Fabri, Honoré, Tractatus physicus de motu locali, 1646

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          <chap id="N22A20">
            <p id="N23ABF" type="main">
              <s id="N23AC1">
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              produci </s>
              <s id="N23ACB">vno inſtanti ab ipſo corpore grani, vt ſinum rectum arcus infe­
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              rioris ad ſinum totum; </s>
              <s id="N23AD1">ſit enim pondus in L, impetus productus in L
                <lb/>
              eſt ad productum in O, vt ſinus BL ad LA; </s>
              <s id="N23AD7">ſit in H, vt ſinus HC ad
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              HA; </s>
              <s id="N23ADD">ſit in O vt OA ad OA, ſit in D vt nihil ad DA: </s>
              <s id="N23AE1">hinc vides con­
                <lb/>
              trarias vices impetus producti in ſingulis punctis, & determinationis,
                <lb/>
              quæ eſt à potentia applicata in A; </s>
              <s id="N23AE9">quippè ille continuò imminuitur ab
                <lb/>
              O ad D; </s>
              <s id="N23AEF">hæc verò continuo creſcit; </s>
              <s id="N23AF3">ille totus eſt in O nullus in D; </s>
              <s id="N23AF7">hæc
                <lb/>
              tota in D, nulla in O; </s>
              <s id="N23AFD">ille eſt ad totum, vt ſinus arcus inferioris ad ſi­
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              num totum; hæc verò eſt ad totam, ſeu maximam, vt ſinus arcus ſuperio­
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              ris ad ſinum totum. </s>
            </p>
            <p id="N23B05" type="main">
              <s id="N23B07">
                <emph type="center"/>
                <emph type="italics"/>
              Corollarium
                <emph.end type="italics"/>
              6.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N23B14" type="main">
              <s id="N23B16">Sextò, hinc colligo rationem à priori huius imminutionis impetus; </s>
              <s id="N23B1A">
                <lb/>
              cum enim impetus deſtruatur ne ſit fruſtrà; </s>
              <s id="N23B1F">certè propter
                <expan abbr="eãdem">eandem</expan>
              ratio­
                <lb/>
              nem non producitur, ne ſcilicet ſit fruſtrà; </s>
              <s id="N23B29">cùm enim impetus ſit vt mo­
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              tus, ſit mobile in L cum duplici determinatione alteram per lineam LA
                <lb/>
              alteram L
                <foreign lang="grc">δ</foreign>
              ; </s>
              <s id="N23B35">ſit autem hæc ad illam vt LA ad LR, vel vt L
                <foreign lang="grc">δ</foreign>
              æqualis
                <lb/>
              LA ad L
                <foreign lang="grc">β</foreign>
              æqualem LR, ſitque arcus LO grad. 30. LR eſt ſubdupla
                <lb/>
              LA; </s>
              <s id="N23B47">ſit
                <foreign lang="grc">β υ</foreign>
              æqualis L
                <foreign lang="grc">δ</foreign>
              , ipſique parallela, &
                <foreign lang="grc">υ δ</foreign>
              æqualis L
                <foreign lang="grc">β</foreign>
              & paralle­
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              la; </s>
              <s id="N23B5D">certè hoc poſito, motus erit per L
                <foreign lang="grc">υ</foreign>
              , ſcilicet per diagonalem, vt ſæ­
                <lb/>
              piùs ſuprà demonſtrauimus; </s>
              <s id="N23B67">igitur ſi tantùm eſſet determinatio L
                <foreign lang="grc">δ</foreign>
              mo­
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              tus eſſet L
                <foreign lang="grc">δ</foreign>
              ; </s>
              <s id="N23B75">ſi verò conjungatur determinatio L
                <foreign lang="grc">β</foreign>
              , motus erit L
                <foreign lang="grc">υ</foreign>
              ; </s>
              <s id="N23B81">ſed
                <lb/>
              impetus eſt vt motus; </s>
              <s id="N23B87">igitur impetus L
                <foreign lang="grc">δ</foreign>
              , cum vtraque determinatione
                <lb/>
              conjunctus non haberet totum ſuum effectum, id eſt motum L
                <foreign lang="grc">δ</foreign>
              ; </s>
              <s id="N23B95">igitur
                <lb/>
              aliquid illius eſt fruſtrà; </s>
              <s id="N23B9B">igitur producitur tantùm impetus vt L
                <foreign lang="grc">υ</foreign>
              ; </s>
              <s id="N23BA3">ſed
                <lb/>
              vt L
                <foreign lang="grc">υ</foreign>
              ad L
                <foreign lang="grc">δ</foreign>
              , ita LB ad LA; nam triangula L
                <foreign lang="grc">υ δ</foreign>
              , & BLA ſunt æqua­
                <lb/>
              lia, & æquiangula, vt patet. </s>
            </p>
            <p id="N23BB7" type="main">
              <s id="N23BB9">
                <emph type="center"/>
                <emph type="italics"/>
              Corollarium
                <emph.end type="italics"/>
              7.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N23BC5" type="main">
              <s id="N23BC7">Septimò colligo, ſingulis inſtantibus mutari determinationem quæ eſt
                <lb/>
              ab A, & conſequenter determinationem mixtam, ipſamque acceſſionem
                <lb/>
              impetus noui: </s>
              <s id="N23BCF">hinc etiam rectè explicatur, in quo poſitum ſit illud impe­
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              dimentum ratione cuius corpus rectà deorſum non tendit; quippè in
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              eo tantùm poſitum eſt, quod ſit noua determinatio, idem dico de reſi­
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              ſtentia. </s>
            </p>
            <p id="N23BD9" type="main">
              <s id="N23BDB">Obſeruabis autem idem præſtare funem affixum in A ratione conti­
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              nuitatis, & vnionis ſuarum partium, quod præſtaret potentia in A fune
                <lb/>
              ipſo trahens, vt conſtat, ſeu pondus contranitens ex rotula appenſum. </s>
            </p>
            <p id="N23BE2" type="main">
              <s id="N23BE4">
                <emph type="center"/>
                <emph type="italics"/>
              Corollarium
                <emph.end type="italics"/>
              8.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N23BF0" type="main">
              <s id="N23BF2">Octauò colligo, creſcere impedimentum ab O in D in ratione ſi­
                <lb/>
              nuum verſorum arcus ſuperioris; </s>
              <s id="N23BF8">cùm enim in L v. g. motus ſit ad mo­
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              tum liberum in O vt L
                <foreign lang="grc">υ</foreign>
              ad L
                <foreign lang="grc">δ</foreign>
              vel vt LB ad LA, impeditur motus vt
                <lb/>
              RO; </s>
              <s id="N23C0C">nam motus, vel impetus in L eſt minor impetu in O, differentia
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              vtriuſque RO, ſed RO eſt ſinus verſus arcus OL; idem dico de
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              reliquis. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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