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-s14397" xml:space="preserve">
              <pb o="113" file="0291" n="306" rhead=""/>
            C 2 ſecans in I, _byperbolam_ in K) & </s>
            <s xml:id="echoid-s14398" xml:space="preserve">connectatur CK; </s>
            <s xml:id="echoid-s14399" xml:space="preserve">erit ſpatium
              <lb/>
            ACIYA _ſectoris byperbolici_ ECK duplum.</s>
            <s xml:id="echoid-s14400" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14401" xml:space="preserve">Nam eſt CIq. </s>
            <s xml:id="echoid-s14402" xml:space="preserve">CAq :</s>
            <s xml:id="echoid-s14403" xml:space="preserve">: ASq. </s>
            <s xml:id="echoid-s14404" xml:space="preserve">CAq:</s>
            <s xml:id="echoid-s14405" xml:space="preserve">: FMq. </s>
            <s xml:id="echoid-s14406" xml:space="preserve">CFq:</s>
            <s xml:id="echoid-s14407" xml:space="preserve">: CAq
              <lb/>
              <note position="right" xlink:label="note-0291-01" xlink:href="note-0291-01a" xml:space="preserve">Fig. 169.</note>
            - CFq. </s>
            <s xml:id="echoid-s14408" xml:space="preserve">CFq. </s>
            <s xml:id="echoid-s14409" xml:space="preserve">componendóque CIq + CAq. </s>
            <s xml:id="echoid-s14410" xml:space="preserve">CAq:</s>
            <s xml:id="echoid-s14411" xml:space="preserve">:
              <lb/>
            CAq. </s>
            <s xml:id="echoid-s14412" xml:space="preserve">CFq. </s>
            <s xml:id="echoid-s14413" xml:space="preserve">hoc eſt (ex _byperbolœ_ natura) IKq. </s>
            <s xml:id="echoid-s14414" xml:space="preserve">CAq:</s>
            <s xml:id="echoid-s14415" xml:space="preserve">: CAq.
              <lb/>
            </s>
            <s xml:id="echoid-s14416" xml:space="preserve">CFq. </s>
            <s xml:id="echoid-s14417" xml:space="preserve">vel IK. </s>
            <s xml:id="echoid-s14418" xml:space="preserve">CE :</s>
            <s xml:id="echoid-s14419" xml:space="preserve">: CE. </s>
            <s xml:id="echoid-s14420" xml:space="preserve">IY. </s>
            <s xml:id="echoid-s14421" xml:space="preserve">itaque _ſpatium_ ACIYA _ſectoris_
              <lb/>
            ECK duplum eſſe perſpicuum eſt è præcedente.</s>
            <s xml:id="echoid-s14422" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14423" xml:space="preserve">XI. </s>
            <s xml:id="echoid-s14424" xml:space="preserve">_Coroll_. </s>
            <s xml:id="echoid-s14425" xml:space="preserve">Hinc ſi Polo E, _Cbordà_ CB, _Sagittâ_ CAdeſcripta ſit
              <lb/>
            _Concbois_ AVV, cui occurrat YFM producta in V; </s>
            <s xml:id="echoid-s14426" xml:space="preserve">erit MV = FY;
              <lb/>
            </s>
            <s xml:id="echoid-s14427" xml:space="preserve">adeóque _ſpatium_ AMV _ſpatio_ AFY æquatur.</s>
            <s xml:id="echoid-s14428" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14429" xml:space="preserve">XII.</s>
            <s xml:id="echoid-s14430" xml:space="preserve">Unde _ſpatiorum_ ejuſmodi _Conchoidalium dim@nſiones_ innoteſcunt.</s>
            <s xml:id="echoid-s14431" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14432" xml:space="preserve">XIII. </s>
            <s xml:id="echoid-s14433" xml:space="preserve">Neſcio, an _operæ_ ſit hoc adjicere _Corollarium_.</s>
            <s xml:id="echoid-s14434" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14435" xml:space="preserve">XIII. </s>
            <s xml:id="echoid-s14436" xml:space="preserve">Sit recta AErectæ RSperpendicularis; </s>
            <s xml:id="echoid-s14437" xml:space="preserve">& </s>
            <s xml:id="echoid-s14438" xml:space="preserve">CE = CA;
              <lb/>
            </s>
            <s xml:id="echoid-s14439" xml:space="preserve">ſintque duæ (ſibimet inverſæ) _conchoides_ AZZ, EYY ad eundem
              <lb/>
            _polum_ E, _communémque regulam_ RS deſcriptæ, ab E verò ducatur
              <lb/>
