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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          <head xml:id="echoid-head59" style="it" xml:space="preserve">Exemp. II.</head>
          <p>
            <s xml:id="echoid-s14836" xml:space="preserve">Sit curva AEG (cnjus Axis AD) proprietate talis, ut ſi à quo-
              <lb/>
            cunque puncto in ipſa ſumpto E, ducatur recta EPad AD normalis;
              <lb/>
            </s>
            <s xml:id="echoid-s14837" xml:space="preserve">
              <note position="left" xlink:label="note-0300-01" xlink:href="note-0300-01a" xml:space="preserve">Fig. 182.</note>
            connectatúrque AE, ſit AEinter deſignatam AR, & </s>
            <s xml:id="echoid-s14838" xml:space="preserve">APpropor-
              <lb/>
            tione media, ſecundum ordinem, cujus exponens ſit {_n_/_m_}; </s>
            <s xml:id="echoid-s14839" xml:space="preserve">reperiatur
              <lb/>
            curva AMB, quam tangat TMad AEparallela.</s>
            <s xml:id="echoid-s14840" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14841" xml:space="preserve">De curva AMadnoto fore _n. </s>
            <s xml:id="echoid-s14842" xml:space="preserve">m_:</s>
            <s xml:id="echoid-s14843" xml:space="preserve">: AE. </s>
            <s xml:id="echoid-s14844" xml:space="preserve">arc. </s>
            <s xml:id="echoid-s14845" xml:space="preserve">AM.</s>
            <s xml:id="echoid-s14846" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14847" xml:space="preserve">Si {_n_/_m_} = {1/2} (vel AEſit inter AR, AP ſimpliciter media) erit
              <lb/>
            AEG circulus, & </s>
            <s xml:id="echoid-s14848" xml:space="preserve">AMB _Ciclois primaria_; </s>
            <s xml:id="echoid-s14849" xml:space="preserve">hujus igitur dimenſio è
              <lb/>
            lege generali habetur.</s>
            <s xml:id="echoid-s14850" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14851" xml:space="preserve">Hæc etiam ex adjuncto _Problemate_ magis ccomprehenſivo pera-
              <lb/>
            guntur.</s>
            <s xml:id="echoid-s14852" xml:space="preserve"/>
          </p>
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          <head xml:id="echoid-head60" style="it" xml:space="preserve">Probl. II.</head>
          <p>
            <s xml:id="echoid-s14853" xml:space="preserve">Curva deſignetur, puta AMB, cujus _axis_ AD, ità ut in hac
              <lb/>
              <note position="left" xlink:label="note-0300-02" xlink:href="note-0300-02a" xml:space="preserve">Fig. 183.</note>
            ſumpto puncto quopiam M, & </s>
            <s xml:id="echoid-s14854" xml:space="preserve">ductâ MPad AD perpendiculâri, & </s>
            <s xml:id="echoid-s14855" xml:space="preserve">
              <lb/>
            poſito rectam MT ipſam tangere, habeant TP, PM relationem aſ-
              <lb/>
            ſignatam.</s>
            <s xml:id="echoid-s14856" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14857" xml:space="preserve">Accipiatur recta quæpiam R, & </s>
            <s xml:id="echoid-s14858" xml:space="preserve">fiat ut TPad PM (quam utique
              <lb/>
            rationem aſſignatâ dabit relatio) ità R ad PY (quæ nempe ſumatur
              <lb/>
            in recta PM, & </s>
            <s xml:id="echoid-s14859" xml:space="preserve">ad axem ADordinetur) ſic ut per ejuſmodi puncta
              <lb/>
            Y tranſeat curva YYK; </s>
            <s xml:id="echoid-s14860" xml:space="preserve">tum ſi ſiat PM = {ſpat. </s>
            <s xml:id="echoid-s14861" xml:space="preserve">APY/R}; </s>
            <s xml:id="echoid-s14862" xml:space="preserve">de curvæ
              <lb/>
            AMB indè conſtabit natura.</s>
            <s xml:id="echoid-s14863" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div500" type="section" level="1" n="58">
          <head xml:id="echoid-head61" style="it" xml:space="preserve">Exemp. I.</head>
          <p>
            <s xml:id="echoid-s14864" xml:space="preserve">Sit ADG _circuli_ quadrans; </s>
            <s xml:id="echoid-s14865" xml:space="preserve">cujus radius æquetur deſignatæ R; </s>
            <s xml:id="echoid-s14866" xml:space="preserve">& </s>
            <s xml:id="echoid-s14867" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0300-03" xlink:href="note-0300-03a" xml:space="preserve">Fig. 184.</note>
            habere debeat TPad PM rationem eandem quam habet R ad arcum
              <lb/>
            AE; </s>
            <s xml:id="echoid-s14868" xml:space="preserve">ergo quum ſit, juxta præſcriptum, R. </s>
            <s xml:id="echoid-s14869" xml:space="preserve">arc. </s>
            <s xml:id="echoid-s14870" xml:space="preserve">AE:</s>
            <s xml:id="echoid-s14871" xml:space="preserve">: R. </s>
            <s xml:id="echoid-s14872" xml:space="preserve">PY; </s>
            <s xml:id="echoid-s14873" xml:space="preserve">e-
              <lb/>
            rit PY = arc. </s>
            <s xml:id="echoid-s14874" xml:space="preserve">AE; </s>
            <s xml:id="echoid-s14875" xml:space="preserve">hinc habetur PM = {APY/R}</s>
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