Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

Table of handwritten notes

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            <s xml:id="echoid-s635" xml:space="preserve">
              <pb o="334" file="0040" n="43" rhead="ΕΞΕΤΑΣΙΣ CYCLOM."/>
            per ea quidem quæ nos adhuc docuit V. </s>
            <s xml:id="echoid-s636" xml:space="preserve">Cl. </s>
            <s xml:id="echoid-s637" xml:space="preserve">inveniri non
              <lb/>
            poſſe. </s>
            <s xml:id="echoid-s638" xml:space="preserve">Etenim inventurus ex datis rationibus, ſol. </s>
            <s xml:id="echoid-s639" xml:space="preserve">Μ Ξ ad
              <lb/>
            ſol. </s>
            <s xml:id="echoid-s640" xml:space="preserve">Λ Σ, & </s>
            <s xml:id="echoid-s641" xml:space="preserve">ſolidi Κ Θ ad ſol. </s>
            <s xml:id="echoid-s642" xml:space="preserve">Δ Γ, rationem tertiam ſo-
              <lb/>
            lidi H Y ad ſol. </s>
            <s xml:id="echoid-s643" xml:space="preserve">X V, in hunc modum rationcinabitur, ut
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            videre eſt ex demonſtratione prop. </s>
            <s xml:id="echoid-s644" xml:space="preserve">44. </s>
            <s xml:id="echoid-s645" xml:space="preserve">ſuprà citatæ, cui hunc
              <lb/>
            caſum convenire liquidò conſtat. </s>
            <s xml:id="echoid-s646" xml:space="preserve">Dicet enim, Notæ ſunt
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            prima & </s>
            <s xml:id="echoid-s647" xml:space="preserve">ſecunda ratio, (iſtæ enim ſunt 53 ad 203, & </s>
            <s xml:id="echoid-s648" xml:space="preserve">5 ad
              <lb/>
            11,) ergo notum quoque quoties prima ſecundam contineat.
              <lb/>
            </s>
            <s xml:id="echoid-s649" xml:space="preserve">Sed quoties prima continet ſecundam, toties ſecunda continet
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            tertiam, (hoc aſſerit prop. </s>
            <s xml:id="echoid-s650" xml:space="preserve">40. </s>
            <s xml:id="echoid-s651" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s652" xml:space="preserve">10. </s>
            <s xml:id="echoid-s653" xml:space="preserve">oper. </s>
            <s xml:id="echoid-s654" xml:space="preserve">Geom.) </s>
            <s xml:id="echoid-s655" xml:space="preserve">Ergo
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            notum quoque quoties ſecunda tertiam contineat. </s>
            <s xml:id="echoid-s656" xml:space="preserve">Quare cum
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            nota ſit ſecunda, etiam tertia nota erit, ea nimirum quam
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            habet ſolidum H Y ad ſol. </s>
            <s xml:id="echoid-s657" xml:space="preserve">X V.</s>
            <s xml:id="echoid-s658" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s659" xml:space="preserve">Conſequenter hoc nunc definiendum ei incumbet, Quo-
              <lb/>
            ties Ratio harum prima ſecundam contineat; </s>
            <s xml:id="echoid-s660" xml:space="preserve">hoc eſt, quo-
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            ties ratio 53 ad 203, contineat rationem 5 ad 11. </s>
            <s xml:id="echoid-s661" xml:space="preserve">Sed enim
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            quo ſenſu verbum continere hîc explicaturus eſt? </s>
            <s xml:id="echoid-s662" xml:space="preserve">Num eo,
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            ut idem ſignificet quod alibi continere per multiplicationem?
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            </s>
            <s xml:id="echoid-s663" xml:space="preserve">utque ratio 53 ad 203 rationem 5 ad 11. </s>
            <s xml:id="echoid-s664" xml:space="preserve">multiplicare dica-
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            tur vel bis (hoc eſt ut illa hujus ſit duplicata, ita enim con-
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            tinere intelligendum videtur in propoſitione 40. </s>
            <s xml:id="echoid-s665" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s666" xml:space="preserve">10,
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            modo citata) vel ter, vel quater, vel ſæpiùs etiam. </s>
            <s xml:id="echoid-s667" xml:space="preserve">Et hoc
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            quidem eſſe non poteſt; </s>
            <s xml:id="echoid-s668" xml:space="preserve">nam ratio 53 ad 203, rationis 5
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            ad 11, neque duplicata eſt neque triplicata vel ulterius mul-
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            tiplex, quum demum ratio 53 ad 256 {13/25} ſit duplicata rationis
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            5 ad 11.</s>
            <s xml:id="echoid-s669" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s670" xml:space="preserve">An igitur verbum Continere in eum ſenſum trahet, quem
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            habet in propoſitione 125. </s>
            <s xml:id="echoid-s671" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s672" xml:space="preserve">8. </s>
            <s xml:id="echoid-s673" xml:space="preserve">Oper. </s>
            <s xml:id="echoid-s674" xml:space="preserve">Geom.</s>
            <s xml:id="echoid-s675" xml:space="preserve">? Vix qui-
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            dem illud ſuſpicari poſſum; </s>
            <s xml:id="echoid-s676" xml:space="preserve">ſed etiamſi vellet rurſus inde
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            abſurdum conſequetur. </s>
            <s xml:id="echoid-s677" xml:space="preserve">Nam ſecundum interpretationem iſtam;
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            </s>
            <s xml:id="echoid-s678" xml:space="preserve">quoties ratio 53 ad 203 continet rationem 5 ad 11, toties
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            hæc ipſa continebit rationem 5075 ad 6413; </s>
            <s xml:id="echoid-s679" xml:space="preserve">hoc autem pa-
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            tebit horum numerorum inter ſe rationis examinanti ſecun-
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            dùm regulam dictæ propoſitionis 125. </s>
            <s xml:id="echoid-s680" xml:space="preserve">Eſſet igitur ratio ſoli-
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            di H Y ad ſol. </s>
            <s xml:id="echoid-s681" xml:space="preserve">X V, hoc eſt, ratio ſegmenti circuli ab ini-
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            tio propoſiti C H G, ad ſegmentum G H E F, eadem </s>
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