Fabri, Honoré, Tractatus physicus de motu locali, 1646

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          <chap id="N24CC8">
            <p id="N25C35" type="main">
              <s id="N25C80">
                <pb pagenum="351" xlink:href="026/01/385.jpg"/>
              BE eſt æqualis
                <foreign lang="grc">δ</foreign>
              B; </s>
              <s id="N25C8D">ſed
                <foreign lang="grc">δ</foreign>
              I eſt æqualis
                <foreign lang="grc">δ</foreign>
              B; igïtur punctum circuli mo­
                <lb/>
              bilis eſt in I, idem prorſus demonſtrabitur de aliis punctis. </s>
            </p>
            <p id="N25C9B" type="main">
              <s id="N25C9D">Quartò, hinc triangula curuilinea BYG, BZH, B
                <foreign lang="grc">δ</foreign>
              I ſunt Iſoſcelia; </s>
              <s id="N25CA5">
                <lb/>
              ipſum vero BVK eſt æquilaterum quia AK eſt Tangens, vt conſtat; </s>
              <s id="N25CAA">
                <lb/>
              immò ſinguli circuli debent tangere ſuum radium, vt patet; porrò miri­
                <lb/>
              fica eſt huius lineæ figura, quæ ſectionem cordis exhibet, quam ideo
                <lb/>
              deinceps lineam cordis appellabimus, cuius ſunt inſignes omninò pro­
                <lb/>
              prietates, quas ſuo loco demonſtrabimus. </s>
            </p>
            <p id="N25CB5" type="main">
              <s id="N25CB7">Quintò, punctum B initio tardiſſimè mouetur cum eo tempore, quo
                <lb/>
              decurrit BG punctum oppoſitum D decurrat D6; </s>
              <s id="N25CBD">ratio eſt, quia motus
                <lb/>
              centri defert D in I, cui motus orbis cum motu centri conſentiens ad­
                <lb/>
              dit P6, cùm tamen motus orbis puncti B ſit contrarius motui centri; </s>
              <s id="N25CC5">
                <lb/>
              adde quod motus centri circa centrum A tribuit maiorem motum
                <lb/>
              puncto D, quàm B iuxta proportionem radiorum; igitur cùm DA
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              ſit tripla BA, motus centri D eſt triplus motus centri B, igitur duplici
                <lb/>
              nomine motus puncti B eſt tardior. </s>
              <s id="N25CD0">Primò, quia motus orbis
                <lb/>
              tantùm addit D, quantum detrahit B. Secundò, quia motus centri addit
                <lb/>
              D motum triplum illius, quem addit B. </s>
            </p>
            <p id="N25CD7" type="main">
              <s id="N25CD9">Sextò poſſunt haberi per
                <expan abbr="analyticã">analyticam</expan>
              proportiones arcuum lineæ motus,
                <lb/>
              quos B ęqualibus
                <expan abbr="tẽporibus">temporibus</expan>
              percurrit v.g.BG, GH, HI, IK, KL, LM,
                <expan abbr="deniq;">denique</expan>
                <lb/>
              vltimus RS æqualis D6; </s>
              <s id="N25CED">indico breuiter huius proportionem, cum BGDP
                <lb/>
              eſt tripla BY, & P6; </s>
              <s id="N25CF3">eſt quadrupla; </s>
              <s id="N25CF7">igitur ferè æqualis BV, ſi ducantur
                <lb/>
              duæ rectæ YB, YG angulus rectilineus GYB eſt æqualis YAB, id eſt
                <lb/>
              15 grad.igitur ita ſe habet arcus BG ad BY vt recta BY ad BA, id eſt ferè,
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              vt 1.ad 4.paulò minùs; </s>
              <s id="N25D01">ſed D6 eſt quadruplus BY; </s>
              <s id="N25D05">igitur BG eſt ad D6
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              vt 1. ad 16.paulò minus; </s>
              <s id="N25D0B">ſed eo maior erit proportio motus D, quo aſ­
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              ſumetur minor arcus; </s>
              <s id="N25D11">vt autem habeatur proportio aſſumpto arcu in­
                <lb/>
              tegro quadrantis eſt vt M S ad MB; porrò eſt ferè eadem proportio
                <lb/>
              motuum punctorum appoſitorum rotæ mobilis, ſiue rotetur in plano re­
                <lb/>
              ctilineæ, ſiue in ſuperficie curua. </s>
            </p>
            <p id="N25D1B" type="main">
              <s id="N25D1D">Septimò, puncta B & E de tempore, quo percurritur arcus quadran­
                <lb/>
              tis percurrunt ſpatia æqualia: </s>
              <s id="N25D23">hinc ET, BM ſunt æquales; </s>
              <s id="N25D27">immò
                <lb/>
              ſi ducantur rectæ BEMTB, erit ET perfectum quadratum vt conſtat,
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              cuius diagonalis erit BM; </s>
              <s id="N25D2F">igitur æqualis BX, quæ omnia conſtant ex
                <lb/>
              ipſis elementis; porrò punctum B velociſſimè omnium mouetur, vt pa­
                <lb/>
              tet ex dictis. </s>
            </p>
            <p id="N25D37" type="main">
              <s id="N25D39">Octauò, quodlibet punctum circuli mobilis BEDF ſuo motu de­
                <lb/>
              ſcribit arcum lineæ cordis, vt certum eſt, qui in mille punctis decuſ­
                <lb/>
              ſantur cum linea puncti, quam deſcribit punctum B v.g. linea puncti D
                <lb/>
              decuſſatur cum linea puncti B in
                <expan abbr="q.">que</expan>
              quippe D q, S q ſunt æquales, linea
                <lb/>
              puncti E cum linea puncti B in L; denique deſcribi poteſt hæc linea
                <lb/>
              BKMN &c. </s>
              <s id="N25D4D">ductis radiis ex centro ad libitum ſine vllo diuiſionis
                <lb/>
              ordine v.g. ducatur A
                <foreign lang="grc">δ</foreign>
              ; </s>
              <s id="N25D59">L nulla habita diuiſionis ratione; </s>
              <s id="N25D5D">ex L deſcri­
                <lb/>
              batur arcus radio L
                <foreign lang="grc">δ</foreign>
              ; </s>
              <s id="N25D67">aſſumantur
                <foreign lang="grc">δ</foreign>
              I,
                <foreign lang="grc">δ</foreign>
              B æquales, per I; </s>
              <s id="N25D73">haud dubiè
                <lb/>
              ducetur linea; idem dico de aliis punctis. </s>
            </p>
          </chap>
        </body>
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    </archimedes>
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