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

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            <s xml:id="echoid-s8935" xml:space="preserve">
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            in unoquoque corpore eſt numerandus. </s>
            <s xml:id="echoid-s8936" xml:space="preserve">Ita _Carteſius_. </s>
            <s xml:id="echoid-s8937" xml:space="preserve">Nem-
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            pe cùm magnitudo quæpiam exinde quod aliis modo quopiam-
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            adnectitur, illorum motus ita particeps eſt, ut ab eo quoad ſi-
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            tum ſuum aliquatenus determinetur, iſte motus hujus compoſitio-
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            nem quaſi pars ingreditur, ab exemplis poſthac adjungendis res
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            luculentius apparebit. </s>
            <s xml:id="echoid-s8938" xml:space="preserve">Motus autem hoc modo componi poſſunt
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            _Progreſſivi_ cum _Progreſſivis, Progreſſivi_ cum _Circumlatititis, Cir-_
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            _cumlatitii_ cum _Circumlatitiis_; </s>
            <s xml:id="echoid-s8939" xml:space="preserve">componi poſſunt, inquam, et decom-
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            poni modis innumeris; </s>
            <s xml:id="echoid-s8940" xml:space="preserve">quorum omnium cùm inire cenſum im-
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            poſſibile ſit, illoſque qui à regularitate deflectunt intelligere difficile
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            ſit, exponere difficiliús; </s>
            <s xml:id="echoid-s8941" xml:space="preserve">nos præcipuos ſaltem aliquos, in uſu magìs
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            poſitos, et explicatu faciliores attingemus. </s>
            <s xml:id="echoid-s8942" xml:space="preserve">Quales imprimis
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            ſunt ii qui è motibus directis et parallelis; </s>
            <s xml:id="echoid-s8943" xml:space="preserve">è directis et rotatitiis,
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            è pluribus rotatitiis componuntur; </s>
            <s xml:id="echoid-s8944" xml:space="preserve">præſertim illi quos qui conſti-
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            tuunt ſimplices motus omnes vel nonnulli ſunt uniformes. </s>
            <s xml:id="echoid-s8945" xml:space="preserve">Nam
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            _uniformitatem nedum R@ſpublic
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            a requirit, ac exigit Eccleſia, ſed_
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            _artes etiam atque ſcientiæ vehementer affectant._ </s>
            <s xml:id="echoid-s8946" xml:space="preserve">Recti motns
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            (quibus parallelos à recta linea directos motus adnumero) pri-
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            mum ſibi non immeritò locum aſlerunt, ut ſimplicitate præcel-
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            lentes, naturæ convenientes et chari, præ cæteris utiles ac uſitati.
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            </s>
            <s xml:id="echoid-s8947" xml:space="preserve">Nec ulla ſané magnitudinis eſt ſpecies (nulla linea, nulla ſuper-
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            ficies, nullum corpus) cujus generatio non è rectis peracta moti-
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            bus concipiatur. </s>
            <s xml:id="echoid-s8948" xml:space="preserve">Omnis, inquam, in uno planô conſtituta linea
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            procreari poteſt è motu parallelo rectæ lineæ, et puncti in ea; </s>
            <s xml:id="echoid-s8949" xml:space="preserve">
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            omnis ſuperficies è motu parallelo plani, et lineæ iu eo (lineæ ſci-
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            licet alicujus è rectis modo jam inſinuato motibus progenitæ)
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            conſequenter et linea quævis etiam in curva ſuperficie deſignata re-
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            ctis motibus effici poteſt. </s>
            <s xml:id="echoid-s8950" xml:space="preserve">Corpus autem ſolidum eodem modo
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            genitum intelligatur, quatenus è ſuperficierum genitura reſultat,
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            et quatenus ab ipſis ità genitis terminatur, ac circumſcribitur
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            Sed quia _ſuperficierum plerarumque curvarum_, quales hactenus _Ma-_
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            _theſis_ excogitavit, & </s>
            <s xml:id="echoid-s8951" xml:space="preserve">linearum in iis non in uno plano jacentium, ge-
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            neratio per alios modos commodiùs explicetur, neque mihi quic-
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            quam ſuccurrit animadverſione dignum quod de iis dicam, de li-
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            nearum ſaltem in uno plano exiſtentium, per rectos et parallelos
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            motus generatione diſpiciam. </s>
            <s xml:id="echoid-s8952" xml:space="preserve">Et quidem has quod attinet, earum nul-
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            la eſt quæ non ex motu parallelo lineæ rectæ, punctique per e-
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            am delati producatur; </s>
            <s xml:id="echoid-s8953" xml:space="preserve">verum hi motus eo contemperari modo de-
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            bent, quem ſpecialis lineæ producendæ natura poſcit; </s>
            <s xml:id="echoid-s8954" xml:space="preserve">nec reſert
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            qualem, velocitatis reſpectu, motum uni tribuas, ad hujus </s>
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