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

Table of handwritten notes

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            <s xml:id="echoid-s8427" xml:space="preserve">
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            eadem ſydera periodos eaſdem, aut ejuſdem periodi partes æquales
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            abſolvunt; </s>
            <s xml:id="echoid-s8428" xml:space="preserve">inæqualia verò juxta quamcunque proportionem, in
              <lb/>
            quibus limiliter, ſeu proportionaliter inæquales periodi conſumun-
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            tur. </s>
            <s xml:id="echoid-s8429" xml:space="preserve">Neque quiſquam objiciat tempus communiter haberi pro men-
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            ſura motûs, & </s>
            <s xml:id="echoid-s8430" xml:space="preserve">conſequenter ad hoc motûs diſſerentias (velocioris,
              <lb/>
            tardioris, accelerati, retardati) adſumendo tempus ut præcogni-
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            tum definiri; </s>
            <s xml:id="echoid-s8431" xml:space="preserve">nec ideò temporis quantitatem è motu, ſed motûs
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            quantitatem à tempore determinari; </s>
            <s xml:id="echoid-s8432" xml:space="preserve">nil enim obſtat quo minùs tem-
              <lb/>
            pus & </s>
            <s xml:id="echoid-s8433" xml:space="preserve">motus hæc ſibi mutuò præſtent oſſicia. </s>
            <s xml:id="echoid-s8434" xml:space="preserve">Sanè veluti ſpatium
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            ex aliqua primùm magnitudine metimur, & </s>
            <s xml:id="echoid-s8435" xml:space="preserve">quantum ſit diſcimus,
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            è ſpatio poſteà reliquas ei congruas magnitudines æſtimanus; </s>
            <s xml:id="echoid-s8436" xml:space="preserve">ità tem-
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            pus primò taxamus è motu quodam, poſteà motus reliquos ex eo di-
              <lb/>
            judicamus; </s>
            <s xml:id="echoid-s8437" xml:space="preserve">quod planè nihil eſt aliud quàm mediante tempore motus
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            alios cum aliis comparare; </s>
            <s xml:id="echoid-s8438" xml:space="preserve">ſicut & </s>
            <s xml:id="echoid-s8439" xml:space="preserve">mediante ſpatio magnitudinum
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            inter ſe rationes inveſtigamus. </s>
            <s xml:id="echoid-s8440" xml:space="preserve">Qui nimirum è temporum propor-
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            tione motuum colligit proportionem, nil aliud quam ex organorum
              <lb/>
            horologicorum, vel ex Solarium motuum ſimul decurſorum propor-
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            tione dictam elicit motuum rationem. </s>
            <s xml:id="echoid-s8441" xml:space="preserve">Quod certè vidit, & </s>
            <s xml:id="echoid-s8442" xml:space="preserve">exertè
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            docuit _Ariſtoteles_: </s>
            <s xml:id="echoid-s8443" xml:space="preserve">@ μόγογ (inquit) {τὴν} κίνησιγτῶκ{ρό}νω με{τρ}{οῦ}{μεν}, α
              <unsure/>
            {λλ}α
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              <lb/>
            {καὶ} @ῆ κινή{ει} τ
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            κ{ρό}νον{δι}ὰ {τὸ} ὸ{ρι}ζε@ {ὺπ}
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            ἀ{λλ}ήλων. </s>
            <s xml:id="echoid-s8444" xml:space="preserve">Porrò, quia tem-
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              <note position="left" xlink:label="note-0184-01" xlink:href="note-0184-01a" xml:space="preserve">_Phy ſ. IV. 18._</note>
            pus, ut oſtenſum, eſt quantum uniformiter extenſum, cujus omnes
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            partes æquabilis motûs partibus reſpectivis, ſeu ſpatiorum æquabili
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            motu peractorum partibus proportione reſpondent, poſſit id quàm
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            optimè per magnitudinem quamlibet δμοιομερῆ repræſentari, hoc eſt
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            menti noſtræ ſeu phantaſiæ proponi; </s>
            <s xml:id="echoid-s8445" xml:space="preserve">per ſimpliciſſimas præſertim,
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            quales ſunt linea recta, & </s>
            <s xml:id="echoid-s8446" xml:space="preserve">circularis; </s>
            <s xml:id="echoid-s8447" xml:space="preserve">quibuſcum etiam & </s>
            <s xml:id="echoid-s8448" xml:space="preserve">tempore
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            ſimilitudines & </s>
            <s xml:id="echoid-s8449" xml:space="preserve">analogiæ non paucæ intercedunt. </s>
            <s xml:id="echoid-s8450" xml:space="preserve">Præterquam enim
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            quòd tempus partes habet omnino ſimilares, rationi conſentaneum
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            eſt ipſum velut unicâ dimenſione præditum quantum conſiderare; </s>
            <s xml:id="echoid-s8451" xml:space="preserve">ip-
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            ſum enim velut ex ſimplici ſupervenientium momentorum additamento,
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            vel ex unius momenti quaſi continuo ſluxu conſtitutum imaginamur,
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            & </s>
            <s xml:id="echoid-s8452" xml:space="preserve">ſolam proinde longitudinem ei ſolemus attribuere; </s>
            <s xml:id="echoid-s8453" xml:space="preserve">nec ejus quan-
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            titatem aliàs quàm ex lineæ decurſæ longitudine determinamus. </s>
            <s xml:id="echoid-s8454" xml:space="preserve">Si-
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            cut, inquam, linea puncti promoti cenſetur veſtigium, à puncto
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            habens quò aliquatenus diviſibilis ſit, à motu verò quòd uno modo,
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            ſecundum longitudinem, dividi poſſit; </s>
            <s xml:id="echoid-s8455" xml:space="preserve">ità tempus velut inſtantis con-
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            tinuò labentis veſtigium concipiatur, ab inſtante nonnullam indiviſi-
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            bilitatem habens, à ſucceſſivo ſluxu quòd eatenus diſpertiri queat. </s>
            <s xml:id="echoid-s8456" xml:space="preserve">Et
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            ſicuti lineæ quantitas ab unica longitudine pendet motum conſe-
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            quente, ità temporis quantitas ab unica conſectatur velut in </s>
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