ſi enim per GD aſcendat in F, & aſſumatur AZ æqualis DF, non
                <lb/>
              deeſſent fortè, qui exiſtimarent arcum aſcenſus per GRA eſſe GRZ
                <lb/>
              æqualem GF; </s>
              <s id="N246D6">ſed plùs impetus deſtruitur in arcu GRZ, quàm in arcu
                <lb/>
              GF, vt patet ex dictis; </s>
              <s id="N246DC">nam nullum eſt punctum in arcu GF, in quo plùs
                <lb/>
              impetus deſtruatur, quàm in alio dato arcus GRZ; </s>
              <s id="N246E2">cùm tamen ſint ali­
                <lb/>
              qua puncta in arcu GRZ, in quibus plùs impetus deſtruitur, quàm in
                <lb/>
              arcu GF, v.g. in puncto R; </s>
              <s id="N246EC">itaque ducatur FD parallela AD: </s>
              <s id="N246F0">dico quòd
                <lb/>
              perueniet pendulum in
                <foreign lang="grc">δ</foreign>
              ; </s>
              <s id="N246FA">quippe cum eodem impetu ad
                <expan abbr="eãdem">eandem</expan>
              altitu­
                <lb/>
              dinem aſcenditur; quæ omnia certa ſunt. </s>
            </p>
            <p id="N24704" type="main">
              <s id="N24706">Obſeruabis ſecundò, ſi affigatur clauus in
                <foreign lang="grc">θ</foreign>
              , ſintque P
                <foreign lang="grc">θ</foreign>
              G æquales, ex
                <lb/>
              hypotheſi Galilei; </s>
              <s id="N24714">pendulum G primò ex G perueniet in P, cum eo ſcili­
                <lb/>
              cet impetu, quo perueniet in T; </s>
              <s id="N2471A">tùm deinde ex P per
                <foreign lang="grc">β</foreign>
              redit in G aucto
                <lb/>
              ſcilicet impetu in deſcenſu P
                <foreign lang="grc">β</foreign>
              G, & ex G iterum aſcendit in P; atque ita
                <lb/>
              deinceps; quippe gyri perennes eſſent, niſi tandem totum filum circa
                <lb/>
              clauum conuolueretur. </s>
            </p>
            <p id="N2472C" type="main">
              <s id="N2472E">Obſeruabis præterea, aliquid ſimile contingere, cum pondus filo pen­
                <lb/>
              dulum in gyros, agimus circa mobilem digitum, v.g. quippe vltimi gyri
                <lb/>
              citiùs abſoluuntur; </s>
              <s id="N24738">quia ſcilicet breuiores ſunt, ſed hæc ſunt facilia; </s>
              <s id="N2473C">ob­
                <lb/>
              ſeruabis tamen cum voluitur filum illud circa digitum pendulum, non
                <lb/>
              moueri motu circulari, ſed ſpirali; vnde cùm motus mixtus ſit, in librum
                <lb/>
              ſequentem reiicimus. </s>
            </p>
            <p id="N24746" type="main">
              <s id="N24748">Obſeruabis deinde, cum pendulum AG deſcendit ex V in G, & prop­
                <lb/>
              ter clauum, à quo retinetur, filum aſcendit in R, aſcenſum GR ferri bre­
                <lb/>
              uiore tempore, quàm aſcenſum GT; </s>
              <s id="N24750">quia aſcenſus GT & GD æquali ſe-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum