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

Table of contents

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[31.] Lect. IV.
Page: 222 (29)
[32.] Lect. VII.
Page: 249 (56)
[33.] Lect. VIII.
Page: 256 (63)
[34.] Lect. IX.
Page: 263 (70)
[35.] Lect. X.
Page: 268 (75)
[36.] Exemp. I.
Page: 274 (81)
[37.] _Exemp_. II.
Page: 275 (82)
[38.] _Exemp_. III
Page: 275 (82)
[39.] Exemp. IV.
Page: 276 (83)
[40.] Eæemp. V.
Page: 277 (84)
[41.] Lect. XI.
Page: 278 (85)
[42.] APPENDICUL A.
Page: 287 (94)
[43.] Lect. XII.
Page: 298 (105)
[44.] APPENDICULA 1.
Page: 303 (110)
[45.] Præparatio Communis.
Page: 303 (110)
[46.] APPENDICULA 2.
Page: 308 (115)
[47.] Conicorum Superſicies dimetiendi Metbodus.
Page: 310 (117)
[48.] Exemplum.
Page: 311 (118)
[49.] Prop. 1.
Page: 312 (119)
[50.] Prop. 2.
Page: 312 (119)
[51.] Prop. 3.
Page: 313 (120)
[52.] Prop. 4.
Page: 313 (120)
[53.] APPENDICULA 3.
Page: 314 (121)
[54.] Problema I.
Page: 314 (121)
[55.] Exemp. I.
Page: 314 (121)
[56.] Exemp. II.
Page: 315 (122)
[57.] Probl. II.
Page: 315 (122)
[58.] Exemp. I.
Page: 315 (122)
[59.] _Exemp_. II.
Page: 316 (123)
[60.] _Probl_. III.
Page: 316 (123)
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          <p>
            <s xml:id="echoid-s12482" xml:space="preserve">II. </s>
            <s xml:id="echoid-s12483" xml:space="preserve">Iiſdem poſitis, atque paratis; </s>
            <s xml:id="echoid-s12484" xml:space="preserve">_ſummarectangulorum_ AZ x AE
              <lb/>
            + BZ x BF + CZ x CG, &</s>
            <s xml:id="echoid-s12485" xml:space="preserve">e. </s>
            <s xml:id="echoid-s12486" xml:space="preserve">æquatur _trienti cubi_ ex baſe
              <lb/>
              <note position="left" xlink:label="note-0264-01" xlink:href="note-0264-01a" xml:space="preserve">Fig. 122.</note>
            DH.</s>
            <s xml:id="echoid-s12487" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12488" xml:space="preserve">Nam ob HL. </s>
            <s xml:id="echoid-s12489" xml:space="preserve">LG:</s>
            <s xml:id="echoid-s12490" xml:space="preserve">: PD. </s>
            <s xml:id="echoid-s12491" xml:space="preserve">DH:</s>
            <s xml:id="echoid-s12492" xml:space="preserve">: PD x DH. </s>
            <s xml:id="echoid-s12493" xml:space="preserve">DHq; </s>
            <s xml:id="echoid-s12494" xml:space="preserve">erit HL x
              <lb/>
            DHq = LG x PD x DH. </s>
            <s xml:id="echoid-s12495" xml:space="preserve">hoc eſt HL x HOq = DC x Dψ x
              <lb/>
            DH. </s>
            <s xml:id="echoid-s12496" xml:space="preserve">Similíque diſcurſu, LK x LYq = CB x CZ x CG. </s>
            <s xml:id="echoid-s12497" xml:space="preserve">& </s>
            <s xml:id="echoid-s12498" xml:space="preserve">KI
              <lb/>
            x KYq = BA x BZ x BF, &</s>
            <s xml:id="echoid-s12499" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12500" xml:space="preserve">Verùm HL x HOq + LK x
              <lb/>
            LYq + KI x KYq, &</s>
            <s xml:id="echoid-s12501" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12502" xml:space="preserve">adæquant trientem cubi ex DH; </s>
            <s xml:id="echoid-s12503" xml:space="preserve">itaque
              <lb/>
            liquet Propoſitum.</s>
            <s xml:id="echoid-s12504" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12505" xml:space="preserve">III. </s>
            <s xml:id="echoid-s12506" xml:space="preserve">Simili ratione conſtabit ſummam AZ x AEq + BZ x BFq
              <lb/>
            + CZ x CGq, &</s>
            <s xml:id="echoid-s12507" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12508" xml:space="preserve">æquari τῶ{DH_qq_;</s>
            <s xml:id="echoid-s12509" xml:space="preserve">/4} & </s>
            <s xml:id="echoid-s12510" xml:space="preserve">eſſe ſummam AZ x
              <lb/>
            AE cub. </s>
            <s xml:id="echoid-s12511" xml:space="preserve">+ BZ x BE cub. </s>
            <s xml:id="echoid-s12512" xml:space="preserve">+ CZ x CG cub &</s>
            <s xml:id="echoid-s12513" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12514" xml:space="preserve">= {DH {5/ }/5}; </s>
            <s xml:id="echoid-s12515" xml:space="preserve">ac
              <lb/>
            eodem in continuum tenore.</s>
