Fabri, Honoré, Tractatus physicus de motu locali, 1646

List of thumbnails

< >
191
191 		192
192
193
193 		194
194
195
195 		196
196
197
197 		198
198
199
199 		200
200
< >
page |< < of 491 > >|
    <archimedes>
      <text>
        <body>
          <chap id="N1A407">
            <p id="N1B1A8" type="main">
              <s id="N1B1AA">
                <pb pagenum="167" xlink:href="026/01/199.jpg"/>
                <emph type="italics"/>
              portione arithmetica ſimplici
                <emph.end type="italics"/>
              ; </s>
              <s id="N1B1BD">ſit enim verticalis, AG horizontalis AN,
                <lb/>
              linea projectionis AD; </s>
              <s id="N1B1C3">ſitque primum ſegmentum AD, quod ſcilicet
                <lb/>
              percurritur eo tempore quo in perpendiculari deorſum percurritur DF,
                <lb/>
              id eſt, v.g. ſexta eius pars, ducatur AFG, ſitque FG 5. partium, quarum
                <lb/>
              ſcilicet AD eſt 6. aſſumatur GH æqualis DF, ducaturque FHI; </s>
              <s id="N1B1CF">ſitque
                <lb/>
              HI 4. partium, aſſumatur IP æqualis GH, ducaturque HP; </s>
              <s id="N1B1D5">accipiatur
                <lb/>
              PK 3. partium; </s>
              <s id="N1B1DB">iam motus naturalis acceleratur eo modo quo ſuprà di­
                <lb/>
              ctum eſt iuxta rationem inclinationis deorſum; </s>
              <s id="N1B1E1">itaque aſſumatur KL
                <lb/>
              paulo maior IP; ſimiliter ducatur PLM, ſitque LM duarum partium,
                <lb/>
              & MN paulò maior KL, tum ſit LNO, ſitque NO 1. partis, & OB ma­
                <lb/>
              ior MN, & ducatur curua per puncta A.F.H.P.L.N.B. & habebis
                <lb/>
              intentum. </s>
            </p>
            <p id="N1B1ED" type="main">
              <s id="N1B1EF">Porrò hæc linea non eſt parabolica, vt conſtat ex Geometria & plura
                <lb/>
              puncta habebis ſi minora ſpatiola aſſumas; ſuppono enim DF eſſe tan­
                <lb/>
              tùm id ſpatij quod primo inſtanti in perpendiculari deorſum à corpore
                <lb/>
              graui percurritur. </s>
            </p>
            <p id="N1B1F9" type="main">
              <s id="N1B1FB">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              56.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1B207" type="main">
              <s id="N1B209">
                <emph type="italics"/>
              Aliter hæc linea poteſt deſcribi ſuppoſita retardatione per numeros impa­
                <lb/>
              res; vt habes in fig.
                <emph.end type="italics"/>
              46.T.1. in qua AC eſt verticalis, AB horizontalis,
                <lb/>
              AD inclinata 9. partium, FG 7. HI 5. reliqua vt ſuprà dictum eſt. </s>
            </p>
            <p id="N1B216" type="main">
              <s id="N1B218">Si verò linea inclinata recedat longiùs ab horizontali, & accedat pro­
                <lb/>
              piùs ad verticalem; vt habeantur puncta, transferantur eadem ſpatia, &
                <lb/>
              habebis puncta, per quæ deſcribes prædictam lineam. </s>
            </p>
            <p id="N1B220" type="main">
              <s id="N1B222">Denique ſi inclinata accedat propiùs ad horizontalem, transferantur
                <lb/>
              ſimiliter ſpatia vnius in alteram. </s>
            </p>
            <p id="N1B227" type="main">
              <s id="N1B229">Obſeruabis autem crementa deſcenſus in GH. IB eſſe iuxta nume­
                <lb/>
              ros impares 1.3.5.7.&c. </s>
              <s id="N1B22E">quandoquidem aſſumitur ſpatium quod confi­
                <lb/>
              citur in tempore ſenſibili, habita tamen ſemper ratione accelerationis,
                <lb/>
              quæ fit in plano inclinato, vnde creſcit ſemper proportio acceleratio­
                <lb/>
              nis, vt ſuprà demonſtrauimus; quæ certè proportionum inæqualitas ef­
                <lb/>
              ficit, ne poſſint accuratè deſcribi prædictæ lineæ, ſed tantùm rudi Miner­
                <lb/>
              uâ, cum ſingulis inſtantibus mutetur proportio accelerationis. </s>
            </p>
            <p id="N1B23C" type="main">
              <s id="N1B23E">
                <emph type="center"/>
                <emph type="italics"/>
              Scholium.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1B24A" type="main">
              <s id="N1B24C">Obſeruabis nondum eſſe à nobis determinatam proportionem illam,
                <lb/>
              in qua deſtruitur impetus violentus in motu mixto, quæ tamen ex dictis
                <lb/>
              ſuprà poteſt colligi; quippe deſtruitur pro rata, ideſt qua proportione
                <lb/>
              linea motus mixti eſt minor linea compoſita ex vtroque, ſit ergo. </s>
            </p>
            <p id="N1B256" type="main">
              <s id="N1B258">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              57.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1B264" type="main">
              <s id="N1B266">
                <emph type="italics"/>
              Impetus violentus ſolus deſtruitur in arcu aſcenſus
                <emph.end type="italics"/>
              ; </s>
              <s id="N1B26F">probatur, quia natu­
                <lb/>
              ralis non creſcit, vt patet; conſtat enim arcus aſcenſus ex naturali æqua­
                <lb/>
              bili, ſed aliquis impetus decreſcit, vt conſtat ex dictis, igitur ſolus
                <lb/>
              violentus. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum