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

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            <s xml:id="echoid-s13833" xml:space="preserve">
              <pb o="104" file="0282" n="297" rhead=""/>
            AEG æquatur _Circulari ſegmento_ ADB demonſtrationem, ne longiùs
              <lb/>
            evager, obmittam.</s>
            <s xml:id="echoid-s13834" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13835" xml:space="preserve">XXXIV. </s>
            <s xml:id="echoid-s13836" xml:space="preserve">Sint duo _circuli_ AIMG, AKNH ſeſe contingentes ad A;
              <lb/>
            </s>
            <s xml:id="echoid-s13837" xml:space="preserve">
              <note position="left" xlink:label="note-0282-01" xlink:href="note-0282-01a" xml:space="preserve">Fig. 154.</note>
            communique diametro AHG, utcunque perpendicularis ducatur recta
              <lb/>
            DN M: </s>
            <s xml:id="echoid-s13838" xml:space="preserve">habebit_ſegmentum_ AIMD ad _ſegmentum_ AKND mino-
              <lb/>
            rem rationem, quam recta DM ad rectam DN.</s>
            <s xml:id="echoid-s13839" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13840" xml:space="preserve">Nam ſit AR ad AG perpendicularis, ac ipſi AH æqualis; </s>
            <s xml:id="echoid-s13841" xml:space="preserve">& </s>
            <s xml:id="echoid-s13842" xml:space="preserve">
              <lb/>
            connectatur HR, cui occurrat recta MD in X; </s>
            <s xml:id="echoid-s13843" xml:space="preserve">ducatúrque recta
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            GXS; </s>
            <s xml:id="echoid-s13844" xml:space="preserve">tum ad axem AG _parametrum_ AS per N deſcripta con-
              <lb/>
            cipiatur _Ellipſis_ ALNG; </s>
            <s xml:id="echoid-s13845" xml:space="preserve">hæc (utì ſatis manifeſtum) intra arcum
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            AKN tota cadet. </s>
            <s xml:id="echoid-s13846" xml:space="preserve">Eſt autem ſegm. </s>
            <s xml:id="echoid-s13847" xml:space="preserve">AIMD. </s>
            <s xml:id="echoid-s13848" xml:space="preserve">ſegm. </s>
            <s xml:id="echoid-s13849" xml:space="preserve">ALND:</s>
            <s xml:id="echoid-s13850" xml:space="preserve">:
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            DM. </s>
            <s xml:id="echoid-s13851" xml:space="preserve">DN. </s>
            <s xml:id="echoid-s13852" xml:space="preserve">ergo ſegm. </s>
            <s xml:id="echoid-s13853" xml:space="preserve">AI MD. </s>
            <s xml:id="echoid-s13854" xml:space="preserve">ſegm. </s>
            <s xml:id="echoid-s13855" xml:space="preserve">AKND &</s>
            <s xml:id="echoid-s13856" xml:space="preserve">lt;</s>
            <s xml:id="echoid-s13857" xml:space="preserve">DM. </s>
            <s xml:id="echoid-s13858" xml:space="preserve">DN.</s>
            <s xml:id="echoid-s13859" xml:space="preserve"/>
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            <s xml:id="echoid-s13860" xml:space="preserve">XXXV. </s>
            <s xml:id="echoid-s13861" xml:space="preserve">Sit Ellipſis YFZT, cujus axes conjugati YZ, FT; </s>
            <s xml:id="echoid-s13862" xml:space="preserve">ſit item
              <lb/>
            recta DC axi majori YZ parallela; </s>
            <s xml:id="echoid-s13863" xml:space="preserve">& </s>
            <s xml:id="echoid-s13864" xml:space="preserve">per D, F, C tranſeat circulus
              <lb/>
              <note position="left" xlink:label="note-0282-02" xlink:href="note-0282-02a" xml:space="preserve">Fig + 154.</note>
            DFCV centrum habens K, in ellipſis axe minore FT ſitum; </s>
            <s xml:id="echoid-s13865" xml:space="preserve">dico
              <lb/>
            circuli partem DOFPC intra ellipſis partem DMFNC jacere.</s>
            <s xml:id="echoid-s13866" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13867" xml:space="preserve">Nam ſit FI ad FV perpendicularis, & </s>
            <s xml:id="echoid-s13868" xml:space="preserve">in hac ſumatur FS = FV; </s>
            <s xml:id="echoid-s13869" xml:space="preserve">& </s>
            <s xml:id="echoid-s13870" xml:space="preserve">
              <lb/>
            connectatur VS, cui DC producta occurrat in X; </s>
            <s xml:id="echoid-s13871" xml:space="preserve">& </s>
            <s xml:id="echoid-s13872" xml:space="preserve">connexa TX
              <lb/>
            ipſi FI occurat in R. </s>
            <s xml:id="echoid-s13873" xml:space="preserve">& </s>
            <s xml:id="echoid-s13874" xml:space="preserve">cum ſit GDq = FG x GV = FG x GX;
              <lb/>
            </s>
            <s xml:id="echoid-s13875" xml:space="preserve">liquet ipſam FR eſſe ellipſis, axi FT congruam, parametrum; </s>
            <s xml:id="echoid-s13876" xml:space="preserve">unde
              <lb/>
            conſtat Propoſitum.</s>
            <s xml:id="echoid-s13877" xml:space="preserve"/>