            <s xml:id="echoid-s12516" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12517" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s12518" xml:space="preserve">Exhinc conſectantur haud aſpernanda _Theoremata_: </s>
            <s xml:id="echoid-s12519" xml:space="preserve">Sit
              <lb/>
            VDψφ ſpatium quodlibet, cujus axis VD, ut dictum, æquiſectus;
              <lb/>
            </s>
            <s xml:id="echoid-s12520" xml:space="preserve">
              <note position="left" xlink:label="note-0264-02" xlink:href="note-0264-02a" xml:space="preserve">Fig. 122.</note>
            ſi concipiantur ſingula ſpatia VAZφ, VBZφ, VCZφ, &</s>
            <s xml:id="echoid-s12521" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12522" xml:space="preserve">in
              <lb/>
            ſuas ordinatas AZ, BZ, CZ, &</s>
            <s xml:id="echoid-s12523" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12524" xml:space="preserve">reſpectivè ſingulas duci, quæ pro-
              <lb/>
            veniet ſumma adæquabitur ipſius ſpatii VDψφ ſemiquadrato.</s>
            <s xml:id="echoid-s12525" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12526" xml:space="preserve">Nam (utì priùs oſtenſum) figuræ VDψ φ adaptari poteſt ſpatium
              <lb/>
            VDH; </s>
            <s xml:id="echoid-s12527" xml:space="preserve">tale nimirum ut ductà quâvis ad curvam VH perpendiculari,
              <lb/>
            ceu EP, ſit AP ſibireſpondenti applicatæ AZ æqualis; </s>
            <s xml:id="echoid-s12528" xml:space="preserve"> unde
              <note position="left" xlink:label="note-0264-03" xlink:href="note-0264-03a" xml:space="preserve">_Præced_. Lect. X.</note>
              <note symbol="(_b_)" position="left" xlink:label="note-0264-04" xlink:href="note-0264-04a" xml:space="preserve">1 _hujus_.</note>
              <note position="left" xlink:label="note-0264-05" xlink:href="note-0264-05a" xml:space="preserve">Fig. 122.</note>
            ſpatium VAZ φ = {AE_q_/2}; </s>
            <s xml:id="echoid-s12529" xml:space="preserve">& </s>
            <s xml:id="echoid-s12530" xml:space="preserve">VBZ φ = {BF_q_;</s>
            <s xml:id="echoid-s12531" xml:space="preserve">/2} & </s>
            <s xml:id="echoid-s12532" xml:space="preserve">VCZ φ = {CG_q_/2}
              <lb/>
            &</s>
            <s xml:id="echoid-s12533" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12534" xml:space="preserve">quapropter omnia VAZφ x AZ + VBZφ x BZ + VCZφ
              <lb/>
            x CZ, &</s>
            <s xml:id="echoid-s12535" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12536" xml:space="preserve">æquabuntur omnibus {AE_q_ x AZ + BF_q_ x BZ + CG_q_ x CZ/2}
              <lb/>
            hoc eſt τῶ {DH_qq_/4 x 2}; </s>
            <s xml:id="echoid-s12537" xml:space="preserve"> hoc eſt τῶ {VDψφ x VDψφ/2.</s>
            <s xml:id="echoid-s12538" xml:space="preserve">}</s>
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          <note symbol="(_c_)" position="left" xml:space="preserve">3 _hujus_.</note>
          <p>
            <s xml:id="echoid-s12539" xml:space="preserve">V. </s>
            <s xml:id="echoid-s12540" xml:space="preserve">Quòd ſi ducantur omnia √ VAZφ, √ VBZφ, √ VCZφ,
              <lb/>
            &</s>
            <s xml:id="echoid-s12541" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12542" xml:space="preserve">in ſuas applicatas AZ, BZ, CZ, &</s>
            <s xml:id="echoid-s12543" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12544" xml:space="preserve">reſpectivè proveniet ag-
              <lb/>
            gregatum æquale duabus tertiis radicis quadratæ facti ex ipſo ſpatio
              <lb/>
            VDψφ cubato (τῶ {2/3} √ VDψφ {3/ })</s>
          </p>
          <p>
            <s xml:id="echoid-s12545" xml:space="preserve">Nam adaptatâ curvâ VH, eſt √ VAZ φ = AE√ {1/2}; </s>
            <s xml:id="echoid-s12546" xml:space="preserve">& </s>
            <s xml:id="echoid-s12547" xml:space="preserve">√ VBZφ
              <lb/>
            = BF √ {1/2}, & </s>
            <s xml:id="echoid-s12548" xml:space="preserve">VCZφ = √ CG √ {1/2}, &</s>
            <s xml:id="echoid-s12549" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12550" xml:space="preserve">Cùm itaque </s>
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