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-s14577" xml:space="preserve">
              <pb o="116" file="0294" n="309" rhead=""/>
            ta recta BD; </s>
            <s xml:id="echoid-s14578" xml:space="preserve">curvam verò tangat recta BT; </s>
            <s xml:id="echoid-s14579" xml:space="preserve">ſitque BP rectæ BD
              <lb/>
            particula indefinitè parva; </s>
            <s xml:id="echoid-s14580" xml:space="preserve">ducatúrque recta POad DTparallela,
              <lb/>
              <note position="left" xlink:label="note-0294-01" xlink:href="note-0294-01a" xml:space="preserve">Fig. 174.</note>
            curvam ſecans ad N; </s>
            <s xml:id="echoid-s14581" xml:space="preserve">dico PNad NOrationem habere majorem quâ-
              <lb/>
            vis deſignabili, puta quàm R ad S.</s>
            <s xml:id="echoid-s14582" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14583" xml:space="preserve">Nam ſit DE. </s>
            <s xml:id="echoid-s14584" xml:space="preserve">ET:</s>
            <s xml:id="echoid-s14585" xml:space="preserve">: RS; </s>
            <s xml:id="echoid-s14586" xml:space="preserve">connexaque recta BEcurvam ſecet in
              <lb/>
            G, rectam POin K; </s>
            <s xml:id="echoid-s14587" xml:space="preserve">per G verò ducatur FHad DAparallela.
              <lb/>
            </s>
            <s xml:id="echoid-s14588" xml:space="preserve">quoniam igitur BP ponitur indefinitè parva, eſt BP &</s>
            <s xml:id="echoid-s14589" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s14590" xml:space="preserve">BF; </s>
            <s xml:id="echoid-s14591" xml:space="preserve">adeóq; </s>
            <s xml:id="echoid-s14592" xml:space="preserve">
              <lb/>
            PK &</s>
            <s xml:id="echoid-s14593" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s14594" xml:space="preserve">PN (nam ſubtenſa BGintra curvam tota cadit). </s>
            <s xml:id="echoid-s14595" xml:space="preserve">ergo PN. </s>
            <s xml:id="echoid-s14596" xml:space="preserve">
              <lb/>
            NO &</s>
            <s xml:id="echoid-s14597" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s14598" xml:space="preserve">PK. </s>
            <s xml:id="echoid-s14599" xml:space="preserve">KO:</s>
            <s xml:id="echoid-s14600" xml:space="preserve">: DE. </s>
            <s xml:id="echoid-s14601" xml:space="preserve">ET:</s>
            <s xml:id="echoid-s14602" xml:space="preserve">: R.</s>
            <s xml:id="echoid-s14603" xml:space="preserve">S.</s>
            <s xml:id="echoid-s14604" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14605" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s14606" xml:space="preserve">Hinc, ſi baſis DBin partes ſecetur indeſinitè multas ad puncta
              <lb/>
            Z; </s>
            <s xml:id="echoid-s14607" xml:space="preserve">& </s>
            <s xml:id="echoid-s14608" xml:space="preserve">per hæc ducantur rectæ ad DAparallelæ curvam ſecantes pun-
              <lb/>
            ctis E, F, G; </s>
            <s xml:id="echoid-s14609" xml:space="preserve">per hæc verò ducantur _Tangentes_ BQ, ER, FS, GT
              <lb/>
            parallelis ZE, ZF, ZG, DA occurrentes punctis Q, R, S, T;
              <lb/>
            </s>
            <s xml:id="echoid-s14610" xml:space="preserve">habebit recta ADad omnes interceptas EQ, FR, GS, AT(ſi-
              <lb/>
            mul ſumptas) rationem quàvis aſſignabili majorem.</s>
            <s xml:id="echoid-s14611" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14612" xml:space="preserve">Nam ducantur rectæ EY, FX, GV ad BD parallelæ. </s>
            <s xml:id="echoid-s14613" xml:space="preserve">Habent
              <lb/>
            igitur rectæ ZE, YF, XG, VA ad rectas EQ, FR, GS, AT (ſin-
