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-s12138" xml:space="preserve">
              <pb o="80" file="0258" n="273" rhead=""/>
            rùm ex jam modò oſtenſis GT curvam DOG tangit; </s>
            <s xml:id="echoid-s12139" xml:space="preserve">ergò KS ip-
              <lb/>
            ſam DKE continget.</s>
            <s xml:id="echoid-s12140" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12141" xml:space="preserve">Notetur eſſe DG q. </s>
            <s xml:id="echoid-s12142" xml:space="preserve">DK q:</s>
            <s xml:id="echoid-s12143" xml:space="preserve">: 2 R. </s>
            <s xml:id="echoid-s12144" xml:space="preserve">DS.</s>
            <s xml:id="echoid-s12145" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12146" xml:space="preserve">Nam eſt DG q. </s>
            <s xml:id="echoid-s12147" xml:space="preserve">DK q = DG. </s>
            <s xml:id="echoid-s12148" xml:space="preserve">DK + DG. </s>
            <s xml:id="echoid-s12149" xml:space="preserve">DK = R. </s>
            <s xml:id="echoid-s12150" xml:space="preserve">P +
              <lb/>
            DT. </s>
            <s xml:id="echoid-s12151" xml:space="preserve">DS = R. </s>
            <s xml:id="echoid-s12152" xml:space="preserve">P + 2 P. </s>
            <s xml:id="echoid-s12153" xml:space="preserve">DS = 2 RP. </s>
            <s xml:id="echoid-s12154" xml:space="preserve">P x DS = 2 R. </s>
            <s xml:id="echoid-s12155" xml:space="preserve">DS.
              <lb/>
            </s>
            <s xml:id="echoid-s12156" xml:space="preserve">itaque DG q. </s>
            <s xml:id="echoid-s12157" xml:space="preserve">DKQ:</s>
            <s xml:id="echoid-s12158" xml:space="preserve">: 2 R. </s>
            <s xml:id="echoid-s12159" xml:space="preserve">DS.</s>
            <s xml:id="echoid-s12160" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12161" xml:space="preserve">Hæc autem perinde vera ſunt, nec abſimili modo demonſtrantur;
              <lb/>
            </s>
            <s xml:id="echoid-s12162" xml:space="preserve">etiam ſi projectæ à D rectæ DA, DG, DE, &_</s>
            <s xml:id="echoid-s12163" xml:space="preserve">c_. </s>
            <s xml:id="echoid-s12164" xml:space="preserve">pares ſint (quo ca-
              <lb/>
            ſu curva AGEZ _Circulus_ erit, & </s>
            <s xml:id="echoid-s12165" xml:space="preserve">_Curva_ DKE _Spiralis Archimedæa_)
              <lb/>
            aut à DA continuò creſcant.</s>
            <s xml:id="echoid-s12166" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12167" xml:space="preserve">Exindè verò facilè colligitur hoc _Theorema_:</s>
            <s xml:id="echoid-s12168" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12169" xml:space="preserve">XIV. </s>
            <s xml:id="echoid-s12170" xml:space="preserve">Sint duæ curvæ AGE, DKE ità verſus ſe relatæ, ut à de-
              <lb/>
            ſignato in curva DKE puncto D ductis rectis DA, DG (quarum
              <lb/>
            hæc ipſam DKE ſecetin K) ſit ſemper _Quadratum_ ex DK _Quadru-_
              <lb/>
              <note position="left" xlink:label="note-0258-01" xlink:href="note-0258-01a" xml:space="preserve">Fig. 114.</note>
            _plum ſpatii_ ADG; </s>
            <s xml:id="echoid-s12171" xml:space="preserve">ductâ DH ad DG perpendiculari, & </s>
            <s xml:id="echoid-s12172" xml:space="preserve">facto DK.
