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

Table of figures

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[141] Fig. 22.* 19. Maii.
[142] Fig. 23.* 20. Maii.
[143] Fig. 24.* c a * 27. Maii.
[144] Fig. 25.c * 31. Maii. a *
[145] Fig. 26.* 13. Iun.
[146] Fig. 27.* 16. Ian. 1656.
[147] Fig. 28.* 19. Febr.
[148] Fig. 29.* 16. Mart.
[149] Fig. 30.* 30. Mart.
[150] Fig. 31.* 18. Apr.
[151] Fig. 32.* 17. Iun.
[152] Fig. 33.* 19. Oct.
[153] Fig. 34.* 21. Oct.
[154] Fig. 35.* 9. Nov.
[155] Fig. 36.* 27. Nov.
[156] Fig. 37.* 16. Dec.
[157] Fig. 38.* 18. Ian. 1657.
[158] Fig. 39.* 29. Mart.
[159] Fig. 40.* 30. Mart.
[160] Fig. 41.* 18. Maii.
[161] Fig. 42.* 19. Maii.
[162] Fig. 43.* 17. Dec.
[163] Fig. 44.* 18. Dec.
[164] Fig. 45.* 27. Dec.
[165] Fig. 46.* 11. Mart 1658.
[166] Fig. 47.* 16. Mart.
[167] Fig. 48.* 23. Mart.
[168] Fig. 49.* 3. Apr.
[169] Fig. 50.* 10. Nov.
[170] Fig. 51.* 16. Ian. 1659.
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          <p>
            <s xml:id="echoid-s4903" xml:space="preserve">
              <pb o="506" file="0228" n="239" rhead="CHRIST. HUGENII"/>
            ſive etiam - 3y
              <emph style="super">3</emph>
            + ayx eſſe affirmatam, ac proinde 3y
              <emph style="super">3</emph>
            - ayx
              <lb/>
            eſſe negatam: </s>
            <s xml:id="echoid-s4904" xml:space="preserve">aut quando 3xx - ay fuerit affirmata, tunc
              <lb/>
            - 3y
              <emph style="super">3</emph>
            + ayx eſſe negatam; </s>
            <s xml:id="echoid-s4905" xml:space="preserve">ac proinde 3y
              <emph style="super">3</emph>
            - ayx eſſe affir-
              <lb/>
            matam. </s>
            <s xml:id="echoid-s4906" xml:space="preserve">Per hæc itaque apparet ex quantitatibus per regulam in-
              <lb/>
            ventis, quæ erant {3y
              <emph style="super">3</emph>
            - ayx/3xx - ay} = z judiciari poſſe ad utrum ca-
              <lb/>
            ſum conſtructio tangentis pertineat; </s>
            <s xml:id="echoid-s4907" xml:space="preserve">nempe excomperta diſſi-
              <lb/>
            militudine affectionis in diviſore & </s>
            <s xml:id="echoid-s4908" xml:space="preserve">dividendo, ſequi ad prio-
              <lb/>
            rem caſum eam pertinere, hoc eſt z, ſive F E, accipiendam
              <lb/>
            eſſe verſus A: </s>
            <s xml:id="echoid-s4909" xml:space="preserve">ex ſimilitudine vero eorum affectionis ſequi ad
              <lb/>
            contrariam partem ſumendam.</s>
            <s xml:id="echoid-s4910" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">TAB. XLV.
            <lb/>
          fig. 6.</note>
          <p>
            <s xml:id="echoid-s4911" xml:space="preserve">Poteſt autem quantitas z ſive FE per regulam inventa, non-
              <lb/>
            nunquam ad ſimpliciores terminos reduci ope æquationis datæ,
              <lb/>
            quæ naturam curvæ continet: </s>
            <s xml:id="echoid-s4912" xml:space="preserve">velut in hac curva A C, axem
              <lb/>
            habente A D, verticem A, cujuſque ea eſt proprietas ut, ſi à
              <lb/>
            puncto C in eâ ſumpta, applicetur ordinatim C D, fiat pro-
              <lb/>
            ductum ex cubo B D (eſt autem B punctum in axe extra cur-
              <lb/>
            vam datam) in quadratum D A æquale cubo quadrato DC. </s>
            <s xml:id="echoid-s4913" xml:space="preserve">Si-
              <lb/>
            ve ponendo B A = a, B D = x, D C = y, fiat æquatio cur-
              <lb/>
            væ naturam continens, iſta x
              <emph style="super">5</emph>
            - 2ax
              <emph style="super">4</emph>
            + aax
              <emph style="super">3</emph>
            - y
              <emph style="super">5</emph>
            = o. </s>
            <s xml:id="echoid-s4914" xml:space="preserve">Hîc
              <lb/>
            ponendo CG eſſe tangentem, quæ occurrat axi in G, vocan-
              <lb/>
            doque GD, z, fit ſecundum regulam z = {- 5y
              <emph style="super">5</emph>
            /5x
              <emph style="super">4</emph>
            - 8ax
              <emph style="super">3</emph>
            + 3aaxx}.
              <lb/>
            </s>
            <s xml:id="echoid-s4915" xml:space="preserve">Quia autem ex datâ æquatione eſt y
              <emph style="super">5</emph>
            = x
              <emph style="super">5</emph>
            - 2ax
              <emph style="super">4</emph>
            + aax
              <emph style="super">3</emph>
            , re-
              <lb/>
            ſtituendo pro 5y id quod ipſi æquale eſt, fiet z =
              <lb/>
            {- 5x
              <emph style="super">5</emph>
            + 10ax
              <emph style="super">4</emph>
            - 5aax
              <emph style="super">3</emph>
            /5x
              <emph style="super">4</emph>
            - 8ax
              <emph style="super">3</emph>
            + 3aaxx}; </s>
            <s xml:id="echoid-s4916" xml:space="preserve">ſive dividendo per xx, erit z =
              <lb/>
            {- 5x
              <emph style="super">3</emph>
            + 10axx - 5aax/5xx - 8ax + 3aa,}. </s>
            <s xml:id="echoid-s4917" xml:space="preserve">Et rurſus, dividendo hanc fractionem
              <lb/>
            per x - a, habebitur z = {-5xx + 5ax/5x - 3a}. </s>
            <s xml:id="echoid-s4918" xml:space="preserve">Quod ſignificat
              <lb/>
            faciendum ut ſicut B D quinquies ſumpta minus B A ter, ſive
              <lb/>
            ut B A bis unà cum A D quinquies ad AD quinquies, ita BD
              <lb/>
            ad D G; </s>
            <s xml:id="echoid-s4919" xml:space="preserve">atque ita G C tacturam in C curvam A C.</s>
            <s xml:id="echoid-s4920" xml:space="preserve"/>
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