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

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            dividatur BC in partes æquales, & </s>
            <s xml:id="echoid-s8771" xml:space="preserve">connectantur latera VD, VE
              <lb/>
            non erunt Superficies BVD, DVE, EVC æquales inter ſe, ſed
              <lb/>
            inſerutabili plerumque ratione; </s>
            <s xml:id="echoid-s8772" xml:space="preserve">juxta varias angulorum incluſorum,
              <lb/>
            & </s>
            <s xml:id="echoid-s8773" xml:space="preserve">laterum inæqualium differentias, inæquales; </s>
            <s xml:id="echoid-s8774" xml:space="preserve">id quod hactenus
              <lb/>
            ill
              <unsure/>
            o
              <unsure/>
            s divexavit & </s>
            <s xml:id="echoid-s8775" xml:space="preserve">torſit, _qui dimetiendæ coni ſcaleni ſuperficiei incu-_
              <lb/>
            buerunt.</s>
            <s xml:id="echoid-s8776" xml:space="preserve">‖ Ex his conſectatur quòd poſſit hujuſmodi circumlatio
              <lb/>
            facta quadantenus concipi motu quoque tali lineæ rectæ genetricis,
              <lb/>
            ità ut ejus ſingula quæque puncta parallelωs lata ſimiles directrici lineæ
              <lb/>
            lineas deſcribant, modo tamen concipiatur linea genetrix ubique pro-
              <lb/>
            portionaliter aut contrahi, vel dilatari ſecundum omnes ſui partes.
              <lb/>
            </s>
            <s xml:id="echoid-s8777" xml:space="preserve">Quomodo nempe ſi recta VB ita ſenſim diduci concipiatur, ut pun-
              <lb/>
            ctum B totam lineam BC perambulet, etiam punctum G parallelo-
              <lb/>
            ad BC motu delata, lineam GH ipſi BC ſimilem deſcribet. </s>
            <s xml:id="echoid-s8778" xml:space="preserve">Qui-
              <lb/>
            nimò ſi conſimili pacto curva BC, directo quoad lineam rectam BV
              <lb/>
            motu ſitúque ſemper ad ſeipſam parallelo concipiatur promoveri, ſic
              <lb/>
            ut ejus ſingula quæque puncta lineas rectas deſcribant, ſecum omnes
              <lb/>
            in punctum V concurrentes; </s>
            <s xml:id="echoid-s8779" xml:space="preserve">hoc eſt ità ut ipſa per totum ſuum pro-
              <lb/>
            greſſum juxta ſuas omnes partes analogicè contrahatur, ad verticem
              <lb/>
            uſque V; </s>
            <s xml:id="echoid-s8780" xml:space="preserve">producentur ex hujuſmodi motibus Superficies conicæ pror-
              <lb/>
            ſus eædem cum jam proximè tractatis. </s>
            <s xml:id="echoid-s8781" xml:space="preserve">Verùm hujuſmodi motus ima-
              <lb/>
            ginarii ſunt, & </s>
            <s xml:id="echoid-s8782" xml:space="preserve">quales rerum natura reſpuit. </s>
            <s xml:id="echoid-s8783" xml:space="preserve">Explicandæ tamen
              <lb/>
            hujuſmodi Superficierum naturæ deſervire poſſunt, & </s>
            <s xml:id="echoid-s8784" xml:space="preserve">ſupponi ſaltem
              <lb/>
            ut per _divinam potentiam effectibiles._</s>
            <s xml:id="echoid-s8785" xml:space="preserve">‖ Ad hæc, ſi _linea directrix_
              <lb/>
            in motu proximè memorato ſupponatur undique clauſa, ſic ut figuram
              <lb/>
            quamvis comprehendat, Superficies curva progenita cum hac figura,
              <lb/>
            ceu baſe, corpus ſolidum includet pyramidale, vel conicum (ſtrictè
              <lb/>
            vel laxè pro dictæ figuræ natura ſumptum) cujus generalia ſympto-
              <lb/>
            mata ſatìs è dictis eluceſcunt. </s>
            <s xml:id="echoid-s8786" xml:space="preserve">Nempe quòd à parallelis ad hujuſce
              <lb/>
            ſolidi baſin planis abſcindentur ſimiles ad verticem Superficies, ſimiléſ-
              <lb/>
            que baſes intercipientur, & </s>
            <s xml:id="echoid-s8787" xml:space="preserve">ſimilia corpora Solida progignentur. </s>
            <s xml:id="echoid-s8788" xml:space="preserve">
              <lb/>
            Verbo dicam, quæ de _Conis_ generatim _E@clides, Apollonius,_ aliique
              <lb/>
            tradiderunt, ea conicis ho@ modo factis, ſervatâ debitâ analogia,
              <lb/>
            convenient, & </s>
            <s xml:id="echoid-s8789" xml:space="preserve">ſimili ferme modo demonſtrabuntur convenire.</s>
            <s xml:id="echoid-s8790" xml:space="preserve">‖ Ve-
              <lb/>
            rùm uſitatiſſimus apud Mathematicos corpora progignendi modus eſt
              <lb/>
            is qui peculiari nomine _Rotatio_ dicitur, & </s>
            <s xml:id="echoid-s8791" xml:space="preserve">fit ſuppoſito lineam quam-
              <lb/>
            vis, aut quamlibet Superſiciem planam cirea rectam lineam fixam,
              <lb/>
            tanquam axem, revolvi. </s>
            <s xml:id="echoid-s8792" xml:space="preserve">Quomodo ex motu Semiperipheriæ circu-
              <lb/>
            laris circa diametrum producitur _Sphærica Superſicies,_ ex motu Se-
              <lb/>
            micirculi ipſius circa eundem _Sphæra_ detornatur; </s>
            <s xml:id="echoid-s8793" xml:space="preserve">ex motu lineæ rectæ
              <lb/>
            circa lineam ipſi parallelam _Superſicies Cylindrica;_ </s>
            <s xml:id="echoid-s8794" xml:space="preserve">ex motu parallelo-
              <lb/>
            grammi rectanguli circa latus unum ipſé _Cylindrus rectus;_ </s>
            <s xml:id="echoid-s8795" xml:space="preserve">ex motu </s>
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