              <lb/>
            </s>
            <s xml:id="echoid-s12173" xml:space="preserve">DG:</s>
            <s xml:id="echoid-s12174" xml:space="preserve">: DG. </s>
            <s xml:id="echoid-s12175" xml:space="preserve">DH; </s>
            <s xml:id="echoid-s12176" xml:space="preserve">connexâque HK; </s>
            <s xml:id="echoid-s12177" xml:space="preserve">erit HK curvæ DKE per-
              <lb/>
            pendicularis.</s>
            <s xml:id="echoid-s12178" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12179" xml:space="preserve">Nam concipiatur linea DOKO, per K tranſiens, naturâque talis
              <lb/>
            ut ad illam à D projectæ (ceu DK) ſe habeant in eadem quâ ſpatia ADG
              <lb/>
            ratione (quales lineas attigimus in proximè ſuperiori) & </s>
            <s xml:id="echoid-s12180" xml:space="preserve">lineam
              <lb/>
            DOK tangat recta KT, lineam DKE recta KS; </s>
            <s xml:id="echoid-s12181" xml:space="preserve">conveniant âu-
              <lb/>
            tem hæ cum ipſa HD punctis T, S; </s>
            <s xml:id="echoid-s12182" xml:space="preserve">eſt igitur (è præcedente) DG@q.
              <lb/>
            </s>
            <s xml:id="echoid-s12183" xml:space="preserve">DKq:</s>
            <s xml:id="echoid-s12184" xml:space="preserve">: {DK/2}. </s>
            <s xml:id="echoid-s12185" xml:space="preserve">DT. </s>
            <s xml:id="echoid-s12186" xml:space="preserve">hoc eft DH. </s>
            <s xml:id="echoid-s12187" xml:space="preserve">DK:</s>
            <s xml:id="echoid-s12188" xml:space="preserve">: {DK.</s>
            <s xml:id="echoid-s12189" xml:space="preserve">/2} DT; </s>
            <s xml:id="echoid-s12190" xml:space="preserve">hoc eſt (quo-
              <lb/>
            niam è mox præmonſtratis DS = 2 DT) DH. </s>
            <s xml:id="echoid-s12191" xml:space="preserve">DK:</s>
            <s xml:id="echoid-s12192" xml:space="preserve">: ({DK.</s>
            <s xml:id="echoid-s12193" xml:space="preserve">/2} {DS.</s>
            <s xml:id="echoid-s12194" xml:space="preserve">
              <note symbol="* it" position="left" xlink:label="note-0258-02" xlink:href="note-0258-02a" xml:space="preserve">In 12 hujus.</note>
            :</s>
            <s xml:id="echoid-s12195" xml:space="preserve">:) DK. </s>
            <s xml:id="echoid-s12196" xml:space="preserve">DS. </s>
            <s xml:id="echoid-s12197" xml:space="preserve">Liquet igitur rectam HK tangenti KS perpendicu-
              <lb/>
            larem eſſe: </s>
            <s xml:id="echoid-s12198" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s12199" xml:space="preserve">E. </s>
            <s xml:id="echoid-s12200" xml:space="preserve">D.</s>
            <s xml:id="echoid-s12201" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12202" xml:space="preserve">Ità Propoſiti noſtri priore (quam innuebamus) parte quomodo-
              <lb/>
            t
              <unsure/>
            unque defuncti ſumus. </s>
            <s xml:id="echoid-s12203" xml:space="preserve">Cui ſupplendæ, appendiculæ inſtar, ſub-
              <lb/>
            nectemus à nobis uſitatum methodum ex Calculo tangentes reperien-
              <lb/>
            di. </s>
            <s xml:id="echoid-s12204" xml:space="preserve">Quanquam haud ſcio, poſt tot ejuſmodi pervulgatas atque pro-
              <lb/>
            tritas methodos, an id ex uſu ſit facere. </s>
            <s xml:id="echoid-s12205" xml:space="preserve">Facio ſaltem ex Amici con-
              <lb/>
            ſilio; </s>
            <s xml:id="echoid-s12206" xml:space="preserve">eóque libentiùs, quòd præ cæteris, quas tractavi, compendio-
              <lb/>
            ſa videtur, ac generalis. </s>
            <s xml:id="echoid-s12207" xml:space="preserve">In hunc procedo modum.</s>
            <s xml:id="echoid-s12208" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12209" xml:space="preserve">Sint AP, PM poſitione datæ rectæ lineæ (quarum PM propo-
              <lb/>
            ſitam curvam ſecet in M) & </s>
            <s xml:id="echoid-s12210" xml:space="preserve">MT curvam tangere ponatur ad </s>
          </p>
        </div>
      </text>
    </echo>
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