Fabri, Honoré, Tractatus physicus de motu locali, 1646

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    <archimedes>
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        <body>
          <chap id="N22A20">
            <p id="N233FB" type="main">
              <s id="N23413">
                <pb pagenum="307" xlink:href="026/01/341.jpg"/>
              AKC acquiritur æqualis acquiſitæ in AC; </s>
              <s id="N2341E">nam in AK, A
                <foreign lang="grc">ω</foreign>
              acquiritur
                <lb/>
              æqualis; </s>
              <s id="N23426">tùm etiam in KC,
                <foreign lang="grc">ω</foreign>
              C; Item in tribus acquiritur æqualis ac­
                <lb/>
              quiſitæ in duabus, atque ita deinceps. </s>
            </p>
            <p id="N23430" type="main">
              <s id="N23432">Præterea velocitas acquiſita in chordis mediis.v.g. </s>
              <s id="N23435">in chorda LI eſt
                <lb/>
              æqualis acquiſitæ in LZ, vel RT, vel in ſinu toto AB, minùs ſinu verſo
                <lb/>
              arcus LA, & ſinu recto arcus IC; ſed hæc ſunt ſatis facilia. </s>
            </p>
            <p id="N2343D" type="main">
              <s id="N2343F">Idem dico de chordis arcus quadrantis funependuli AEB figura Lem­
                <lb/>
              ma.4. v. g. de chorda IB, in qua velocitas acquiſita eſt æqualis acqui­
                <lb/>
              ſitæ in RB, vel in duabus ILB, vel in tribus 4. 5. atque ita deinceps:
                <lb/>
              hinc etiam vides in quadrante EB acquiri æqualem velocitatem, ſiue
                <lb/>
              EA ſit perpendicularis deorſum, ſiue AB. </s>
            </p>
            <p id="N23450" type="main">
              <s id="N23452">
                <emph type="center"/>
                <emph type="italics"/>
              Lemma
                <emph.end type="italics"/>
              14.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N2345E" type="main">
              <s id="N23460">
                <emph type="italics"/>
              Citiùs deſcendet corpus per duas EIB, quàm per IB
                <emph.end type="italics"/>
              ; </s>
              <s id="N23469">quia deſcenſus eſt
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              æquè diuturnus per EB, & IB; ſed citiùs deſcendit per EIB, quàm per
                <lb/>
              EB, vt iam ſuprà dictum eſt in Lem. 8. igitur citiùs per EIB, quàm
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              per IB. </s>
            </p>
            <p id="N23475" type="main">
              <s id="N23477">
                <emph type="center"/>
                <emph type="italics"/>
              Lemma
                <emph.end type="italics"/>
              15.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N23483" type="main">
              <s id="N23485">
                <emph type="italics"/>
              Citiùs deſcendet per
                <emph.end type="italics"/>
                <emph type="italics"/>
              duas chordas BHF, quàm per duas BGF, à quiete
                <emph.end type="italics"/>
                <lb/>
              B; </s>
              <s id="N23495">ſint enim duæ BHF, ſitque BH. v.g. chorda arcus 30.grad.ſc.5 1764.
                <lb/>
              earum partium, quarum ſinus totus eſt 100000. ſit Tangens BE; </s>
              <s id="N2349D">ſit HD
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              perpendicularis in BH, & HT in BD; </s>
              <s id="N234A3">certè HT eſt media proportio­
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              nalis inter DT, & TB; </s>
              <s id="N234A9">eſtque differentia ſinus totius, & ſinus OH 60.
                <lb/>
              grad. eſt autem OH 86603. igitur HT 13397. quadretur HT, produ­
                <lb/>
              ctum diuidatur per BT 50000. quotiens dabit TD 3589. quæ ſi adda­
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              tur BT, habebitur tota BD 53589. quadretur BD; </s>
              <s id="N234B5">aſſumatur ſubduplum
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              quadrati, ex quo extrahatur radix; </s>
              <s id="N234BB">habebitur KD, vel BK 37893. ſit
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              autem LF 200000. ad 141422. æqualem BF, ita BF ad LH 100000.
                <lb/>
              certè tempus per LH eſt ad tempus per BH, vt LH ad BH; </s>
              <s id="N234C3">ſed tempus
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              per LH eſt ad tempus per LF, vt LH ad 141422.igitur tempus per BH
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              eſt ad tempus per HF facto initio motus ex L, vt BH 51764. ad 41422.
                <lb/>
              igitur ad tempus per BHF, vt 51764.ad 93186. porrò BH & BK æqua­
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              li tempore percurruntur; </s>
              <s id="N234CF">igitur tempus per BK eſt BH, id eſt 51764.
                <lb/>
              cùm autem ſpatia in eadem linea ſint in ratione duplicata temporum;
                <lb/>
              certè ſpatium BK acquiſitum tempore 51764.eſt ad ſpatium acquiſitum
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              in BF tempore 93186. vt quadratum 51764. ad quadratum 93186.id eſt,
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              vt 2679511696.ad 8676630576.vnde factâ regulâ trium habeo ſpatium
                <lb/>
              decurſum in BF 122702. tempore 93186. ſed tota BF eſt 141422. igitur
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              citiùs percurruntur duæ BHF, quàm BF. </s>
            </p>
            <p id="N234DF" type="main">
              <s id="N234E1">Præterea ſint duæ BGF, BG eſt 100000.ſit perpendicularis G 4 cùm
                <lb/>
              angulus GB 4.ſit grad.30. erit vt 5 G ad GB, ita BG ad B 4. igitur B 4.
                <lb/>
              erit 115469. ſit 4.3.perpendicularis in BF, quadratum B 4. eſt duplum
                <lb/>
              quadrati B 3.igitur B 3. erit 81655. iam verò FN eſt ſecans grad.75. ſci­
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              licet 386370.igitur GN eſt 334606. detracta ſcilicet FG æquali BH; </s>
              <s id="N234ED">ſit
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              autem NG ad 359557. vt hæc ad NF; </s>
              <s id="N234F3">certè tempus per BG eſt ad tem-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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