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-s8991" xml:space="preserve">
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            modi ſuppoſita linearum generatione poterimus indipiſci. </s>
            <s xml:id="echoid-s8992" xml:space="preserve">Simpli-
              <lb/>
            citatis autem & </s>
            <s xml:id="echoid-s8993" xml:space="preserve">perſpicuitatis cauſâ ſupponamus alterum ex his
              <lb/>
            motibus, rectæ nimirum paralleliſmum ſervantis, eſſe ſemper uni-
              <lb/>
            formem, & </s>
            <s xml:id="echoid-s8994" xml:space="preserve">quænam ex alterius quoad velocitatem generalibus
              <lb/>
            differentiis generales emergant linearum productarum affectiones ad-
              <lb/>
            nitamur elicere. </s>
            <s xml:id="echoid-s8995" xml:space="preserve">Adnitamur inquam, at proxima lectione.</s>
            <s xml:id="echoid-s8996" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div222" type="section" level="1" n="31">
          <head xml:id="echoid-head34" xml:space="preserve">
            <emph style="sc">Lect</emph>
          . IV.</head>
          <p>
            <s xml:id="echoid-s8997" xml:space="preserve">Propoſitum eſt nobis è compoſitione motuum (qualem proximè
              <lb/>
            deſcripſimus) emergentes linearum affectiones indagare ac ex-
              <lb/>
              <note position="right" xlink:label="note-0207-01" xlink:href="note-0207-01a" xml:space="preserve">Fig. 18.</note>
            ponere. </s>
            <s xml:id="echoid-s8998" xml:space="preserve">Quorſum imprimìs methodi cauſà repeto ſi recta AZ per
              <lb/>
            rectam AY ſibi perpetuò parallela feratur uniformiter, et in ea
              <lb/>
            quoque punctum M uniformiter deportetur, quâvis velocitate, li-
              <lb/>
            nea recta proveniet. </s>
            <s xml:id="echoid-s8999" xml:space="preserve">Sumantur enim duæ quævis lineæ mobilis
              <lb/>
            AZ poſitiones, ad B ſcilicet & </s>
            <s xml:id="echoid-s9000" xml:space="preserve">C; </s>
            <s xml:id="echoid-s9001" xml:space="preserve">& </s>
            <s xml:id="echoid-s9002" xml:space="preserve">quia motus per AY po-
              <lb/>
            nitur uniformis, erunt decurſa ſpatia AB, AC ad ſe, ut _Tempo-_
              <lb/>
            _ra_; </s>
            <s xml:id="echoid-s9003" xml:space="preserve">ſed et ob motum uniformem puncti M etiam rectæ BM,
              <lb/>
            CM ſe habebunt ut eadem tempora; </s>
            <s xml:id="echoid-s9004" xml:space="preserve">eſt igitur AB. </s>
            <s xml:id="echoid-s9005" xml:space="preserve">AC:</s>
            <s xml:id="echoid-s9006" xml:space="preserve">:
              <lb/>
            BM. </s>
            <s xml:id="echoid-s9007" xml:space="preserve">CM. </s>
            <s xml:id="echoid-s9008" xml:space="preserve">Unde liquet puncta A, M, M in una recta linea ex-
              <lb/>
            iſtere. </s>
            <s xml:id="echoid-s9009" xml:space="preserve">Parique ratione conſtat idem de punctis omnibuſcunque,
              <lb/>
            quibus punctum M per totum ſuum curſum inſiſtit, aut coincidit,
              <lb/>
            Supponatur ſecundò punctum M motu continuo increſcente deſerri
              <lb/>
            (juxta quamlibet velocitatis rationem, regulari modo quocunque
              <lb/>
            nil intereſt, an irregulari) aio _ſuppoſitionem banc conſectari progeni-_
              <lb/>
            _tarum linearum quas apponemus proprietates generales_ (quales uni
              <lb/>
            tali linearum generi convenientes certè præſtat ex unimoda com-
              <lb/>
            muni generatione ſimul univerſas elicere, quàm de ſingulis, ut
              <lb/>
              <note position="right" xlink:label="note-0207-02" xlink:href="note-0207-02a" xml:space="preserve">Fig. 19.</note>
            paſſim fieri ſolet, ſingulas ſeparatim oſtendere.) </s>
            <s xml:id="echoid-s9010" xml:space="preserve">Notetur inte-
              <lb/>
            reà, quòd brevitatis cauſâ motum parallelum uniformem rectæ AZ
              <lb/>
            per AY appellabo ſubinde _motum tranſverſum_; </s>
            <s xml:id="echoid-s9011" xml:space="preserve">puncti verò mo-
              <lb/>
            ventis ab A in linea AZ motum vocitabo _deſcenſum_, aut _motum_
              <lb/>
            _deſcendentem_, habito ſcilicet ad figuram exhibitam reſpectu. </s>
            <s xml:id="echoid-s9012" xml:space="preserve">Item
              <lb/>
            quòd, ob motûs per AY et ei parallelas uniformitatem, poſſit
              <lb/>
            ea cum ipſius partibus motûs tempus, et ejus partes repræſentare.
              <lb/>
            </s>
            <s xml:id="echoid-s9013" xml:space="preserve">Jam ad dictas proprietates expendendas accedo.</s>
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