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