Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of figures

< >
[31. Figure]
[32. Figure]
[33. Figure]
[34. Figure]
[35. Figure]
[36. Figure]
[37. Figure]
[38. Figure]
[39. Figure]
[40. Figure]
[41. Figure]
[42. Figure]
[43. Figure]
[44. Figure]
[45. Figure]
[46. Figure]
[47. Figure]
[48. Figure]
[49. Figure]
[50. Figure]
[51. Figure]
[52. Figure]
[53. Figure]
[54. Figure]
[55. Figure]
[56. Figure]
[57. Figure]
[58. Figure]
[59. Figure]
[60. Figure]
< >
page |< < (43) of 213 > >|
DEIIS QVAE VEH. IN AQVA.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="57">
          <p>
            <s xml:space="preserve">
              <pb o="43" file="0101" n="101" rhead="DEIIS QVAE VEH. IN AQVA."/>
            ad quadratum bd: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam habet portio ad humidum in
              <lb/>
            grauitate, eandem quadratum nt habet ad bd quadratũ,
              <lb/>
            ex iis, quæ dicta ſunt: </s>
            <s xml:space="preserve">conſtat n t lineæ ψ æqualem eſſe,
              <lb/>
            quare & </s>
            <s xml:space="preserve">portio-
              <lb/>
              <anchor type="figure" xlink:label="fig-0101-01a" xlink:href="fig-0101-01"/>
            nes a n z, a g q
              <lb/>
            ſunt æquales. </s>
            <s xml:space="preserve">Et
              <lb/>
            quoniam in por
              <lb/>
            tionibus æquali
              <lb/>
            bus, & </s>
            <s xml:space="preserve">ſimilibus
              <lb/>
            a g q l, a n z l, ab
              <lb/>
            extremitatibus
              <lb/>
            baſiũ ductæ ſunt
              <lb/>
            a q, a z, quæ æ-
              <lb/>
            quales portiões
              <lb/>
            abſcindunt: </s>
            <s xml:space="preserve">per
              <lb/>
            ſpicuum eſt an-
              <lb/>
            gulos facere æ-
              <lb/>
            quales cum por
              <lb/>
            tionum diame-
              <lb/>
            tris: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">triangu-
              <lb/>
            lorum n fs, g ω c, angulos, qui ad f ω æquales eſſe: </s>
            <s xml:space="preserve">itemque
              <lb/>
            æquales inter ſe, s b, c b; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">s r, c r, quare & </s>
            <s xml:space="preserve">n χ, g y æquales:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">χ t y i. </s>
            <s xml:space="preserve">cũq; </s>
            <s xml:space="preserve">g h dupla ſit ipſius h i, erit n χ minor, quàm
              <lb/>
            duplaipſius χ t. </s>
            <s xml:space="preserve">Sit igitur n m ipſius m t dupla: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta
              <lb/>
            m K protrahatur ad e. </s>
            <s xml:space="preserve">Itaque centrum grauitatis totius
              <lb/>
            erit punctum K: </s>
            <s xml:space="preserve">partis eius, quæ eſt in humido, punctũ m: </s>
            <s xml:space="preserve">
              <lb/>
            eius autem, quæ extra humidum in linea protracta, quod
              <lb/>
            ſit e. </s>
            <s xml:space="preserve">ergo ex proxime demonſtratis patet, nõ manere por
              <lb/>
            tionem, ſed inclinari adeo, ut baſis nullo modo ſuperficiẽ
              <lb/>
            humidi contingat. </s>
            <s xml:space="preserve">At uero portionem conſiſtere ita, uta-
              <lb/>
            xis cum ſuperficie humidi faciat angulum angulo φ mino-
              <lb/>
            rem, ſic demonſtrabitur. </s>
            <s xml:space="preserve">conſiſtat enim, ſi fieri poteſt, ut
              <lb/>
            non faciat angulum minorem angulo φ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">alia eadem diſ-
              <lb/>
            ponantur; </s>
            <s xml:space="preserve">ut in ſubiecta figura. </s>
            <s xml:space="preserve">eodem modo demonſtra</s>
          </p>
        </div>
      </text>
    </echo>