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

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            parabolica AMX vel etiam aliter poſita A μ Y (prout hic motus ac-
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            celeratus gradu ponitur alius ac alius.) </s>
            <s xml:id="echoid-s8890" xml:space="preserve">Quòd ſi quâpiam aliâ ratione
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            creſcere concipiatur, aut minui dicti puncti vel lineæ velocitas alia pro-
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            gignetur inde, pro ratione _bypotbeſis_, diverſa ſpecies magnitudinis. </s>
            <s xml:id="echoid-s8891" xml:space="preserve">In his
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            conſpicitur exemplis quòd eodem ſubinde recidant _compoſitio motuum_
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            _et concurſus_; </s>
            <s xml:id="echoid-s8892" xml:space="preserve">quod exinde quidem contingit, quia rectæ cujuſpiam paral-
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            lelo motu latæſingula puncta rectas deſcribunt ſibi parallelas; </s>
            <s xml:id="echoid-s8893" xml:space="preserve">unde fit ut
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            perinde ſit an punctum ejus aliquod in ipſa fixum deferatur cum ea, vel
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            ſolutum per lineam ejus directioni parallelam; </s>
            <s xml:id="echoid-s8894" xml:space="preserve">ut nempe utrùm punctum
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            M in AC fixum cum ea deferatur, an liberè decurrat per rectam AB eâ-
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            dem velocitate. </s>
            <s xml:id="echoid-s8895" xml:space="preserve">At ſæpe non ita facile per horum utrumlibet modum
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            _magni@udinum generatio_ declaretur, ſit enim recta AB æquabiliter rc-
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            tata (hoc eſt, ita ut temporibus æqualibus æquales efficiat angulos)
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            et ſimultaneè punctum M ab A in ipſa recta AB continuo motu
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            feratur, etiam uniformi; </s>
            <s xml:id="echoid-s8896" xml:space="preserve">ex iſta _motuum_ compoſitione linea quæ-
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            dam producetur, _belix_ ſcilicet _Archimedea_ (nam talia conſultò pro-
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            ponimus _exempla, quò celebrium apud Matbematicos magnitudinum_
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            _obiter naturam inſinuem_, et inſtillem minùs ad hæc exercitatis; </s>
            <s xml:id="echoid-s8897" xml:space="preserve">id
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            tranſcurrens moneo) cujus generatio per nullos, opinor, mobi-
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              <note position="right" xlink:label="note-0203-01" xlink:href="note-0203-01a" xml:space="preserve">Fig. 14.</note>
            lium concurſus, liquidò commodéque ſatis explicetur; </s>
            <s xml:id="echoid-s8898" xml:space="preserve">ita nimirum
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            ut motuum iſtorum, vel eorum quantitatem determinantium angulo-
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            rum, ſeu linearum, ratio, quantitaſve dignoſcantur. </s>
            <s xml:id="echoid-s8899" xml:space="preserve">Generari qui-
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            dem poterit è concurſu paralleli motûs rectæ AC; </s>
            <s xml:id="echoid-s8900" xml:space="preserve">vel circularis
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            motûs rectæ BA circa Centrum quodvis B, concurſu cum prædi-
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            cto regulari motu circa Centrum A; </s>
            <s xml:id="echoid-s8901" xml:space="preserve">at quæ ſit tum futura recta-
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            rum AM, Aμ; </s>
            <s xml:id="echoid-s8902" xml:space="preserve">vel angulorum ABM, ABμ quantitas difficilè
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              <note position="right" xlink:label="note-0203-02" xlink:href="note-0203-02a" xml:space="preserve">Fig. 15.</note>
            conſtabit. </s>
            <s xml:id="echoid-s8903" xml:space="preserve">E contrà, ſi recta BA circa Centrum B motu rotetur
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            uniformi; </s>
            <s xml:id="echoid-s8904" xml:space="preserve">et ſimul recta AC per AB parallelωs, & </s>
            <s xml:id="echoid-s8905" xml:space="preserve">uniformiter defe-
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            ratur, rectarum BA, AC ita latarum interſectio continua lineam quan-
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            dam efficiet (illam nempe, quæ quadratrix dici ſolet) cujus ge-
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            neratio non ità clarè per ſtrictè dictam motuum compoſitionem ex-
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            pediatur, aut explicetùr. </s>
            <s xml:id="echoid-s8906" xml:space="preserve">Generari quidem poteſt per motum re-
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            ctum alicujus puncti M in AB delatâ parallelωs ad primò poſitam
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            AB; </s>
            <s xml:id="echoid-s8907" xml:space="preserve">vel ex puucto tali in AC parallelo quoque delatâ; </s>
            <s xml:id="echoid-s8908" xml:space="preserve">vel per
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            motum puncti in AB, circa B; </s>
            <s xml:id="echoid-s8909" xml:space="preserve">vel circa A rotatâ, rectè ab A
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            verſus B, vel à B verſus A decurrentis; </s>
            <s xml:id="echoid-s8910" xml:space="preserve">ſed hujuſmodi ſnppoſi-
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            tâ quâpiam motuum compoſitione, quænam ſit rectarum AM,
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            aut BM; </s>
            <s xml:id="echoid-s8911" xml:space="preserve">vel angulorum BAM aut ABM aut AMB, vel aliarum
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            quarumvis magnitudinum hoſce motus determinantium quantitas,
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            aut inter ſe relatio, difficulter innoteſcat. </s>
            <s xml:id="echoid-s8912" xml:space="preserve">Qua præcipuè de </s>
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