Fabri, Honoré, Tractatus physicus de motu locali, 1646

List of thumbnails

< >
81
81 		82
82
83
83 		84
84
85
85 		86
86
87
87 		88
88
89
89 		90
90
< >
page |< < of 491 > >|
    <archimedes>
      <text>
        <body>
          <chap id="N1137F">
            <pb pagenum="52" xlink:href="026/01/084.jpg"/>
            <p id="N145C3" type="main">
              <s id="N145C5">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              93.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N145D1" type="main">
              <s id="N145D3">
                <emph type="italics"/>
              Impetus propagatur eodem inſtanti, id eſt, ſine temporis ſucceſſione.
                <emph.end type="italics"/>
              </s>
              <s id="N145DA"> Proba­
                <lb/>
              tur; </s>
              <s id="N145DF">ſit enim applicata potentia in A, dico ſimul produci impetum in
                <lb/>
              BCDE; </s>
              <s id="N145E5">quia ſi primo inſtanti produceretur in A, & ſecundo in B, vel
                <lb/>
              A moueretur ante B, vel impetus in A eſſet fruſtrà; </s>
              <s id="N145EB">vtrumque eſt abſur­
                <lb/>
              dum; nam totum AE, ſimul mouetur. </s>
            </p>
            <p id="N145F1" type="main">
              <s id="N145F3">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              94.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N145FF" type="main">
              <s id="N14601">
                <emph type="italics"/>
              Tribus tantùm modis propagari poteſt impetus ratione intenſionis.
                <emph.end type="italics"/>
              </s>
              <s id="N14608"> Primò
                <lb/>
              ſi æqualiter omnibus partibus ſubjecti diſtribuatur; id eſt vniformiter. </s>
              <s id="N1460E">
                <lb/>
              Secundò, ſi plùs partibus propioribus, & minùs remotioribus. </s>
              <s id="N14612">Tertiò, è
                <lb/>
              contra, ſi plùs remotioribus, & minùs propioribus; </s>
              <s id="N14618">tribus etiam ratione
                <lb/>
              perfectionis eo modo, quo diximus de intenſione; </s>
              <s id="N1461E">at verò nouem mo­
                <lb/>
              dis propagari poteſt ratione vtriuſque; patet ex regula combinationum; </s>
              <s id="N14624">
                <lb/>
              ſi enim 3. ducantur in 3. habebis 9. Iam ſupereſt, vt videamus, an reue­
                <lb/>
              rà omnibus iſtis modis impetus re ipſa propagetur; </s>
              <s id="N1462B">quod licèt difficile
                <lb/>
              ſit, & vix hactenus explicatum: Audeo tamen polliceri meum ſuper hac
                <lb/>
              re conatum non prorſus inutilem fore. </s>
            </p>
            <p id="N14633" type="main">
              <s id="N14635">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              95.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N14641" type="main">
              <s id="N14643">
                <emph type="italics"/>
              Impetus propagatur vniformiter in mobili, cuius omnes partes mouentur
                <lb/>
              æquali motu
                <emph.end type="italics"/>
              ; </s>
              <s id="N1464E">probatur, quia impetus non cognoſcitur niſi per motum;
                <lb/>
              igitur vbi eſt æqualis motus, debet eſſe æqualis impetus in omnibus par­
                <lb/>
              tibus, id eſt æqualis graduum heterogeneorum collectio, in quo non
                <lb/>
              eſt difficultas. </s>
            </p>
            <p id="N14658" type="main">
              <s id="N1465A">
                <emph type="center"/>
                <emph type="italics"/>
              Scholium.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N14666" type="main">
              <s id="N14668">Obſeruabis illud mobile moueri motu æquali ſecundum omnes ſui
                <lb/>
              partes, quod mouetur motu recto; quippe fieri non poteſt, quin omnes
                <lb/>
              partes, quæ mouentur motu recto ſimplici, motu etiam æquali mouean­
                <lb/>
              tur. </s>
            </p>
            <p id="N14672" type="main">
              <s id="N14674">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              96.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N14680" type="main">
              <s id="N14682">
                <emph type="italics"/>
              Cum duo corpora ſeſe mutuò tangunt, impetus in vtroque propagatur
                <emph.end type="italics"/>
              ſint
                <lb/>
              v. g. globi A & B, æquales ſibi inuicem contigui in C, ſit applicata po­
                <lb/>
              tentia in D, non modò producet impetum in globo A, ſed etiam in B: </s>
              <s id="N14693">
                <lb/>
              probatur primò, quia ſe habent per modum vnius, vt patet ex reſiſten­
                <lb/>
              tia, nec enim A moueri poteſt ſine B per lineam DE, quod certè cla­
                <lb/>
              riſſimum eſt; probatur ſecundò quia ſi A produceret impetum in B, duo
                <lb/>
              globi, vel 3. vel 5. vel infiniti tantùm reſiſterent, quantùm vnicus glo­
                <lb/>
              bus, quod falſum & abſurdum eſt. </s>
              <s id="N146A0">Tertiò, Ratio à priori eſt; </s>
              <s id="N146A4">quia ideo
                <lb/>
              producitur, & propagatur impetus in toto A; </s>
              <s id="N146AA">quia vna pars non poteſt
                <lb/>
              moueri ſine alia per Th. 33. ſed non poteſt A moueri niſi moueatur B;
                <lb/>
              igitur in vtroque ſimul, & æqualiter propagatur impetus. </s>
            </p>
            <p id="N146B2" type="main">
              <s id="N146B4">
                <emph type="center"/>
                <emph type="italics"/>
              Corollarium
                <emph.end type="italics"/>
              1.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N146C1" type="main">
              <s id="N146C3">Hinc ratio manifeſta cur maior ſit reſiſtentia duorum quàm vnius. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum