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

Table of handwritten notes

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            <s xml:id="echoid-s7378" xml:space="preserve">III. </s>
            <s xml:id="echoid-s7379" xml:space="preserve">_Superſiciem planam media dirimentem (aquam ſiplacet ac aërem)_
              <lb/>
              <note position="left" xlink:label="note-0130-01" xlink:href="note-0130-01a" xml:space="preserve">Fig. 182.</note>
            repræſentet recta PQ, & </s>
            <s xml:id="echoid-s7380" xml:space="preserve">aquæ inſit recta FP ad PQ perpen-
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            dicularis. </s>
            <s xml:id="echoid-s7381" xml:space="preserve">ſiat autem FP. </s>
            <s xml:id="echoid-s7382" xml:space="preserve">XP :</s>
            <s xml:id="echoid-s7383" xml:space="preserve">: R. </s>
            <s xml:id="echoid-s7384" xml:space="preserve">I; </s>
            <s xml:id="echoid-s7385" xml:space="preserve">erit X P imago abſoluta rectæ
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            FP; </s>
            <s xml:id="echoid-s7386" xml:space="preserve">continet illa ſcilicet omnes locos punctorum, quæ in FP, oculo
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            apparentes in ipſa FP ſito. </s>
            <s xml:id="echoid-s7387" xml:space="preserve">verùm ſi ponatur oculus uſpiam extra FP,
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            velut ad O, ei tota FP citra XP apparebit. </s>
            <s xml:id="echoid-s7388" xml:space="preserve">tranſeat videlicet ali-
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            cujus radii FM refractus per O, & </s>
            <s xml:id="echoid-s7389" xml:space="preserve">protrahatur OM, ut occurrat ipſi
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            FP in K. </s>
            <s xml:id="echoid-s7390" xml:space="preserve">eſt ergò (ſecundum præmonſtrata) punctum Kinter X, & </s>
            <s xml:id="echoid-s7391" xml:space="preserve">
              <lb/>
            P. </s>
            <s xml:id="echoid-s7392" xml:space="preserve">itidem (è prius oſtenſis) puncti F imago quæ in refracto OMK,
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            ad oculum O relata, inter K, & </s>
            <s xml:id="echoid-s7393" xml:space="preserve">M cadit, veluti puta ad φ. </s>
            <s xml:id="echoid-s7394" xml:space="preserve">ſimili ratione
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            cujuſvis alterius in ipſa FP accepti puncti, ceu R, imago (cogita ρ)
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            citra rectam XP, verſus oculum, jacet. </s>
            <s xml:id="echoid-s7395" xml:space="preserve">totius itaque rectæ FP imago
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            talis eſt, qualem curva linea φρ P refert. </s>
            <s xml:id="echoid-s7396" xml:space="preserve">quòd ſi P F infinitè protra-
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            hatur, ejus totius imago P ρρ verſus aſymptoton OBA, ad PF paralle-
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            lam, accedens excurrit.</s>
            <s xml:id="echoid-s7397" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7398" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s7399" xml:space="preserve">_Delineatur autem curva P ρ φ hoc modo._ </s>
            <s xml:id="echoid-s7400" xml:space="preserve">ab O ducatur utcun-
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            que recta OMK ſecans rectam PQ in M; </s>
            <s xml:id="echoid-s7401" xml:space="preserve">& </s>
            <s xml:id="echoid-s7402" xml:space="preserve">(poſito fore S = √ Rq
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            - Iq) ſit PH = {Sq x PM cub/Iq x FPq}; </s>
            <s xml:id="echoid-s7403" xml:space="preserve">atque per H ducatur H φ ad PR
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            parallela, ipſi OK occurrens in φ; </s>
            <s xml:id="echoid-s7404" xml:space="preserve">erit φ in dicta linea; </s>
            <s xml:id="echoid-s7405" xml:space="preserve">nempe, ſi
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            OMK ipſius M F refractus concipiatur, erit punctum φ ipſius F ima-
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            go. </s>
            <s xml:id="echoid-s7406" xml:space="preserve">eodem modo reliqua lineæ P ρ ρ puncta deſignantur.</s>
            <s xml:id="echoid-s7407" xml:space="preserve"/>
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            <s xml:id="echoid-s7408" xml:space="preserve">V. </s>
            <s xml:id="echoid-s7409" xml:space="preserve">Quinetiam adſumptâ rectâ FG ad PQ parallelâ, ductâque
              <lb/>
              <note position="left" xlink:label="note-0130-02" xlink:href="note-0130-02a" xml:space="preserve">Fig. 182.</note>
            GQ ad FP (vel ABO): </s>
            <s xml:id="echoid-s7410" xml:space="preserve">parallelâ; </s>
            <s xml:id="echoid-s7411" xml:space="preserve">item per X ductà X α Y ad PQ
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            parallelâ, erit quidem recta X α Y rectæ FAG imago abſoluta;
              <lb/>
            </s>
            <s xml:id="echoid-s7412" xml:space="preserve">verùm ejus imago ad oculum O relata citra rectam XY tota jacet, eám-
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            que curva φαγ repræſentat, admodum jamjam præſcriptum puncta-
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            tim delineabilis. </s>
            <s xml:id="echoid-s7413" xml:space="preserve">itaque compoſitæ lineæ PFGQ, circa axem OBA
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            rotatæ, imago fornicem referet arcuatam. </s>
            <s xml:id="echoid-s7414" xml:space="preserve">id quod experiri vos velim
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            vaſculi cylindrici aquâ repleti ſuperficiem inſpectando.</s>
            <s xml:id="echoid-s7415" xml:space="preserve"/>
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            <s xml:id="echoid-s7416" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s7417" xml:space="preserve">Quòd ſirecta viſibilis FG ad PQ inclinata ſit, cum ea conve-
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              <note position="left" xlink:label="note-0130-03" xlink:href="note-0130-03a" xml:space="preserve">Fig. 183.</note>
            niens in V; </s>
            <s xml:id="echoid-s7418" xml:space="preserve">& </s>
            <s xml:id="echoid-s7419" xml:space="preserve">connectatur XV, erit rurſus XY ipſius FG imago ab-
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            ſoluta; </s>
            <s xml:id="echoid-s7420" xml:space="preserve">relatam verò curva φαγ repræſentat.</s>
            <s xml:id="echoid-s7421" xml:space="preserve"/>
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            <s xml:id="echoid-s7422" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s7423" xml:space="preserve">Quòd ſi viciſſim _oculus O in aqua ponatur conſtitutus,_ & </s>
            <s xml:id="echoid-s7424" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0130-04" xlink:href="note-0130-04a" xml:space="preserve">Fig. 184.</note>
            ab indèreſpiciatur recta P F in aëre poſita, fiátque rurſus PF. </s>
            <s xml:id="echoid-s7425" xml:space="preserve">PX :</s>
            <s xml:id="echoid-s7426" xml:space="preserve"/>
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