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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[71.] _Theor_. IV.
Page: 321 (128)
[72.] _Theor_. V.
Page: 322 (129)
[73.] _Theor_. VI.
Page: 323 (130)
[74.] _Theor_. VII.
Page: 323 (130)
[75.] Lect. XIII.
Page: 324 (131)
[76.] Æquationum Series prima.
Page: 324 (131)
[77.] _Notetur autem_,
Page: 325 (132)
[78.] Series ſecunda.
Page: 325 (132)
[79.] Not.
Page: 326 (133)
[80.] Series tertia.
Page: 326 (133)
[81.] Not.
Page: 327 (134)
[82.] Not.
Page: 328 (135)
[83.] Series quarta.
Page: 329 (136)
[84.] Not.
Page: 329 (136)
[85.] Series quinta.
Page: 330 (137)
[86.] Series ſexta.
Page: 331 (138)
[87.] Not.
Page: 331 (138)
[88.] Series ſeptima.
Page: 332 (139)
[89.] Not.
Page: 332 (139)
[90.] Series octava.
Page: 333 (140)
[91.] Series nona.
Page: 333 (140)
[92.] Not.
Page: 333 (140)
[93.] Series decima.
Page: 334 (141)
[94.] Series undecima.
Page: 335 (142)
[95.] Not.
Page: 335 (142)
[96.] Series duodecima
Page: 336 (143)
[97.] Series decima tertia
Page: 336 (143)
[98.] Not.
Page: 336 (143)
[99.] Laus DEOO ptimo Maximo. FINIS.
Page: 340 (147)
[100.] ERRATA
Page: 341
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            <s xml:id="echoid-s897" xml:space="preserve">Pro refractione vero: </s>
            <s xml:id="echoid-s898" xml:space="preserve">Incidat radius AB medio EF in B; </s>
            <s xml:id="echoid-s899" xml:space="preserve">& </s>
            <s xml:id="echoid-s900" xml:space="preserve">iſthic
              <lb/>
            refringatur in B _a_ dico permutatim radium _a_ B regredientem in BA
              <lb/>
            refringi. </s>
            <s xml:id="echoid-s901" xml:space="preserve">Nam per occurſum B ducatur QBP media dirimenti EF
              <lb/>
              <note position="left" xlink:label="note-0042-01" xlink:href="note-0042-01a" xml:space="preserve">Fig. 20.</note>
            perpendicularis; </s>
            <s xml:id="echoid-s902" xml:space="preserve">& </s>
            <s xml:id="echoid-s903" xml:space="preserve">in hac utcunque ſumpto puncto P ducatur PG
              <lb/>
            ad AB protractam perpendicularis, ut & </s>
            <s xml:id="echoid-s904" xml:space="preserve">PH ad B _a_; </s>
            <s xml:id="echoid-s905" xml:space="preserve">& </s>
            <s xml:id="echoid-s906" xml:space="preserve">produca-
              <lb/>
            tur _a_ BS. </s>
            <s xml:id="echoid-s907" xml:space="preserve">Eſt ergo PG ſinus rectus anguli incidentiæ ABQ ad
              <lb/>
            radium BP; </s>
            <s xml:id="echoid-s908" xml:space="preserve">& </s>
            <s xml:id="echoid-s909" xml:space="preserve">PH ſinus anguli refracti QBS ad eundem radium
              <lb/>
            BP. </s>
            <s xml:id="echoid-s910" xml:space="preserve">Cùm ìtaque ratio PG ad PH refractionem metiatur è ſuperiori
              <lb/>
            medio factam in inferius; </s>
            <s xml:id="echoid-s911" xml:space="preserve">etiam viciſſim rectarum PH, PG propor-
              <lb/>
            tio refractionem determinabit ab inferiori medio factam in ſuperius.
              <lb/>
            </s>
            <s xml:id="echoid-s912" xml:space="preserve">Unde ſi radius _a_ B jam ponatur incidens; </s>
            <s xml:id="echoid-s913" xml:space="preserve">cùm ſint PH, PG recti ſi-
              <lb/>
            nus anguli incidentiæ PBH, & </s>
            <s xml:id="echoid-s914" xml:space="preserve">anguli PBG, liquidum eſt ipſam HB
              <lb/>
            in BA refringi.</s>
            <s xml:id="echoid-s915" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s916" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s917" xml:space="preserve">Angulo incidentiæ majori major competit angulus inflexus.
