Fabri, Honoré, Tractatus physicus de motu locali, 1646

List of thumbnails

< >
251
251 		252
252
253
253 		254
254
255
255 		256
256
257
257 		258
258
259
259 		260
260
< >
page |< < of 491 > >|
    <archimedes>
      <text>
        <body>
          <chap id="N1C940">
            <p id="N1E0FE" type="main">
              <s id="N1E119">
                <pb pagenum="221" xlink:href="026/01/253.jpg"/>
              ſemper haberet ſuum effectum; </s>
              <s id="N1E122">igitur non eſſet fruſtrà; igitur per Schol.
                <lb/>
              Th.152.l.1. </s>
            </p>
            <p id="N1E129" type="main">
              <s id="N1E12B">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              60.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1E137" type="main">
              <s id="N1E139">
                <emph type="italics"/>
              Ille motus acceleratur per partes inæquales
                <emph.end type="italics"/>
              ; </s>
              <s id="N1E142">quia ſcilicet motus additus
                <lb/>
              in O minor eſſet quàm in N, & in G quàm in O per Th. 56. igitur per
                <lb/>
              partes inæquales acceleraretur, immò poteſt determinari proportio cre­
                <lb/>
              menti motus in ſingulis; </s>
              <s id="N1E14C">cum enim in O ſit vt YP, in QL. in Yvt T
                <foreign lang="grc">δ</foreign>
                <lb/>
              ad AC; certè creſcit in proportione ſinuum rectorum ad ſinum totum. </s>
            </p>
            <p id="N1E155" type="main">
              <s id="N1E157">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              61.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1E163" type="main">
              <s id="N1E165">
                <emph type="italics"/>
              Mobile deſcendens ex O in E tranſit per tot plana inclinata diuerſa, quot
                <lb/>
              ſunt puncta in tota EO vt conſtat, vel potiùs quot poſſunt duci Tangentes di­
                <lb/>
              uerſæ in toto arcu PE
                <emph.end type="italics"/>
              ; quippe Tangens puncti P eſſet parallela IG, idem
                <lb/>
              dico de omnibus aliis punctis arcus PE. </s>
            </p>
            <p id="N1E174" type="main">
              <s id="N1E176">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              62.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1E182" type="main">
              <s id="N1E184">
                <emph type="italics"/>
              Motus funependuli in quolibet puncto arcus, per quem deſcendit, eſt ad mo­
                <lb/>
              tum in perpendiculari, vt ſinus reſidui arcus ad ſemidiametrum
                <emph.end type="italics"/>
              ; </s>
              <s id="N1E18F">v.g. ſit fune­
                <lb/>
              pendulum AD in perpendiculari, quod vibrari poſſit circa punctum im­
                <lb/>
              mobile A, eleuetur in A
                <foreign lang="grc">β</foreign>
              , ducatur Tangens
                <foreign lang="grc">β</foreign>
              V motus funependiculi in
                <lb/>
              puncto
                <foreign lang="grc">β</foreign>
              ſcilicet initio, idem eſt, qui eſſet in plano inclinato
                <foreign lang="grc">β</foreign>
              V vt patet,
                <lb/>
              atqui motus in inclinato plano
                <foreign lang="grc">β</foreign>
              V eſt ad motum in
                <expan abbr="perpẽdiculari">perpendiculari</expan>
              vt
                <foreign lang="grc">α</foreign>
              V.
                <lb/>
              ad
                <foreign lang="grc">β</foreign>
              V, ſed
                <foreign lang="grc">α</foreign>
              V eſt ad
                <foreign lang="grc">β</foreign>
              V vt
                <foreign lang="grc">αβ</foreign>
              ad A
                <foreign lang="grc">β</foreign>
              , ſunt enim triangula proportionalia;
                <lb/>
              igitur motus initio ſcilicet in puncto arcus putà B eſt ad motum in per­
                <lb/>
              pendiculari etiam initio conſideratum, vt ſinus rectus reſidui arcus, putà
                <lb/>
                <foreign lang="grc">β</foreign>
              D ad ſemidiametrum, vel ſinum totum, id eſt
                <foreign lang="grc">α β</foreign>
              ad A
                <foreign lang="grc">β</foreign>
              , idem dico de
                <lb/>
              omnibus aliis punctis. </s>
            </p>
            <p id="N1E1E2" type="main">
              <s id="N1E1E4">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              63.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1E1F0" type="main">
              <s id="N1E1F2">
                <emph type="italics"/>
              Hinc proportio accelerationis motus in deſcenſu funependuli ſeu incremen­
                <lb/>
              ti in ſingulis punctis additi eſt in proportione huiuſmodi ſinuum minorum ſem­
                <lb/>
              per & minorum
                <emph.end type="italics"/>
              ; v.g. motus in puncto B eſt vt BA ſemidiameter in
                <foreign lang="grc">τ</foreign>
              vt
                <foreign lang="grc">τ</foreign>
                <lb/>
                <foreign lang="grc">μ</foreign>
              in
                <foreign lang="grc">β</foreign>
              vt
                <foreign lang="grc">β α</foreign>
              , id eſt licèt maior ſit motus in
                <foreign lang="grc">τ</foreign>
              quàm in B, cum ſcilicet
                <lb/>
              deſcendit ex B in
                <foreign lang="grc">τ</foreign>
              , vt illa portio crementi quæ in ipſo puncto
                <foreign lang="grc">τ</foreign>
              addi­
                <lb/>
              tur eſt ad primam in B vt
                <foreign lang="grc">τ μ</foreign>
              ad BA. </s>
            </p>
            <p id="N1E229" type="main">
              <s id="N1E22B">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              64.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1E237" type="main">
              <s id="N1E239">
                <emph type="italics"/>
              Hinc velocitas acquiſita in arcu BT eſt ad acquiſitam in arcu B
                <foreign lang="grc">β</foreign>
              , vt
                <lb/>
              omnes ſinus eiuſdem arcus B
                <foreign lang="grc">τ</foreign>
              ad omnes ſinus arcus B
                <foreign lang="grc">β</foreign>
              , & hæc ad acquiſi­
                <lb/>
              tum in toto quadrante BD, vt hi ad omnes ſinus quadrantis
                <emph.end type="italics"/>
              ; </s>
              <s id="N1E252">ſimiliter poteſt
                <lb/>
              comparari acquiſita tantùm in arcu BT, cum acquiſita in arcu
                <foreign lang="grc">τ β</foreign>
              vel
                <foreign lang="grc">β</foreign>
                <lb/>
              D, quod probatur; quia motus, qui reſpondet ſingulis punctis arcus initio
                <lb/>
              eſt in proportione ſinuum ſeu tranſuerſarum BA,
                <foreign lang="grc">τ μ, β α</foreign>
              , &c. </s>
              <s id="N1E267">igitur ſi
                <lb/>
              à ſingulis punctis arcus quadrantis in rectam lineam compoſiti duce­
                <lb/>
              rentur; </s>
              <s id="N1E26F">haùd dubiè prædictam aream quaſi occupabunt; igitur acquiſita
                <lb/>
              in vno puncto eſt ad acquiſitam in alio puncto vt linea tranſuerſa ad </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum