Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

Table of figures

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            <s xml:id="echoid-s9289" xml:space="preserve">XVII. </s>
            <s xml:id="echoid-s9290" xml:space="preserve">Huic ſuppar modus dictas @rectas AP, TP comparandi
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            tali _Theoremate_ continetur: </s>
            <s xml:id="echoid-s9291" xml:space="preserve">Si ad rectam aliquam lineam (hoc eſt
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            ad cjus ſingula quæque puncta) applicentur rectæ lineæ parallelæ, ad
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              <note position="left" xlink:label="note-0216-01" xlink:href="note-0216-01a" xml:space="preserve">Fig. 23, 24.</note>
            rectam AD conſimiliter diviſam applicatarum differentiis proportio-
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            nales, reſultantis hinc plani ad parallelogrammum æque altum, ad
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            eandémque baſin poſitum, rectarum AP, TP proportionem exhi-
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            bebit. </s>
            <s xml:id="echoid-s9292" xml:space="preserve">Ut ſi rectæ AD, α δ ſimiliter (in partes ſcilicet æquales in-
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            definitè multas) dividantur; </s>
            <s xml:id="echoid-s9293" xml:space="preserve">& </s>
            <s xml:id="echoid-s9294" xml:space="preserve">rectæ β μ, γ μ, δ μ rectis BM, NM,
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            OM (quæ differentiæ ſunt rectarum ad AD applicatarum, incipi-
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            endo à puncto A) proportionales ſint, erit ut figura α δ μ ad paral-
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            lelogrammum α
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            δ μ φ, ita AP ad TP. </s>
            <s xml:id="echoid-s9295" xml:space="preserve">Cum enim recta quæpiam
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            ex applicatis ad AD; </s>
            <s xml:id="echoid-s9296" xml:space="preserve">puta _v.</s>
            <s xml:id="echoid-s9297" xml:space="preserve">g._ </s>
            <s xml:id="echoid-s9298" xml:space="preserve">DM æquetur omnibus ſeipsâ mi-
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            norum differentiis (ipſis nempe BM, NM, OM) & </s>
            <s xml:id="echoid-s9299" xml:space="preserve">trilineum
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            α δ μ conſtituatur è rectis β μ, γ μ δ μ eâdem proportione creſcen-
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            tibus; </s>
            <s xml:id="echoid-s9300" xml:space="preserve">ut & </s>
            <s xml:id="echoid-s9301" xml:space="preserve">recta CM æquatur ipſis BM, NM; </s>
            <s xml:id="echoid-s9302" xml:space="preserve">& </s>
            <s xml:id="echoid-s9303" xml:space="preserve">ei reſpondens
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            trilineum α γ μ quaſi conflatur è parallelis β μ, γ μ pari ratione
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            creſcentibus; </s>
            <s xml:id="echoid-s9304" xml:space="preserve">& </s>
            <s xml:id="echoid-s9305" xml:space="preserve">hoc ſemper eveniat; </s>
            <s xml:id="echoid-s9306" xml:space="preserve">omnino patet trilinea α δ μ,
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            α γ μ, α β μ rectis DM, CM, BM proportionari; </s>
            <s xml:id="echoid-s9307" xml:space="preserve">proindéque
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            modum hunc in priorem recidere; </s>
            <s xml:id="echoid-s9308" xml:space="preserve">nec ab eo reipsâ differre. </s>
            <s xml:id="echoid-s9309" xml:space="preserve">Notetur
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            autem hic rectas β μ, γ μ, δ μ velocitates repræſentare, quas pun-
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            ctum mobile curvam delineans obtinet in reſpectivis ejus punctis M;
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            </s>
            <s xml:id="echoid-s9310" xml:space="preserve">ut & </s>
            <s xml:id="echoid-s9311" xml:space="preserve">trilinea α β μ, α γ μ, α δ μ velocitates aggregatas exhibent ab
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            initio ad definita reſpectiva temporis inſtantia; </s>
            <s xml:id="echoid-s9312" xml:space="preserve">quibus (ut jam olim
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            præmonitum) reſpondentia ſpatia BM, CM, DM proportionantur.</s>
            <s xml:id="echoid-s9313" xml:space="preserve"/>
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            <s xml:id="echoid-s9314" xml:space="preserve">XVIII. </s>
            <s xml:id="echoid-s9315" xml:space="preserve">E ſupradictis porrò conſectatur, quòd ſi _Circulus,_
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            _Ellipſis_, ejuſmodíque curvæ recurrentes hoc progenitæ concipiantur
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            modo, punctum eas deſcribens infinitam in recursûs puncto veloci-
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            tatem habebit. </s>
            <s xml:id="echoid-s9316" xml:space="preserve">Nempe ſi quadrans AFM ità generetur; </s>
            <s xml:id="echoid-s9317" xml:space="preserve">quoniam
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              <note position="left" xlink:label="note-0216-02" xlink:href="note-0216-02a" xml:space="preserve">Fig. 25.</note>
            tangens TM diametro AZ eſt parallela, nec illa proinde cum hac
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            niſi ad infinitam diſtantiam convenit; </s>
            <s xml:id="echoid-s9318" xml:space="preserve">ergô velocitas in M ad veloci-
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            tatem uniformis motûs per AY ſe habebit, ut infinita recta ad ipſam
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            PM; </s>
            <s xml:id="echoid-s9319" xml:space="preserve">unde velocitas iſta ad M prorſus infinita ſit oportet. </s>
            <s xml:id="echoid-s9320" xml:space="preserve">Ità quidem
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              <note position="left" xlink:label="note-0216-03" xlink:href="note-0216-03a" xml:space="preserve">II. _preced_.</note>
            quoad hujuſmodi curvas; </s>
            <s xml:id="echoid-s9321" xml:space="preserve">at quoad alias ad infinitum ſenſim continu-
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            atas (quales _parabolæ & </s>
            <s xml:id="echoid-s9322" xml:space="preserve">byperbolæ_) deſcendentis puncti velocitas in
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            quovis deſignato curvæ puncto finita eſt. </s>
            <s xml:id="echoid-s9323" xml:space="preserve">Verùm his omiſſis ad alias
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            propoſitæ curvæ proprietates exponendas progrediamur.</s>
            <s xml:id="echoid-s9324" xml:space="preserve"/>
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