              <lb/>
            </s>
            <s xml:id="echoid-s918" xml:space="preserve">(Angulum inflexum vocito, qui à perpendiculari continetur & </s>
            <s xml:id="echoid-s919" xml:space="preserve">in-
              <lb/>
            flexo; </s>
            <s xml:id="echoid-s920" xml:space="preserve">is proinde reſpectivè dicitur angulus reflexus, vel refractus. </s>
            <s xml:id="echoid-s921" xml:space="preserve">
              <lb/>
            Angulus autem inflectionis (hoc eſt reflectionis reſpectivè, vel refracti-
              <lb/>
            onis) appellatur is, qui comprehenditur ab incidente & </s>
            <s xml:id="echoid-s922" xml:space="preserve">inflexo; </s>
            <s xml:id="echoid-s923" xml:space="preserve">inci-
              <lb/>
            dentiæ verò, nè quis ſecùs accipiat, apud nos angulus eſt, quem con-
              <lb/>
            tinent incidens & </s>
            <s xml:id="echoid-s924" xml:space="preserve">perpendicularis.) </s>
            <s xml:id="echoid-s925" xml:space="preserve">Quod propoſitum ſpectat effatum,
              <lb/>
            id è poſitis principiis manifeſtè conſectatur. </s>
            <s xml:id="echoid-s926" xml:space="preserve">Etenim in reflectione
              <lb/>
            ipſi anguli reflexi angulis incidentiæ proportionales ſunt; </s>
            <s xml:id="echoid-s927" xml:space="preserve">in refracti-
              <lb/>
            one ſaltem recti ſinus angulorum refractorum ſinubus angulorum in-
              <lb/>
            cidentiæ proportionantur. </s>
            <s xml:id="echoid-s928" xml:space="preserve">Unde liquido conſtat propoſitum: </s>
            <s xml:id="echoid-s929" xml:space="preserve">quorſum
              <lb/>
            verba, quorſum Schemata multiplicem?</s>
            <s xml:id="echoid-s930" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s931" xml:space="preserve">V. </s>
            <s xml:id="echoid-s932" xml:space="preserve">Cùm incidentes ad ſuperficiem mediam ſeſe decuſſant, iidem
              <lb/>
            ſeſe inflectionem paſſi decuſſabunt, eodem ordine ſervato, quem directè
              <lb/>
            progedientes habuiſſent (utique ſic ut perpendiculari poſt inflectionem
              <lb/>
            propior incedat qui propior antea fuit.)</s>
            <s xml:id="echoid-s933" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s934" xml:space="preserve">Hæc propoſitio reverà non differt à præcedente; </s>
            <s xml:id="echoid-s935" xml:space="preserve">quò demirer
              <lb/>
              <note position="left" xlink:label="note-0042-02" xlink:href="note-0042-02a" xml:space="preserve">_Herig. Diop. 8_.</note>
            eam à non nemine principia noſtra uſurpante aliunde compro-
              <lb/>
            bari.</s>
            <s xml:id="echoid-s936" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s937" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s938" xml:space="preserve">Angulo incidentiæ majori major convenit angul@s inflectionis.
              <lb/>
            </s>
            <s xml:id="echoid-s939" xml:space="preserve">Quoad refiectionem, res extra dubium evidens eſt; </s>
            <s xml:id="echoid-s940" xml:space="preserve">angulus enim refle-
              <lb/>
            ctionis incidentiæ majori conveniens eum planè continet, qui minori
              <lb/>
            incidentiæ reſpondet. </s>
            <s xml:id="echoid-s941" xml:space="preserve">Pro refractione vero: </s>
            <s xml:id="echoid-s942" xml:space="preserve">ſit recta QBP refrin-
              <lb/>
            genti perpendicularis; </s>
            <s xml:id="echoid-s943" xml:space="preserve">incidant autem radii ABG, DBH (ſcilicet </s>
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