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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[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
[101.] Addenda Lectionibus Geometricis.
Page: 342 (149)
[102.] _Probl_. I.
Page: 342 (149)
[103.] _Probl_. II.
Page: 342 (149)
[104.] _Probl_. III.
Page: 342 (149)
[105.] Addenda Lectionibus Geometricis.
Page: 343 (150)
[106.] _Theor_. I.
Page: 343 (150)
[107.] _Theor_. II.
Page: 343 (150)
[108.] _Theor_. III.
Page: 343 (150)
[109.] _Theor_. IV.
Page: 344 (151)
[110.] _Theor_. V.
Page: 344 (151)
[111.] _Theor_. VI.
Page: 344 (151)
[112.] FINIS.
Page: 344 (151)
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        <div xml:id="echoid-div588" type="section" level="1" n="105">
          <head xml:id="echoid-head109" style="it" xml:space="preserve">Addenda Lectionibus Geometricis.</head>
          <p>
            <s xml:id="echoid-s16514" xml:space="preserve">Inſervit hoc ſuperficiebus deſignandis, quarum in promptu ſit di-
              <lb/>
            menſio, etenim (ductâ ME ad AD parallelâ) Superficies Solidi
              <lb/>
            ex plani BM E circa axem DB rotatu progeniti adæquat {Periph/Rad}
              <lb/>
            x GD X; </s>
            <s xml:id="echoid-s16515" xml:space="preserve">ut habetur in 11
              <emph style="sub">a</emph>
            Lectionis XII.</s>
            <s xml:id="echoid-s16516" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s16517" xml:space="preserve">In Lect. </s>
            <s xml:id="echoid-s16518" xml:space="preserve">XI. </s>
            <s xml:id="echoid-s16519" xml:space="preserve">appendice, numero XXXIII. </s>
            <s xml:id="echoid-s16520" xml:space="preserve">de Cycloide profer-
              <lb/>
            tur Tbeorema quoddam, id quod ex bujuſmodi generaliori
              <lb/>
            Tbeoremate deduci potuiſſet.</s>
            <s xml:id="echoid-s16521" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16522" xml:space="preserve">SI t AM B curva quælibet, cujus Axis AD , baſis DB , ſit item
              <lb/>
              <note position="left" xlink:label="note-0328-01" xlink:href="note-0328-01a" xml:space="preserve">Fig. 223.</note>
            curva AN E talis, ut ſi arbitrariè ducatur PM N ad DB E pa-
              <lb/>
            rallela, poſitoque rectam TN curvam AN E tangere, ſit TN parallela
              <lb/>
            ſubtenſæ AM ; </s>
            <s xml:id="echoid-s16523" xml:space="preserve">completo Rectangulo AD EG erit Spatium trili-
              <lb/>
            neum AE G æquale Segmento AD B.</s>
            <s xml:id="echoid-s16524" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s16525" xml:space="preserve">Huic ſuppar Theorema tale eſt: </s>
            <s xml:id="echoid-s16526" xml:space="preserve">liſdem poſitis, ſi tam Segmentum
              <lb/>
            AD B, quam Spatium AE G circa Axem AG convertantur; </s>
            <s xml:id="echoid-s16527" xml:space="preserve">erit
              <lb/>
            productum è Segmento AD BS olidum producti ex AE G duplum.</s>
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          <p>
            <s xml:id="echoid-s16529" xml:space="preserve">E tangentium porrò contemplatione ſuborta eſt methodus, per
              <lb/>
            quam expediſſimè plurima circa maximas quantitates Theoremata
              <lb/>
            deducuntur; </s>
            <s xml:id="echoid-s16530" xml:space="preserve">quæ certè ſi tempeſtivè ſe objeciſſent, digna cenſuiſſem
              <lb/>
            quæ Lectionibus inſererentur, ex iis indigitabo nonnulla.</s>
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            <s xml:id="echoid-s16532" xml:space="preserve">Sit curva quæpiam AL B, cujus Axis AD , baſis DB ; </s>
            <s xml:id="echoid-s16533" xml:space="preserve">& </s>
            <s xml:id="echoid-s16534" xml:space="preserve">huic
              <lb/>
              <note position="right" xlink:label="note-0328-02" xlink:href="note-0328-02a" xml:space="preserve">Fig. 224.</note>
            parallelæ LG , λ γ; </s>
            <s xml:id="echoid-s16535" xml:space="preserve">item LT curvam tangat.</s>
            <s xml:id="echoid-s16536" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div591" type="section" level="1" n="106">
          <head xml:id="echoid-head110" xml:space="preserve">_Theor_. I.</head>
          <p>
            <s xml:id="echoid-s16537" xml:space="preserve">Sit _m_ numerus quicunque, poteſtates exponens; </s>
            <s xml:id="echoid-s16538" xml:space="preserve">ſi ponatur
              <lb/>
            DG {_m_ - 1/} x TG = GL {_m_/}, erit DG {_m_/} + GL {_m_/} maximum, ſeu
              <lb/>
            majus quam D γ {_m_/} + γ λ {_m_/}.</s>
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          <head xml:id="echoid-head111" xml:space="preserve">_Theor_. II.</head>
          <p>
            <s xml:id="echoid-s16540" xml:space="preserve">Itidem ſumpto numero _m_, ſi ponatur BL {_m_ - 1/} x TL = GL {_m_/};
              <lb/>
            </s>
            <s xml:id="echoid-s16541" xml:space="preserve">erit GL {_m_/} + BL {_m_/} maximum ſeu majus quam γ λ {_m_/} + B λ {_m_/}.</s>
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          <head xml:id="echoid-head112" xml:space="preserve">_Theor_. III.</head>
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            <s xml:id="echoid-s16543" xml:space="preserve">Sint numeri quilibet _m_, _n_; </s>
            <s xml:id="echoid-s16544" xml:space="preserve">ſi ponatur _m_ x TG = _n_ x DG , erit
              <lb/>
            DG {_m_/} x GL {_n_/} maximum, ſeu majus quam D γ {_m_/} x γ λ {_n_/}.</s>
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