Fabri, Honoré, Tractatus physicus de motu locali, 1646

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        <body>
          <chap id="N1EE3A">
            <pb pagenum="243" xlink:href="026/01/275.jpg"/>
            <p id="N1F672" type="main">
              <s id="N1F674">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              30.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1F680" type="main">
              <s id="N1F682">
                <emph type="italics"/>
              Hinc quâ proportione planum minùs confert ad nouam determinationem,
                <lb/>
              plùs remanet prioris determinationis; </s>
              <s id="N1F68A">quò verò plùs illud confert, huius minùs
                <lb/>
              restat
                <emph.end type="italics"/>
              ; </s>
              <s id="N1F693">hinc, cum planum totam confert
                <expan abbr="nouã">nouam</expan>
                <expan abbr="determinationẽ">determinationem</expan>
              vt in per­
                <lb/>
              pendiculari DD, nihil prioris remanet; </s>
              <s id="N1F6A1">hinc ſi linea incidentiæ ſit pa­
                <lb/>
              rallela plano BF nulla fiet noua determinatio, tota priore intacta; </s>
              <s id="N1F6A7">ſi ve­
                <lb/>
              rò ſit perpendicularis GD, tota determinatio eſt noua, & nihil prioris
                <lb/>
              remanet; ſi demum lineæ incidentiæ ſint aliæ, confert vtrumque ad no­
                <lb/>
              uam determinationem pro rata. </s>
            </p>
            <p id="N1F6B1" type="main">
              <s id="N1F6B3">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              31.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1F6BF" type="main">
              <s id="N1F6C1">
                <emph type="italics"/>
              Si pellatur mobile per AD in planum FB, determinatio lineæ reflexionis
                <lb/>
              erit quaſi mixta ſinistrorſum
                <emph.end type="italics"/>
              ; </s>
              <s id="N1F6CC">ſi enim ex D propagaretur motus in E rectè
                <lb/>
              ſiniſtrorſum acquireret DF in linea BF, vt patet; </s>
              <s id="N1F6D2">igitur ſi ſit linea inci­
                <lb/>
              dentiæ AD, noua determinatio per DH conſtabit partim ex eo, quòd
                <lb/>
              planum reflectens confert partim ex eo, quod remanet prioris determi­
                <lb/>
              nationis, quod reſpondet DF, & ex eo quod confert planum FB, quod
                <lb/>
              reſpondet DP; </s>
              <s id="N1F6DE">quia ictus per AD eſt ad ictum per GD, vt PD ad DP
                <lb/>
              vel DG; </s>
              <s id="N1F6E4">ſed eſt eadem ratio impedimenti eademque determinationis
                <lb/>
              per Theoremata ſuperiora; atqui ex DPDF fit DHGO. igitur deter­
                <lb/>
              minatio lineæ reflexæ eſt mixta, quod erat probandum. </s>
            </p>
            <p id="N1F6EC" type="main">
              <s id="N1F6EE">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              32.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1F6FA" type="main">
              <s id="N1F6FC">
                <emph type="italics"/>
              Hinc decreſcit determinatio, quam confert planum iuxta rationem ſinuum
                <lb/>
              verſorum in
                <emph.end type="italics"/>
              GD. v. g. ſi ſit linea incidentiæ AD; </s>
              <s id="N1F70B">ducatur APH paral­
                <lb/>
              lela FB, determinatio quam confert planum, decreſcit ſinu verſo PG; </s>
              <s id="N1F711">ſi
                <lb/>
              verò ſit linea incidentiæ ID, decreſcit ſinu verſo LG; atque ita dein­
                <lb/>
              ceps; at verò creſcit portio prioris determinationis lineæ incidentiæ
                <lb/>
              iuxta rationem ſinuum rectorum in DB v. g. ſi ſit linea incidentiæ AD,
                <lb/>
              creſcit ſinu recto AP æquali BD ſi ſit IL creſcit ſinu recto IL vel RD. </s>
            </p>
            <p id="N1F721" type="main">
              <s id="N1F723">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              33.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1F72F" type="main">
              <s id="N1F731">
                <emph type="italics"/>
              Hinc angulus reflexionis eſt æqualis angulo incidentiæ, & hoc eſt principium
                <lb/>
              poſitiuum huius æqualitatis angulorum.
                <emph.end type="italics"/>
              ſit enim linea incidentiæ AD, du­
                <lb/>
              catur APH, AB, HF; </s>
              <s id="N1F73E">certè DF & DB ſunt æquales APPH; </s>
              <s id="N1F742">item­
                <lb/>
              que ABPDHF ſunt æquales; </s>
              <s id="N1F748">atqui determinatio lineæ reflexionis
                <lb/>
              eſt mixta ex DFH; </s>
              <s id="N1F74E">igitur erit DH; </s>
              <s id="N1F752">ſed triangula DFH, DAB ſunt
                <lb/>
              æqualia & anguli HDFADB ſunt æquales: </s>
              <s id="N1F758">ſimiliter ſit linea inciden­
                <lb/>
              tiæ ID, ducatur IN parallela AHIRNM; </s>
              <s id="N1F75E">certè duo anguli IDR,
                <lb/>
              NDM ſunt æquales; </s>
              <s id="N1F764">idem dico de omnibus aliis lineis incidentiæ, &
                <lb/>
              hæc eſt vera ratio poſitiua à priori, de qua plura infrà; </s>
              <s id="N1F76A">non deeſt etiam
                <lb/>
              negatiua, quia ſcilicet poſita linea incidentiæ AD cùm ſiniſtrorſum ſint
                <lb/>
              infiniti anguli inæquales angulo incidentiæ; </s>
              <s id="N1F772">non eſt potior ratio, cur
                <lb/>
              per vnum fiat quàm per alium, & cum ſit tantùm vnus æqualis HDM in
                <lb/>
              eodem ſcilicet plano; </s>
              <s id="N1F77A">certè per illum fieri debet; </s>
              <s id="N1F77E">quippe quod vnum
                <lb/>
              eſt, determinatum eſt, vt ſæpè diximus aliàs; </s>
              <s id="N1F784">nec eſt quòd aliqui delica-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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