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

Table of Notes

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            <s xml:id="echoid-s8625" xml:space="preserve">
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            puncta quævis EE rectâ lineâ connectantur, iíſque reſpondentia
              <lb/>
            puncta BB rectâ quoque jungantur; </s>
            <s xml:id="echoid-s8626" xml:space="preserve">quoniam rectæ EB ſibimet
              <lb/>
            æquantur (etenim nil aliud ſunt, quam eadem ipſa linea diverſum
              <lb/>
              <note position="right" xlink:label="note-0193-01" xlink:href="note-0193-01a" xml:space="preserve">Fig. 5.</note>
            ſitum obtinens) ac parallelæ ſecundum _hypotbeſin_, erunt rectæ EE,
              <lb/>
            BB æquales ac parallelæ. </s>
            <s xml:id="echoid-s8627" xml:space="preserve">Unde patet curvas EE, BB adæquari ſi-
              <lb/>
            bimet, & </s>
            <s xml:id="echoid-s8628" xml:space="preserve">aſſimilari. </s>
            <s xml:id="echoid-s8629" xml:space="preserve">Adæquari quia ſubtenſæ omnes EE ſubtenſis BB
              <lb/>
            ſingillatim æquantur; </s>
            <s xml:id="echoid-s8630" xml:space="preserve">aſſimilari, quia rectæ AB cum ſubtenſis adja-
              <lb/>
            centibus reſpectivis EE, & </s>
            <s xml:id="echoid-s8631" xml:space="preserve">BB pares angulos conſtituunt, adeóque
              <lb/>
            rectæ ipſæ EE pares iis, quos rectæ BB; </s>
            <s xml:id="echoid-s8632" xml:space="preserve">ipſæ illæ cum ſeipſis, & </s>
            <s xml:id="echoid-s8633" xml:space="preserve">
              <lb/>
            hæ cum ſeipſis (nam in hujuſmodi proportionalitate partium, & </s>
            <s xml:id="echoid-s8634" xml:space="preserve">an-
              <lb/>
            gulorum æqualitate, ſicut alibi fortaſſe luculentiùs & </s>
            <s xml:id="echoid-s8635" xml:space="preserve">fuſiùs diſſere-
              <lb/>
            mus, omnis conſiſtit linearum, & </s>
            <s xml:id="echoid-s8636" xml:space="preserve">quarumcunque magnitudinum ſimi-
              <lb/>
            litudo.) </s>
            <s xml:id="echoid-s8637" xml:space="preserve">Quod ſi vice commutatâ linea curva BC fiat linea _Genetriæ
              <unsure/>
            ,_
              <lb/>
            & </s>
            <s xml:id="echoid-s8638" xml:space="preserve">recta BA _directrix_, hoc eſt ſi BC per BA ſibi parallela feratur,
              <lb/>
              <note position="right" xlink:label="note-0193-02" xlink:href="note-0193-02a" xml:space="preserve">Fig. 6.</note>
            producetur eadem ipſiſſima parallelogramma Superficies; </s>
            <s xml:id="echoid-s8639" xml:space="preserve">& </s>
            <s xml:id="echoid-s8640" xml:space="preserve">ſingula
              <lb/>
            rectæ BC puncta, veluti F, rectas lineas ad BA parallelas deſcri-
              <lb/>
            bent; </s>
            <s xml:id="echoid-s8641" xml:space="preserve">neque non interceptæ FF reſpectivis BB pares erunt; </s>
            <s xml:id="echoid-s8642" xml:space="preserve">quod
              <lb/>
            & </s>
            <s xml:id="echoid-s8643" xml:space="preserve">pari modo ex ſuppoſito perpetuo curvæ BC paralleliſmo facilè con-
              <lb/>
            ſectatur. </s>
            <s xml:id="echoid-s8644" xml:space="preserve">Sit denique curva quævis (vel è rectis angulos efficientibus
              <lb/>
            compoſita, quæ curvæ quoque nomen meritò ferat; </s>
            <s xml:id="echoid-s8645" xml:space="preserve">_Archimedes_
              <lb/>
            ſaltem è rectis compoſitas lineas, utì figurarum circulis inſcriptarum
              <lb/>
            aut adſcriptarum perimetros, {και} {πα}λῶν {γρ}αμμ@ν nomine complecti-
              <lb/>
            tur; </s>
            <s xml:id="echoid-s8646" xml:space="preserve">ut & </s>
            <s xml:id="echoid-s8647" xml:space="preserve">viciſſim curvæ quævis lineæ cenſeri poſſunt è rectis, innu-
              <lb/>
            meris quidem illis indefinitè parvis, adjacentibus, & </s>
            <s xml:id="echoid-s8648" xml:space="preserve">deinceps ſe-
              <lb/>
            cum angulos efficientibus, conſlatæ) ſit, inquam, talis aliqua curva
              <lb/>
            BC, in plano quovis conſtituta, tum in alio plano, vel ſuper lineæ
              <lb/>
            BC planum ut libet elevata, recta AB ſibi continuò feratur parallela,
              <lb/>
            modo quo ſemel ac iterum oſtendimus; </s>
            <s xml:id="echoid-s8649" xml:space="preserve">deſcribetur hujuſmodi motu
              <lb/>
            _Superficies cylindrica_ (vel certè _priſmatica, ſi linea directrix è rectis_
              <lb/>
            ponatur compoſita) & </s>
            <s xml:id="echoid-s8650" xml:space="preserve">_cylindrica_ quidem ſtrictè dicta, ſi _directrix
              <unsure/>
            _
              <lb/>
            _fuerit linea circularis, aut elliptica_; </s>
            <s xml:id="echoid-s8651" xml:space="preserve">latiore verò ſenſu talis, ſi curva
              <lb/>
            fuerit alterius generis ut _parabolica_ puta, vel _hyperbolica_, vel alia
              <lb/>
            quæpiam. </s>
            <s xml:id="echoid-s8652" xml:space="preserve">In hoc autem motu lineæ quoque genetricis ſingula puncta
              <lb/>
            ſimiles & </s>
            <s xml:id="echoid-s8653" xml:space="preserve">æquales deſcribunt curvæ directrici lineas; </s>
            <s xml:id="echoid-s8654" xml:space="preserve">æquales
              <lb/>
            (ut in mox præcedente diſcurſu) quoniam EB pares ac paral-
              <lb/>
            lelæ ſunt; </s>
            <s xml:id="echoid-s8655" xml:space="preserve">adeóque EE, BB quoque pares, ac parallelæ
              <lb/>
            ſimiles; </s>
            <s xml:id="echoid-s8656" xml:space="preserve">*quoniam etiam anguli EEE, angulis BBB æquantur.
              <lb/>
            </s>
            <s xml:id="echoid-s8657" xml:space="preserve">
              <note position="right" xlink:label="note-0193-03" xlink:href="note-0193-03a" xml:space="preserve">10. XI
                <unsure/>
              . El
                <unsure/>
              @m.</note>
            Quinetiam reciprocè deſcribatur eadem Superficies ponendo curvam
              <lb/>
            BC perrectam AB parallelωs deportari. </s>
            <s xml:id="echoid-s8658" xml:space="preserve">Quomodò ſingula quoque
              <lb/>
            curvæ BC puncta rectas parallelas & </s>
            <s xml:id="echoid-s8659" xml:space="preserve">pares interceptis </s>
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