Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

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          <pb o="106" file="0284" n="299" rhead=""/>
          <p>
            <s xml:id="echoid-s13973" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s13974" xml:space="preserve">Iiſdem ſtantibus, ſit curva AYI talis, ut ordinata FY ſit in-
              <lb/>
            ter congruas FM, FZ proportione media; </s>
            <s xml:id="echoid-s13975" xml:space="preserve">erit _ſolidum_ ex ſpatio αδβ
              <lb/>
              <note position="left" xlink:label="note-0284-01" xlink:href="note-0284-01a" xml:space="preserve">Fig. 156,
                <lb/>
              157.</note>
            circa axem α β rotato factum æquale _ſolido_, quod à _ſpatio_ ADI circa
              <lb/>
            axem AD converſo procreatur.</s>
            <s xml:id="echoid-s13976" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13977" xml:space="preserve">Nam eſt MN. </s>
            <s xml:id="echoid-s13978" xml:space="preserve">NR:</s>
            <s xml:id="echoid-s13979" xml:space="preserve">: PM. </s>
            <s xml:id="echoid-s13980" xml:space="preserve">MF:</s>
            <s xml:id="echoid-s13981" xml:space="preserve">: PM x MF. </s>
            <s xml:id="echoid-s13982" xml:space="preserve">MF q:</s>
            <s xml:id="echoid-s13983" xml:space="preserve">:FZ x
              <lb/>
            FM. </s>
            <s xml:id="echoid-s13984" xml:space="preserve">MFq. </s>
            <s xml:id="echoid-s13985" xml:space="preserve">unde MN x MFq = NR x FZ x FM; </s>
            <s xml:id="echoid-s13986" xml:space="preserve">hoc eſt
              <lb/>
            μ ν x μ φ q = NR x FYq. </s>
            <s xml:id="echoid-s13987" xml:space="preserve">Unde liquet Propoſitum.</s>
            <s xml:id="echoid-s13988" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13989" xml:space="preserve">V. </s>
            <s xml:id="echoid-s13990" xml:space="preserve">Simili ratione colligetur, ſi FY ponatur inter FM, FZ _bime-_
              <lb/>
              <note position="left" xlink:label="note-0284-02" xlink:href="note-0284-02a" xml:space="preserve">Fig. 156,
                <lb/>
              157.</note>
            _media_, fore _ſummam cuborum_ ex applicatis (quales μ φ) à curva α φ δ
              <lb/>
            ad rectam α β, æqualem _ſummæ cuborum_ ex explicatis à curva AYI ad
              <lb/>
            rectam AD. </s>
            <s xml:id="echoid-s13991" xml:space="preserve">paríque modo ſe res habebit quoad cæteras _poteſta-_
              <lb/>
            _tes._</s>
            <s xml:id="echoid-s13992" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13993" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s13994" xml:space="preserve">Porrò, ſtantibus reliquis, ſit curva VXO talis, ut EX ipſi MP
              <lb/>
            æquetur; </s>
            <s xml:id="echoid-s13995" xml:space="preserve">& </s>
            <s xml:id="echoid-s13996" xml:space="preserve">curva πξψ talis, ut μ ξ æ quetur ipſi PF; </s>
            <s xml:id="echoid-s13997" xml:space="preserve">erit ſpatium
              <lb/>
              <note position="left" xlink:label="note-0284-03" xlink:href="note-0284-03a" xml:space="preserve">Fig. 156.</note>
            α π ψ β æqua le ſpatio DV OB.</s>
            <s xml:id="echoid-s13998" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13999" xml:space="preserve">Nam eſt MN. </s>
            <s xml:id="echoid-s14000" xml:space="preserve">MR:</s>
            <s xml:id="echoid-s14001" xml:space="preserve">: MP. </s>
            <s xml:id="echoid-s14002" xml:space="preserve">PF; </s>
            <s xml:id="echoid-s14003" xml:space="preserve">adeoque MN x PF = MR
              <lb/>
            x MP. </s>
            <s xml:id="echoid-s14004" xml:space="preserve">hoc eſt μ ν x μ ξ = ES x EX. </s>
            <s xml:id="echoid-s14005" xml:space="preserve">vel rectang. </s>
            <s xml:id="echoid-s14006" xml:space="preserve">ET = rectang.
              <lb/>
            </s>
            <s xml:id="echoid-s14007" xml:space="preserve">μ σ. </s>
            <s xml:id="echoid-s14008" xml:space="preserve">Unde liquet Propoſitum.</s>
            <s xml:id="echoid-s14009" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14010" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s14011" xml:space="preserve">Subnotetur hoc: </s>
            <s xml:id="echoid-s14012" xml:space="preserve">Si curva AB ſit _Parabola_, cujus _Axis_ AD,
              <lb/>
              <note position="left" xlink:label="note-0284-04" xlink:href="note-0284-04a" xml:space="preserve">Fig. 156.</note>
            _parameter_ R; </s>
            <s xml:id="echoid-s14013" xml:space="preserve">erit curva VXO _byperbola_, cujus _centrum_ D, _Axis_ DV,
              <lb/>
            cujuſque _parameter_ axi R æquatur (ſcilicet ob EXq = (PMq =
              <lb/>
            PFq + FMq = {R q/4}+FMq = {R q/4}+ DEq = ) DVq+ DEq).
              <lb/>
            </s>
            <s xml:id="echoid-s14014" xml:space="preserve">item _ſpatium_ α β ψ π erit _Rectangulum_; </s>
            <s xml:id="echoid-s14015" xml:space="preserve">quoniam ſingulæ applicatæ
              <lb/>
            μ ξ ipſi {R/2} æquantur. </s>
            <s xml:id="echoid-s14016" xml:space="preserve">Conſtat itaque dato _ſpatio byperbolico_ DVOB
              <lb/>
            curvam AMB dari; </s>
            <s xml:id="echoid-s14017" xml:space="preserve">& </s>
            <s xml:id="echoid-s14018" xml:space="preserve">viciſſim. </s>
            <s xml:id="echoid-s14019" xml:space="preserve">Hoc obiter.</s>
            <s xml:id="echoid-s14020" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14021" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s14022" xml:space="preserve">Adnotari poſſet etiam omnia ſimul quadrata ex applicatis
              <lb/>
            ad rectam α β à curva π ξ ψ æquari rectangulis omnibus ex PE, EX
              <lb/>
              <note position="left" xlink:label="note-0284-05" xlink:href="note-0284-05a" xml:space="preserve">Fig. 157.</note>
            ad rectam DB applicatis (ſeu computatis); </s>
            <s xml:id="echoid-s14023" xml:space="preserve">cubos ex μ ξ æquari ipſis
              <lb/>
            PFq x EX; </s>
            <s xml:id="echoid-s14024" xml:space="preserve">ac ità porrò.</s>
            <s xml:id="echoid-s14025" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14026" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s14027" xml:space="preserve">Adjungatur etiam (productâ PM Q) ſi ponatur FZ æqua-
              <lb/>
              <note position="left" xlink:label="note-0284-06" xlink:href="note-0284-06a" xml:space="preserve">Fig. 157.</note>
            lis ipſi PQ, & </s>
            <s xml:id="echoid-s14028" xml:space="preserve">μ φ ipſi AQ; </s>
            <s xml:id="echoid-s14029" xml:space="preserve">_ſpatium_ α β δ _ſpatio_ AD LK æ-
              <lb/>
            quari.</s>
            <s xml:id="echoid-s14030" xml:space="preserve"/>
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