              <lb/>
              <note position="left" xlink:label="note-0294-02" xlink:href="note-0294-02a" xml:space="preserve">Fig. 175.</note>
            gulæ ad ſingulas ſibi in directum poſitas reſpectivè) rationem deſigna-
              <lb/>
            bili quâcunque majorem. </s>
            <s xml:id="echoid-s14614" xml:space="preserve">ergò ſimul omnes iſtæ ad has ſimul omnes
              <lb/>
            _rationem_ habent deſignabili quâvis _majorem;_ </s>
            <s xml:id="echoid-s14615" xml:space="preserve">hoc eſt recta AD ad EQ
              <lb/>
            + FR + GS + AT ejuſmodi rationem habet.</s>
            <s xml:id="echoid-s14616" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14617" xml:space="preserve">V. </s>
            <s xml:id="echoid-s14618" xml:space="preserve">Hinc inter computandum, omnes EQ, FR, GS, AT ſimul ac-
              <lb/>
            ceptæ nihilo æquivalent; </s>
            <s xml:id="echoid-s14619" xml:space="preserve">ſeu rectæ ZE, ZQ; </s>
            <s xml:id="echoid-s14620" xml:space="preserve">& </s>
            <s xml:id="echoid-s14621" xml:space="preserve">ZF, YR, &</s>
            <s xml:id="echoid-s14622" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14623" xml:space="preserve">æ-
              <lb/>
            quantur; </s>
            <s xml:id="echoid-s14624" xml:space="preserve">item tangentium particulæ BQ, ER, &</s>
            <s xml:id="echoid-s14625" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14626" xml:space="preserve">reſpectivis _curvœ_
              <lb/>
            portiunculis BE, EF, &</s>
            <s xml:id="echoid-s14627" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14628" xml:space="preserve">pares, & </s>
            <s xml:id="echoid-s14629" xml:space="preserve">quaſi coincidentes haberi poſſunt.
              <lb/>
            </s>
            <s xml:id="echoid-s14630" xml:space="preserve">quin & </s>
            <s xml:id="echoid-s14631" xml:space="preserve">adſumere tutò licet, quæ evidentèr his cohærent.</s>
            <s xml:id="echoid-s14632" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s14633" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s14634" xml:space="preserve">Sit porrò _curva_ quævis AB, cujus _Axis_ AD, & </s>
            <s xml:id="echoid-s14635" xml:space="preserve">ad hunc
              <lb/>
              <note position="left" xlink:label="note-0294-03" xlink:href="note-0294-03a" xml:space="preserve">Fig. 176.</note>
            applicata DB; </s>
            <s xml:id="echoid-s14636" xml:space="preserve">æquiſecetur autem DB in partes indefinitè multas ad
              <lb/>
            puncta Z, per quæ ducantur rectæ ad AD parallelæ, curvam AB
              <lb/>
            interſecantes punctis X; </s>
            <s xml:id="echoid-s14637" xml:space="preserve">quibus occurrant per ipſa X ductæ ad BD
              <lb/>
            parallelæ rectæ ME, NF, OG, PH; </s>
            <s xml:id="echoid-s14638" xml:space="preserve">ſit autem ſegmento ADB
              <lb/>
            (rectis AD, DB, & </s>
            <s xml:id="echoid-s14639" xml:space="preserve">curvâ AB comprehenſo) _circumſcripta ſigura_
              <lb/>
            ADBMXNXOXPXRA major _ſpatio_ quodam S; </s>
            <s xml:id="echoid-s14640" xml:space="preserve">dico _ſegmentum_
              <lb/>
            ADB non eſſe minus quàm S.</s>
            <s xml:id="echoid-s14641" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14642" xml:space="preserve">Nam ſi ſieripoteſt ſit ADB minus quàm S exceſſu _rectangulaum_
              <lb/>
            ADLKadæquante, & </s>
            <s xml:id="echoid-s14643" xml:space="preserve">quoniam AReſt indefinitè parva, adeóque
              <lb/>
            minor quàm AK, liquet rectangulum ADZRminus eſſe </s>
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