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            <s xml:id="echoid-s13878" xml:space="preserve">XXXVI. </s>
            <s xml:id="echoid-s13879" xml:space="preserve">Sit circuli, cujus centrum L, ſegmentum DEC, & </s>
            <s xml:id="echoid-s13880" xml:space="preserve">ſumpto
              <lb/>
              <note position="left" xlink:label="note-0282-03" xlink:href="note-0282-03a" xml:space="preserve">Fig 155.</note>
            in ejus axe GE puncto quopiam F, ſit curva DMFC talis, ut ductâ
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            utcunque rectâ RMS ad GE parallelâ, ſit RS. </s>
            <s xml:id="echoid-s13881" xml:space="preserve">RM:</s>
            <s xml:id="echoid-s13882" xml:space="preserve">: GE. </s>
            <s xml:id="echoid-s13883" xml:space="preserve">GF;
              <lb/>
            </s>
            <s xml:id="echoid-s13884" xml:space="preserve">erit DMFC ellipſis, hoc modo determinata: </s>
            <s xml:id="echoid-s13885" xml:space="preserve">Fiat EG. </s>
            <s xml:id="echoid-s13886" xml:space="preserve">FG:</s>
            <s xml:id="echoid-s13887" xml:space="preserve">: GL. </s>
            <s xml:id="echoid-s13888" xml:space="preserve">
              <lb/>
            GH; </s>
            <s xml:id="echoid-s13889" xml:space="preserve">& </s>
            <s xml:id="echoid-s13890" xml:space="preserve">per H erigatur YHZ ad DC parallela, ſitque HY par ipſi LE; </s>
            <s xml:id="echoid-s13891" xml:space="preserve">
              <lb/>
            erunt HY, HF ellipſis ſemiaxes.</s>
            <s xml:id="echoid-s13892" xml:space="preserve"/>
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            <s xml:id="echoid-s13893" xml:space="preserve">Demonſtratum habetur à _Greg. </s>
            <s xml:id="echoid-s13894" xml:space="preserve">à S. </s>
            <s xml:id="echoid-s13895" xml:space="preserve">Vincentio_, L. </s>
            <s xml:id="echoid-s13896" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s13897" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s13898" xml:space="preserve">154.
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            </s>
            <s xml:id="echoid-s13899" xml:space="preserve">_Corol._ </s>
            <s xml:id="echoid-s13900" xml:space="preserve">Hinc ſegm. </s>
            <s xml:id="echoid-s13901" xml:space="preserve">DEC. </s>
            <s xml:id="echoid-s13902" xml:space="preserve">DMFC:</s>
            <s xml:id="echoid-s13903" xml:space="preserve">: EG. </s>
            <s xml:id="echoid-s13904" xml:space="preserve">FG.</s>
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            <s xml:id="echoid-s13906" xml:space="preserve">XXXVII. </s>
            <s xml:id="echoid-s13907" xml:space="preserve">Sint duæ circulorum portiones DEC, DOFC, quarum
              <lb/>
            communis ſubtenſa DC, & </s>
            <s xml:id="echoid-s13908" xml:space="preserve">axis GFE; </s>
            <s xml:id="echoid-s13909" xml:space="preserve">portio major DEC ad portio-
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            nem DOFC majorem rationem habet eâ, quam habet axis GE ad
              <lb/>
            axem GF.</s>
            <s xml:id="echoid-s13910" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13911" xml:space="preserve">Nam ſint L circuli DSEC, & </s>
            <s xml:id="echoid-s13912" xml:space="preserve">K circuli DOFC centra; </s>
            <s xml:id="echoid-s13913" xml:space="preserve">& </s>
            <s xml:id="echoid-s13914" xml:space="preserve">fiat EG.
              <lb/>
            </s>
            <s xml:id="echoid-s13915" xml:space="preserve">FG:</s>
            <s xml:id="echoid-s13916" xml:space="preserve">: GL. </s>
            <s xml:id="echoid-s13917" xml:space="preserve">GH; </s>
            <s xml:id="echoid-s13918" xml:space="preserve">& </s>
            <s xml:id="echoid-s13919" xml:space="preserve">fiat YHZ ad HF perpendicularis & </s>
            <s xml:id="echoid-s13920" xml:space="preserve">ſit HY æ-
              <lb/>
            qualis ipſi LE; </s>
            <s xml:id="echoid-s13921" xml:space="preserve">tum ſemiaxibus HY, HF deſcripta concipiatur ellipſis
              <lb/>
            YDMFCZ; </s>
            <s xml:id="echoid-s13922" xml:space="preserve">è mox prædictis liquet ellipſin DMFC circulo DOFC
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            circumduci. </s>
            <s xml:id="echoid-s13923" xml:space="preserve">Eſt autem circulare ſegmentum DEC ad ſegmentum el-
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            lipticum DMFC, ut GE ad GF; </s>
            <s xml:id="echoid-s13924" xml:space="preserve">quare ſegm DEC ad ſegm circula-
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            re DOFC. </s>
            <s xml:id="echoid-s13925" xml:space="preserve">rationem habet majorem, quàm GE ad GF: </s>
            <s xml:id="echoid-s13926" xml:space="preserve">Quod. </s>
            <s xml:id="echoid-s13927" xml:space="preserve">E.</s>
            <s xml:id="echoid-s13928" xml:space="preserve">D.</s>
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