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

Table of figures

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[Figure 101]
[Figure 102]
[103] Pag. 520.TAB. XLVI.Fig. 1.D C E A X F K V O I L T α M N
[104] Fig. 3.Δ A Φ G F N E M I D H L B C K O P Q Σ R T V X Y Z S Γ Δ Θ @
[105] Fig. 5.C B A D E
[106] Fig. 4.H C L E B A D F K G
[107] Fig. 6.L G C F M A H B E I D K
[108] Fig. 2.G C H B A Y L X P K V Q I O S R F D E N
[Figure 109]
[Figure 110]
[Figure 111]
[Figure 112]
[113] Pag. 542.Fig. 1.♃
[114] Fig. 2.♃
[115] Fig. 3.♂
[116] Fig. 5.25 Mart. 1655. * a b *
[117] Fig. 7.26 Mart. * a b *
[118] Fig. 4.
[119] Fig. 6.
[120] Pag. 550.TAB. XLV III.Fig. 1.* a * b 27. Mart. 1655.
[121] Fig. 2.a * 3. Apr.
[122] Fig. 3.* a c * 9. Apr.
[123] Fig. 4.* a * c 10. Apr.
[124] Fig. 5.* a c * 11. Apr.
[125] Fig. 6.* a c * 12. Apr.
[126] Fig. 7.* c 13. Apr.
[127] Fig. 8.a * 17. Apr.
[128] Fig. 9.* 19. Apr.
[129] Fig. 10.* 20. Apr.
[130] Fig. 11.* 21. Apr.
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              <pb o="431" file="0149" n="158" rhead="ET HYPERBOLÆ QUADRATURA."/>
            æqualibus quantitatibus addendo, ſubtrahendo, multiplican-
              <lb/>
            do, dividendo, &</s>
            <s xml:id="echoid-s3193" xml:space="preserve">c: </s>
            <s xml:id="echoid-s3194" xml:space="preserve">ſicut ſuperius dictum eſt, ſemper ma-
              <lb/>
            net poteſtas ipſius a in ultimo producto ex termino a
              <emph style="super">3</emph>
            + a
              <emph style="super">2</emph>
            b
              <lb/>
            altior poteſtate ulla ipſius a in ultimo producto termini
              <lb/>
            ba
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            a, quoniam illos cum æqualibus quantitatibus ad-
              <lb/>
            dendo, ſubſtrahendo, &</s>
            <s xml:id="echoid-s3195" xml:space="preserve">c, ſemper manent in factis eædem
              <lb/>
            poteſtates, & </s>
            <s xml:id="echoid-s3196" xml:space="preserve">illos in ſe eodem modo multiplicando ſemper
              <lb/>
            magis elevatur altior poteſtas in termino a
              <emph style="super">3</emph>
            + a
              <emph style="super">2</emph>
            b quam ele-
              <lb/>
            vatur depreſſior poteſtas in termino ba
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            a, & </s>
            <s xml:id="echoid-s3197" xml:space="preserve">ex illis
              <lb/>
            eaſdem radices extrahendo, ubi a fuerat elevatior in poteſta-
              <lb/>
            te erit etiam elevatior in radice: </s>
            <s xml:id="echoid-s3198" xml:space="preserve">& </s>
            <s xml:id="echoid-s3199" xml:space="preserve">quoniam eadem reperitur
              <lb/>
            altiſſima poteſtas ipſius a in termino ab
              <emph style="super">2</emph>
            + b
              <emph style="super">3</emph>
            quæ reperitur
              <lb/>
            in termino 2b
              <emph style="super">2</emph>
            a, demonſtratur ut antè altiſſimam poteſta-
              <lb/>
            tem ipſius a in ultimo producto ex termino ab
              <emph style="super">2</emph>
            + b
              <emph style="super">3</emph>
            eandem
              <lb/>
            eſſe cum altiſſima poteſtate ipſius a in ultimo producto ex
              <lb/>
            termino 2b
              <emph style="super">2</emph>
            a: </s>
            <s xml:id="echoid-s3200" xml:space="preserve">in ultimo igitur producto termini a
              <emph style="super">3</emph>
            + a
              <emph style="super">2</emph>
            b
              <lb/>
            reperitur altior poteſtas ipſius a quam in ultimo producto
              <lb/>
            termini ba
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            a, & </s>
            <s xml:id="echoid-s3201" xml:space="preserve">in ultimo producto termini ab
              <emph style="super">2</emph>
            + b
              <emph style="super">3</emph>
              <lb/>
            altiſſima poteſtas ipſius a eadem eſt cum altiſſima poteſtate
              <lb/>
            ipſius a in ultimo producto termini 2b
              <emph style="super">2</emph>
            a; </s>
            <s xml:id="echoid-s3202" xml:space="preserve">& </s>
            <s xml:id="echoid-s3203" xml:space="preserve">igitur ultima
              <lb/>
            producta ex terminis a
              <emph style="super">3</emph>
            + a
              <emph style="super">2</emph>
            b, ab
              <emph style="super">2</emph>
            + b
              <emph style="super">3</emph>
            , eodem modo inter
              <lb/>
            ſe addita, ſubducta, multiplicata, diviſa, &</s>
            <s xml:id="echoid-s3204" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3205" xml:space="preserve">ſemper effi-
              <lb/>
            cient quantitatem, in qua reperitur altior poteſtas ipſius a
              <lb/>
            quam ulla quæ reperiri poteſt in quantitate facta ex eadem
              <lb/>
            prorſus additione, ſubductione, multiplicatione, diviſione,
              <lb/>
            &</s>
            <s xml:id="echoid-s3206" xml:space="preserve">c, productorum à terminis ba
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            a, 2b
              <emph style="super">2</emph>
            a; </s>
            <s xml:id="echoid-s3207" xml:space="preserve">quoniam al-
              <lb/>
            tior poteſtas cum altera poteſtate ſemper altiorem facit po-
              <lb/>
            teſtatem quam depreſſior poteſtas cum eadem altera poteſta-
              <lb/>
            te; </s>
            <s xml:id="echoid-s3208" xml:space="preserve">& </s>
            <s xml:id="echoid-s3209" xml:space="preserve">igitur iſtæ duæ quantitates non poſſunt eſſe indefini-
              <lb/>
            tè æquales, cum reperiatur altior poteſtas ipſius a in una
              <lb/>
            quam in altera: </s>
            <s xml:id="echoid-s3210" xml:space="preserve">atque hinc evidens eſt quod ſector circuli,
              <lb/>
            ellipſeos vel hyperbolæ A B I P non poſſit componi analy-
              <lb/>
            ticè à triangulo A B P & </s>
            <s xml:id="echoid-s3211" xml:space="preserve">trapezio A B F P, quod demon-
              <lb/>
            ſtrandum erat.</s>
            <s xml:id="echoid-s3212" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3213" xml:space="preserve">Ut autem evidentius fiat propoſitum, aliam demonſtratio-
              <lb/>
            nem treviorem faciliorem & </s>
            <s xml:id="echoid-s3214" xml:space="preserve">ex alio medio petitam hic </s>
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