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

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          <p>
            <s xml:id="echoid-s12550" xml:space="preserve">
              <pb o="87" file="0265" n="280" rhead=""/>
            omnia AZ x AE + BZ x BF + CZ x CG, &</s>
            <s xml:id="echoid-s12551" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12552" xml:space="preserve">= {DHcub.</s>
            <s xml:id="echoid-s12553" xml:space="preserve">/3}
              <lb/>
            crunt omnia AZ x √ VAZ φ + BZ x √ VBZφ + CZ x
              <lb/>
            √ VCZφ, &</s>
            <s xml:id="echoid-s12554" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12555" xml:space="preserve">= {DHcub/3} √{1/2} = √ {DH
              <emph style="sub">6</emph>
            /18.</s>
            <s xml:id="echoid-s12556" xml:space="preserve">} Eſt autem DH_q_ =
              <lb/>
            2 VD ψ φ, vel DH
              <emph style="sub">6</emph>
            = 8VD ψ φ {3/ }; </s>
            <s xml:id="echoid-s12557" xml:space="preserve">quapropter omnia AZ x
              <lb/>
            √ VAZ φ + BZ x √ VBZφ + CZ x √ VCZφ, &</s>
            <s xml:id="echoid-s12558" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12559" xml:space="preserve">= √
              <lb/>
            {8/18} VD ψ φ {3/ } = {2/3} √ VDψφ {3/ }.</s>
            <s xml:id="echoid-s12560" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12561" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s12562" xml:space="preserve">_Exempla._ </s>
            <s xml:id="echoid-s12563" xml:space="preserve">Sit VDψ circuli quadrans (cujus radius dicatur
              <lb/>
            R, & </s>
            <s xml:id="echoid-s12564" xml:space="preserve">Peripheria P) ſegmenta VAZ, VBZ, VCZ, &</s>
            <s xml:id="echoid-s12565" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12566" xml:space="preserve">in ſi-
              <lb/>
            nus rectos AZ, BZ, CZ, &</s>
            <s xml:id="echoid-s12567" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12568" xml:space="preserve">ducta conficient {R_q_P_q_/8.</s>
            <s xml:id="echoid-s12569" xml:space="preserve">}</s>
          </p>
          <note position="right" xml:space="preserve">Fig. 123.</note>
          <p>
            <s xml:id="echoid-s12570" xml:space="preserve">Item Summa AZ √ VAZ + BZ √ VBZ + CZ √ VCZ,
              <lb/>
            &</s>
            <s xml:id="echoid-s12571" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12572" xml:space="preserve">= {2/3} √{R
              <emph style="sub">3</emph>
            P
              <emph style="sub">3</emph>
            /8.</s>
            <s xml:id="echoid-s12573" xml:space="preserve">} = √ {R
              <emph style="sub">3</emph>
            P
              <emph style="sub">3</emph>
            /18.</s>
            <s xml:id="echoid-s12574" xml:space="preserve">}</s>
          </p>
          <p>
            <s xml:id="echoid-s12575" xml:space="preserve">Si VD ψ ſit parabolæ ſegmentum, factum è ſegmentis in applicatas
              <lb/>
            erit {2/9} VD_q_ x Aψ_q_; </s>
            <s xml:id="echoid-s12576" xml:space="preserve">ac è radicibus ſegmentorum in applicatas factum
              <lb/>
            erit {2/3} √ {8/2} { /7} VD
              <emph style="sub">3</emph>
            x Dψ
              <emph style="sub">3</emph>
            √ {3/2} {2/4} { /3} VD
              <emph style="sub">3</emph>
            x Dψ
              <emph style="sub">3</emph>
            .</s>
            <s xml:id="echoid-s12577" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12578" xml:space="preserve">Similia plura de factis è _Segmentorum poteſtatibus, autradicibus_
              <lb/>
            _aliis in applicatas, aut ſinus ductis_, hinc extundi poſſent.</s>
            <s xml:id="echoid-s12579" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12580" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s12581" xml:space="preserve">E dictis porrò ſequitur, ſi omnes ( vertici, & </s>
            <s xml:id="echoid-s12582" xml:space="preserve">perpendicula-
              <lb/>
            ribus interjectæ) VP per reſpectiva puncta A, B, C, &</s>
            <s xml:id="echoid-s12583" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12584" xml:space="preserve">Concipian-
              <lb/>
            tur applicatæ, puta ut AY, BY, CY, &</s>
            <s xml:id="echoid-s12585" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12586" xml:space="preserve">reſpectivis VP æquentur;
              <lb/>
            </s>
            <s xml:id="echoid-s12587" xml:space="preserve">erit è ſic applicatis _conſtitutum ſpatium_ ADξθ _æquale ſemiſſe quadrati_
              <lb/>
            _ex ſubtenſa_ VH.</s>
            <s xml:id="echoid-s12588" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12589" xml:space="preserve">Nam, ob omnes VA + VB + VC, &</s>
            <s xml:id="echoid-s12590" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12591" xml:space="preserve">= {VD_q_;</s>
            <s xml:id="echoid-s12592" xml:space="preserve">/2} & </s>
            <s xml:id="echoid-s12593" xml:space="preserve">omnes
              <lb/>
            AP + BP + CP&</s>
            <s xml:id="echoid-s12594" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12595" xml:space="preserve">= {DH_q_,/2} liquet fore omnes VP =
              <lb/>
            {VH_q_.</s>
            <s xml:id="echoid-s12596" xml:space="preserve">/2}</s>
          </p>
          <p>
            <s xml:id="echoid-s12597" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s12598" xml:space="preserve">Porrò, ſi (poſitis iiſdem) ſit curva RXXS talis, ut ſit IX
              <lb/>
            = AP, & </s>
            <s xml:id="echoid-s12599" xml:space="preserve">KX = BP; </s>
            <s xml:id="echoid-s12600" xml:space="preserve">& </s>
            <s xml:id="echoid-s12601" xml:space="preserve">LX = CP, &</s>
            <s xml:id="echoid-s12602" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12603" xml:space="preserve">erit _ſolidum factum </s>
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