Fabri, Honoré, Tractatus physicus de motu locali, 1646

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      <text>
        <body>
          <chap id="N24CC8">
            <p id="N24E81" type="main">
              <s id="N24EA6">
                <pb pagenum="336" xlink:href="026/01/370.jpg"/>
              in I; </s>
              <s id="N24EAF">nec enim deſcendet infra MI, vt conſtat: </s>
              <s id="N24EB3">ſic motus orbis dat LK,
                <lb/>
              vel MK motus centri L
                <foreign lang="grc">μ</foreign>
              vel KI; </s>
              <s id="N24EBD">igitur vterque ſimul LI vel KI: </s>
              <s id="N24EC1">ſi­
                <lb/>
              militer decurſo arcu KH, punctum rotæ L erit in G; </s>
              <s id="N24EC7">nam motus orbis
                <lb/>
              dat LH, vel NH, vel motus centri AC vel LV; igitur ſi aſſumatur HG
                <lb/>
              æqualis LV, vterque motus dabit LIG. </s>
            </p>
            <p id="N24ECF" type="main">
              <s id="N24ED1">
                <emph type="center"/>
                <emph type="italics"/>
              Corollarium
                <emph.end type="italics"/>
              1.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N24EDE" type="main">
              <s id="N24EE0">Hinc colligo, deſcriptionem lineæ, quam ſuo motu ſeu flux^u deſcri­
                <lb/>
              bit punctum L, cuius infinita puncta aſſignari poſſunt, ſi enim diuidatur
                <lb/>
              planum æquale arcui LQ in tot partes, in quot diuiditur arcus LQ, &
                <lb/>
              cuilibet ſinui recto arcus aſſumpti addatur ſegmentum plani conſtans
                <lb/>
              tot partibus, quot partibus arcus aliis arcubus v.g.ſinui MK, KI æqua­
                <lb/>
              lis L
                <foreign lang="grc">μ</foreign>
              , ſinui NH, LV, denique ſinui toti OQ tota LY, habebuntur ſin­
                <lb/>
              gula puncta huius lineæ L, I, G, F quam rotatilem appellamus; quæ certè
                <lb/>
              eò acuratiùs deſcribetur, quò plura eius puncta ſignabuntur, id eſt quò
                <lb/>
              diuidetur arcus LQ in plures arcus, & planum LV in plures partes. </s>
            </p>
            <p id="N24EFA" type="main">
              <s id="N24EFC">
                <emph type="center"/>
                <emph type="italics"/>
              Corollarium
                <emph.end type="italics"/>
              2.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N24F09" type="main">
              <s id="N24F0B">Linea quoque rotatilis puncti A deſcribi poteſt diuiſo arcu AZ in
                <lb/>
              tres arcus, & plano AD in 3. pattes; </s>
              <s id="N24F11">ſint enim ſinus TX, Y
                <foreign lang="grc">π</foreign>
              ſitque TS
                <lb/>
              æqualis AB, YR æqualis AG, & ZP æqualis AD; </s>
              <s id="N24F1B">certè deſcribetur hæc
                <lb/>
              linea per puncta ASRP à quo plura puncta ſignabuntur, eò accuratiùs
                <lb/>
              deſcribetur, quæ omnia conſtant ex dictis; </s>
              <s id="N24F23">nam motus orbis dat AT vel
                <lb/>
              XT motus centri AB; igitur TS. </s>
            </p>
            <p id="N24F29" type="main">
              <s id="N24F2B">
                <emph type="center"/>
                <emph type="italics"/>
              Corollarium
                <emph.end type="italics"/>
              3.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N24F38" type="main">
              <s id="N24F3A">Hinc vides punctum L oppoſitum puncto contactus ita moueri, vt
                <lb/>
              motus orbis addatur motui centri; punctum verò A ita mouetur, vt mo­
                <lb/>
              tus orbis detrahatur motui centri. </s>
            </p>
            <p id="N24F42" type="main">
              <s id="N24F44">
                <emph type="center"/>
                <emph type="italics"/>
              Corollarium
                <emph.end type="italics"/>
              4.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N24F51" type="main">
              <s id="N24F53">Hinc etiam deſcribi poteſt linea, quam deſcribit quodlibet punctum
                <lb/>
              interioris circuli v.g. punctum E; </s>
              <s id="N24F5B">deſcribatur enim arcus quadrátis & 2.
                <lb/>
              diuidatur in 3. arcus æquales, ducanturque per puncta ſignata 3.4. rectæ
                <lb/>
              parallelæ OE, aſſumatur 3. 5. æqualis L
                <foreign lang="grc">μ</foreign>
              & 4, 6, æqualis LV; denique
                <lb/>
              2.7. æqualis LV,
                <expan abbr="connectanturq́ue">connectanturque</expan>
              puncta ſignata per lineam nouam, E
                <lb/>
              5.6.7. hæc eſt linea quam deſcribit ſuo motu mixto punctum C, quæ
                <lb/>
              conſtat ex dictis. </s>
            </p>
            <p id="N24F71" type="main">
              <s id="N24F73">
                <emph type="center"/>
                <emph type="italics"/>
              Corollarium
                <emph.end type="italics"/>
              5.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N24F80" type="main">
              <s id="N24F82">Aliter deſcribi poteſt hæc linea rotatilis; </s>
              <s id="N24F86">ſit enim AD diuiſa v.g. in
                <lb/>
              tres partes æquales,
                <expan abbr="itemq́ue">itemque</expan>
              OE ex punctis
                <foreign lang="grc">ρ</foreign>
              Q, deſcribantur circuli
                <lb/>
              æquales rotæ,
                <expan abbr="aſſumanturq́ue">aſſumanturque</expan>
              arcus BS æqualis LK & arcus CR æqua­
                <lb/>
              lis LK, & habebis puncta SR: </s>
              <s id="N24F9E">ſimiliter aſſumatur arcus
                <foreign lang="grc">μ</foreign>
              I æqualis LK
                <lb/>
              & alter V.G. æqualis LH, & habebis puncta IG, idem fiet pro aliis pun­
                <lb/>
              ctis; hinc vides rotatiles deſcribi poſſe per ſinus, & per arcus. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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