Fabri, Honoré, Tractatus physicus de motu locali, 1646

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    <archimedes>
      <text>
        <body>
          <chap id="N22A20">
            <pb pagenum="304" xlink:href="026/01/338.jpg"/>
            <p id="N230B0" type="main">
              <s id="N230B2">
                <emph type="center"/>
                <emph type="italics"/>
              Lemma
                <emph.end type="italics"/>
              7.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N230BE" type="main">
              <s id="N230C0">
                <emph type="italics"/>
              Cognito tempore, quo percurritur chorda cuiuſlibet arcus, cognoſci poteſt
                <lb/>
              quantum ſpaty eodem tempore percurratur in
                <expan abbr="perpẽdiculari">perpendiculari</expan>
              & in alia chorda
                <emph.end type="italics"/>
              ; </s>
              <s id="N230CF">
                <lb/>
              ſit chorda EL; </s>
              <s id="N230D4">fiat angulus rectus ELM, itemque MDE: </s>
              <s id="N230D8">dico quod
                <lb/>
              eodem tempore percurretur EL EM ED; </s>
              <s id="N230DE">ſimiliter fiat angulus re­
                <lb/>
              ctus EIH, itemque HKE, HQE: dico quod eodem tempore percur­
                <lb/>
              rentur EI, EH, EK,EQ. idem dico de omnibus aliis chordis, quæ
                <lb/>
              omnia conſtant ex his quæ diximus lib.2. & 5. </s>
            </p>
            <p id="N230ED" type="main">
              <s id="N230EF">
                <emph type="center"/>
                <emph type="italics"/>
              Lemma
                <emph.end type="italics"/>
              8.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N230FB" type="main">
              <s id="N230FD">
                <emph type="italics"/>
              Due chorda ELB citiùs percurruntur quàm ſola EB; </s>
              <s id="N23103">itemque due EIB,
                <lb/>
              quàm EB
                <emph.end type="italics"/>
              ; </s>
              <s id="N2310C">quia eodem tempore percurruntur EI,
                <expan abbr="Eq;">Eque</expan>
              & IB eodem
                <lb/>
              tempore percurritur ſiue à G incipiat motus ſiue ab E; </s>
              <s id="N23116">nam ab æquali
                <lb/>
              altitudine æqualis acquiritur impetus, ſed minor eſt proportio EQ ad
                <lb/>
              EB, quam GI ad GB per Lemma quintum; </s>
              <s id="N2311E">igitur ſi ſit media propor­
                <lb/>
              tionalis inter GI, GB, & ſecunda inter EQEB, ſitque vt GI ad pri­
                <lb/>
              mam proportionalem; </s>
              <s id="N23126">ita tempus, quo percurritur EI ad aliud X, & vt
                <lb/>
              EQ ad ſecundam proportionalem, ita idem tempus, quo percurritur EI,
                <lb/>
              vel EQ ad aliud Z; </s>
              <s id="N2312E">certè tempus Z eſt maius tempore X per Lemma
                <lb/>
              4. ſed EQB percurritur tempore Z, & EIB tempore X; </s>
              <s id="N23134">EQ verò, &
                <lb/>
              EI tempore æquali per Lemma 7. igitur duæ EIB citiùs percurruntur,
                <lb/>
              quàm EB; </s>
              <s id="N2313C">idem dico de aliis: hoc ipſum etiam demonſtrauit Galil. in
                <lb/>
              dialogis. </s>
            </p>
            <p id="N23144" type="main">
              <s id="N23146">
                <emph type="center"/>
                <emph type="italics"/>
              Lemma
                <emph.end type="italics"/>
              9.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N23152" type="main">
              <s id="N23154">
                <emph type="italics"/>
              Tres chordæ faciliùs percurruntur, quàm duæ
                <emph.end type="italics"/>
              ; </s>
              <s id="N2315D">ſint enim tres EILB; </s>
              <s id="N23161">
                <lb/>
              ſint duæ ELB. Primò, duæ EIL citiùs percurruntur quàm EL, quia
                <lb/>
              IL eodem tempore percurritur, ſiue initium motus ducatur ab F, ſiue ab
                <lb/>
              E; </s>
              <s id="N2316A">& minor eſt ratio EK ad EL, quàm FI ad FL per Lem.5.EI, & EK
                <lb/>
              æquè citò percurruntur per Lem. 7. igitur ſit vt FI ad mediam propor­
                <lb/>
              tionalem inter FI & FL; </s>
              <s id="N23174">ita tempus Z ad tempus X, & vt EK ad me­
                <lb/>
              diam proportionalem inter EK EL, ita tempus Z ad tempus Y; </s>
              <s id="N2317A">certè
                <lb/>
              tempus Y erit maius tempore X per Lem. 8. igitur citiùs percurrentur
                <lb/>
              duæ EIL, quàm EL; </s>
              <s id="N23184">ſed ſi eodem tempore percurrerentur duæ EIL
                <lb/>
              cum EL; </s>
              <s id="N2318A">certè LB æquali tempore percurreretur, quia eſt idem impetus
                <lb/>
              in L, ſiue ab E per EL, ſiue ab F per FL incipiat motus, vt conſtat, & eſt
                <lb/>
              idem in I, ſiue ab E, ſiue ab F incipiat; </s>
              <s id="N23192">igitur idem in L ſiue ab E per
                <lb/>
              EIL, ſiue ab F per FL, ſiue ab E per EL; </s>
              <s id="N23198">igitur LB æquali tempore
                <lb/>
              percurretur, ſiue motus ſit ab E per ELB, ſiue ab E per EI, LB, poſito
                <lb/>
              quòd EIL & EL æquali tempore percurrantur; </s>
              <s id="N231A0">ſed EIL percurrun­
                <lb/>
              tur citiùs quàm EL; </s>
              <s id="N231A6">igitur citiùs EILB, quàm ELB; </s>
              <s id="N231AA">igitur cùm ELB
                <lb/>
              percurrantur citiùs, quàm EB, & EILB, quàm ELB; </s>
              <s id="N231B0">certè EILB per­
                <lb/>
              curruntur citiùs, quàm EB: Eodem modo demonſtrabitur 4. chordas ci­
                <lb/>
              tiùs percurri, quàm 3. 5. quàm 4. atque ita deinceps. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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