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

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        <div xml:id="echoid-div218" type="section" level="1" n="29">
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            <emph style="sc">Lect</emph>
          . II.</head>
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            <s xml:id="echoid-s8580" xml:space="preserve">VArios, quibus productæ concipiantur magnitudines aggreſſi mo-
              <lb/>
            dos conſiderare, primum & </s>
            <s xml:id="echoid-s8581" xml:space="preserve">præcipuum attingere cæpimus illum,
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            qui motu peragitur locali. </s>
            <s xml:id="echoid-s8582" xml:space="preserve">Cùm verò ſoleant _Matbematici_ diverſi-
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            modos, è quibus aliæ ac aliæ magnitudines reſultant, motus adſumere
              <lb/>
            ceu poſſibiles, duos ad fontes digitum intendimus, è quibus iſtæ mo-
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            tuum differentiæ ſcaturiunt, modum lationis ipſum, & </s>
            <s xml:id="echoid-s8583" xml:space="preserve">quantita-
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            tem vis motivæ; </s>
            <s xml:id="echoid-s8584" xml:space="preserve">quorum poſteriopem haud ita clarum & </s>
            <s xml:id="echoid-s8585" xml:space="preserve">apertum
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            nuperrimè conati ſumus recludere, limpidúmque reddere. </s>
            <s xml:id="echoid-s8586" xml:space="preserve">Jam diffe-
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            rentias quas aſſumunt ipſas proſequemur, & </s>
            <s xml:id="echoid-s8587" xml:space="preserve">quo pacto generationi mag-
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            nitudinum inſervire poſſunt oſtendemus. </s>
            <s xml:id="echoid-s8588" xml:space="preserve">Lationis modum ſpectando
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            generantur magnitudines vel per motus ſimplices, vel per motus com-
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            poſitos, vel ex concurſu motuum (nam compoſitionem à concurſu
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            diſtinguo, quæ tamen à nonnullis confunduntur.) </s>
            <s xml:id="echoid-s8589" xml:space="preserve">De ſimplicium
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            motuum hypotheſibus, ac effectis primò videamus. </s>
            <s xml:id="echoid-s8590" xml:space="preserve">Simplicium mo-
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            tuum duo genera ſunt, ρο@, & </s>
            <s xml:id="echoid-s8591" xml:space="preserve">{πο}
              <unsure/>
            {ρι}φο@, progreſſio, & </s>
            <s xml:id="echoid-s8592" xml:space="preserve">circum-
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            latio. </s>
            <s xml:id="echoid-s8593" xml:space="preserve">Sub progreſſivo motu comprehenditur motus omnis, qui nul-
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            lum fixum locum (loci nomine quamvis magnitudinem, etiam pun-
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            ctum adnumerans, intelligo,) reſpicit, cui velut innectitur, ac affigi-
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            tur; </s>
            <s xml:id="echoid-s8594" xml:space="preserve">ſeu directus iſte motus ſit, ſeu reflexus, ſeu refractus; </s>
            <s xml:id="echoid-s8595" xml:space="preserve">ſive
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            callem certum perſequatur, ſive inconſtanter deſultet, divagetur,
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            exorbitet. </s>
            <s xml:id="echoid-s8596" xml:space="preserve">Quia vero penitus irregularium in arte nulla ratio poteſt
              <lb/>
            haberi, ſufficit _Matbematicis_ ſupponere magnitudinem quamcunque
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            progredi poſſe juxta deſignatam quamlibet orbitam; </s>
            <s xml:id="echoid-s8597" xml:space="preserve">ut _v.</s>
            <s xml:id="echoid-s8598" xml:space="preserve">g._ </s>
            <s xml:id="echoid-s8599" xml:space="preserve">Quod
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            punctum _in linea recta, circulari, elliptica, ſpirali, vel alia quavis_
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            _præſtituta queat incedere._ </s>
            <s xml:id="echoid-s8600" xml:space="preserve">Verùm præcipuæ, hoc eſt maximi, fre-
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            quentiſſimíque pro magnitudinibus efformandis usûs, circa hujuſmodi
              <lb/>
            motus quas _Mathematici_ præſtruunt hypotheſes, ſunt hæ: </s>
            <s xml:id="echoid-s8601" xml:space="preserve">Quôd
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            punctum à præfixo termino in linea recta quouſque libuerit adſignare
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            directè progredi queat, quali motu perſpicuum eſt lineam </s>
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