              <note position="right" xlink:label="note-0291-02" xlink:href="note-0291-02a" xml:space="preserve">Fig. 170.</note>
            utcunque recta EYZ (lineas interſecans, ut vides) ſit etiam _byperbole_
              <lb/>
            _œquilatera_, EKK, cujus _centrum_ C, _ſemiaxis_ CE; </s>
            <s xml:id="echoid-s14440" xml:space="preserve">du&</s>
            <s xml:id="echoid-s14441" xml:space="preserve">âque IK
              <lb/>
            ad AE parallelâ, connectatur CK, erit _ſpatium quadrilineum_
              <lb/>
            AEOYZPA (rectis AE, YZ, & </s>
            <s xml:id="echoid-s14442" xml:space="preserve">_concbis_ EOY, APZ compre-
              <lb/>
            henſum) æquale _quadruplo ſectori Hyperbolico_ ECK.</s>
            <s xml:id="echoid-s14443" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14444" xml:space="preserve">Nam ſi _centro_ E per C ducatur _arcus circularis_ CX; </s>
            <s xml:id="echoid-s14445" xml:space="preserve">è dictis faci-
              <lb/>
            lè colligetur _ſpatium_ APZIC æquari _duplo ſectori hyperbolico_ ECK
              <lb/>
            unà cum _ſectore circulari_ CEX. </s>
            <s xml:id="echoid-s14446" xml:space="preserve">item _ſpatium_ EOYIC æquari _duplo_
              <lb/>
            _ſectori_ ECK, _dempto ſectore_ CEX.</s>
            <s xml:id="echoid-s14447" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14448" xml:space="preserve">Ità quoque facile colligas. </s>
            <s xml:id="echoid-s14449" xml:space="preserve">Ducantur ZF, YGad CS parallelæ;
              <lb/>
            </s>
            <s xml:id="echoid-s14450" xml:space="preserve">& </s>
            <s xml:id="echoid-s14451" xml:space="preserve">protrahantur GYL, LIH. </s>
            <s xml:id="echoid-s14452" xml:space="preserve">ac ob IY = IZ, eſt FZ + GY =
              <lb/>
            2 CI. </s>
            <s xml:id="echoid-s14453" xml:space="preserve">& </s>
            <s xml:id="echoid-s14454" xml:space="preserve">_trapezium_ FGYZ = _rectang._ </s>
            <s xml:id="echoid-s14455" xml:space="preserve">EGLH = 2 CG x CI. </s>
            <s xml:id="echoid-s14456" xml:space="preserve">
              <lb/>
            ergò patet.</s>
            <s xml:id="echoid-s14457" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14458" xml:space="preserve">Adnotari poteſt, ſi lubet, ductâ ATad CSparallelâ, protractâ-
              <lb/>
            que EZT, ſi ponatur N = 2 triang. </s>
            <s xml:id="echoid-s14459" xml:space="preserve">CEI - 2 ſect. </s>
            <s xml:id="echoid-s14460" xml:space="preserve">ECK; </s>
            <s xml:id="echoid-s14461" xml:space="preserve">fore
              <lb/>
            ſpat EZT + EOYE = 2 N.</s>
            <s xml:id="echoid-s14462" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14463" xml:space="preserve">Nempe N + CXI = ſpat. </s>
            <s xml:id="echoid-s14464" xml:space="preserve">AZT. </s>
            <s xml:id="echoid-s14465" xml:space="preserve">& </s>
            <s xml:id="echoid-s14466" xml:space="preserve">N - CXI = ſpat.
              <lb/>
            </s>
            <s xml:id="echoid-s14467" xml:space="preserve">EOY E.</s>
            <s xml:id="echoid-s14468" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14469" xml:space="preserve">XIV. </s>
            <s xml:id="echoid-s14470" xml:space="preserve">Adjiciemus etiam hiſce cognatam _Ciſſoidalis ſpatii_ dimenſio-
              <lb/>
            nem.</s>
            <s xml:id="echoid-s14471" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14472" xml:space="preserve">Sit _Semicirculus_ AMB (cujus centrum C) quem tangat recta
              <lb/>
              <note position="right" xlink:label="note-0291-03" xlink:href="note-0291-03a" xml:space="preserve">Fig. 171.</note>
            AH; </s>
            <s xml:id="echoid-s14473" xml:space="preserve">eique congruens _Ciſſois_ AZZ cujus ſcilicet hæc proprietas </s>
          </p>
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