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-s8821" xml:space="preserve">
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            ponitur ipſum _triangulum rectangulum_ VKD; </s>
            <s xml:id="echoid-s8822" xml:space="preserve">& </s>
            <s xml:id="echoid-s8823" xml:space="preserve">è circulis ad quas
              <lb/>
            ceu radios deſcriptis ipſe _conus_ conflatur. </s>
            <s xml:id="echoid-s8824" xml:space="preserve">Ergò, diſputat, ex ho-
              <lb/>
            rum circulorum peripheriis _Superficies conica_ componetur; </s>
            <s xml:id="echoid-s8825" xml:space="preserve">qnod
              <lb/>
            tamen veritati comperitur adverſari; </s>
            <s xml:id="echoid-s8826" xml:space="preserve">methodúſque proinde fallax
              <lb/>
            eſt. </s>
            <s xml:id="echoid-s8827" xml:space="preserve">Repono, malè calculum hoc pacto iniri; </s>
            <s xml:id="echoid-s8828" xml:space="preserve">& </s>
            <s xml:id="echoid-s8829" xml:space="preserve">in peripheriarum è
              <lb/>
            quibus _Superficies_ conſtant computatione diverſam inſtituendam eſſe
              <lb/>
            rationem ab ea, quâ computantur lineæ quibus _planæ ſuperficies_ con-
              <lb/>
            ſtant, aut plana, è quibus corpora formantur. </s>
            <s xml:id="echoid-s8830" xml:space="preserve">Nempe peripheria-
              <lb/>
            rum Superficiem curvam conſtituentium è revolutione prognatam
              <lb/>
            lineæ VD cenſeri debet è multitudine punctorum, quæ ſunt in ipſa
              <lb/>
              <note position="left" xlink:label="note-0200-01" xlink:href="note-0200-01a" xml:space="preserve">Fig. 10, 11, 12.</note>
            linea genetrice VD; </s>
            <s xml:id="echoid-s8831" xml:space="preserve">quippe cùm per ea ſingula puncta tales peri-
              <lb/>
            pheriæ tranſeant, nec plures tranſire queant; </s>
            <s xml:id="echoid-s8832" xml:space="preserve">quicunque ſit axis, ſeu
              <lb/>
            longiùs diſtans, ſeu propiùs adjacens; </s>
            <s xml:id="echoid-s8833" xml:space="preserve">axis enim ſolummodò, pro
              <lb/>
            longiore vel propiore diſtantia poſitionéque varia, dictarum periphe-
              <lb/>
            riarum magnitudinem determinat. </s>
            <s xml:id="echoid-s8834" xml:space="preserve">Verùm multitudo linearum ex
              <lb/>
            quibus planum DVK ſupponitur conſtare, planorúmque quibus
              <lb/>
            Solidum DVY conſtat, è numero taxanda eſt punctorum in axe
              <lb/>
            VK; </s>
            <s xml:id="echoid-s8835" xml:space="preserve">nec enim plures intra terminos VK parallelæ, ipſi VK perpen-
              <lb/>
            diculares, rectæ, vel plura talia parallela plana duci poſſunt, quam
              <lb/>
            horum punctorum multitudini æquinumera. </s>
            <s xml:id="echoid-s8836" xml:space="preserve">Quod obſervando _diſcri-_
              <lb/>
            _men_ (ſedulò perpendendum) omnem devitabimus errorem, & </s>
            <s xml:id="echoid-s8837" xml:space="preserve">_cur-_
              <lb/>
            _varum bujuſmodi rot@tu genitarum Superficierum facillimo, reor,_
              <lb/>
            _omnium quos rei natura ſubminiſtr at modo perquiremus._ </s>
            <s xml:id="echoid-s8838" xml:space="preserve">Illum com-
              <lb/>
            monſtrabo. </s>
            <s xml:id="echoid-s8839" xml:space="preserve">Pro reperienda v. </s>
            <s xml:id="echoid-s8840" xml:space="preserve">g. </s>
            <s xml:id="echoid-s8841" xml:space="preserve">dimenſione _curvæ ſuperficiei_ lineæ
              <lb/>
            VD circa axem VK revolutione, concipiatur ipſa VD in directum
              <lb/>
            extendi, ità ſcilicet ut ei exæquetur recta VD; </s>
            <s xml:id="echoid-s8842" xml:space="preserve">& </s>
            <s xml:id="echoid-s8843" xml:space="preserve">ad ejus omnia
              <lb/>
            puncta rectæ concipiantur applicari ipſi VD perpendiculares, & </s>
            <s xml:id="echoid-s8844" xml:space="preserve">pe-
              <lb/>
            ripheriis circularibus, è quibus Superficies curva conflatur, ordine
              <lb/>
            pares; </s>
            <s xml:id="echoid-s8845" xml:space="preserve">ſingulæ ſingulis, puta AX ipſi AY, & </s>
            <s xml:id="echoid-s8846" xml:space="preserve">CX ipſi CY, ac
              <lb/>
            ità continuò. </s>
            <s xml:id="echoid-s8847" xml:space="preserve">Erit ex his parallelis rectis conſtitutum planum VDX
              <lb/>
            æquale _dictæ curvæ ſuperficiei;_ </s>
            <s xml:id="echoid-s8848" xml:space="preserve">hujúſque partes illius partibus re-
              <lb/>
            ſpectivis. </s>
            <s xml:id="echoid-s8849" xml:space="preserve">Sin loco _peripberiarum_ applicentur ipſarum reſpectivi radii
              <lb/>
            AZ, BZ, CZ, & </s>
            <s xml:id="echoid-s8850" xml:space="preserve">reliqui; </s>
            <s xml:id="echoid-s8851" xml:space="preserve">ſpatium ex his rectis conſtitutum (quæ
              <lb/>
            ſanè proportionali cum alteris ſerie procedunt) ſe habebit ad _curvam_
              <lb/>
            _Superficiem, ut c@rculi cujuſvis radius ad ejus circumſerentiam._ </s>
            <s xml:id="echoid-s8852" xml:space="preserve">Un-
              <lb/>
            de ſiquâ ratione deprehendi poſſit _Summa radiorum peromnia lineæ_
              <lb/>
            _genetricis puncta tranſeuntium (hoc eſt ſi ſpatii VDZ dimenſionem_
              <lb/>
            reperire contigerit) eo ſtatim innoteſcet _curvæ Superſiciei dimenſio._
              <lb/>
            </s>
            <s xml:id="echoid-s8853" xml:space="preserve">In exemplum, facilitatis ergò, proponatur _conica Superficies_ DVY,
              <lb/>
            è rotatu procreata rectæ VD, circa axem VK. </s>
            <s xml:id="echoid-s8854" xml:space="preserve">Ad rectam VD </s>
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