Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
61 25
62
63 26
64
65 27
66
67 22
68
69 29
70
71 30
72
73 37
74
75 32
76
77 25
78
79 34
80
81 35
82
83 36
84
85 37
86
87 38
88
89 39
90
< >
page |< < (40) of 213 > >|
DE IIS QVAE VEH. IN AQVA.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="54">
          <p>
            <s xml:space="preserve">
              <pb o="40" file="0091" n="91" rhead="DE IIS QVAE VEH. IN AQVA."/>
            ipſi i m æquidiſtãs, & </s>
            <s xml:space="preserve">contingens ſectionem in p; </s>
            <s xml:space="preserve">pt uero
              <lb/>
            æquidiſtans b d, & </s>
            <s xml:space="preserve">p s ad ipſam b d perpendicularis. </s>
            <s xml:space="preserve">Demõ
              <lb/>
            ſtrandũ eſt, portionẽ non cõſiſtereita, ſed inclinari, donec
              <lb/>
            baſis in uno puncto ſuperficiem humidi cõtingat. </s>
            <s xml:space="preserve">Maneãt
              <lb/>
            enim eadem, quæ in ſuperiori figura: </s>
            <s xml:space="preserve">ducaturq; </s>
            <s xml:space="preserve">o c ad b d
              <lb/>
            perpendicularis: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta a x ad q producatur. </s>
            <s xml:space="preserve">erit a x
              <lb/>
            æqualis ipſi x q. </s>
            <s xml:space="preserve">deĩde ducatur o χ ipſi a q æquidiſtãs. </s>
            <s xml:space="preserve">Quo
              <lb/>
            niã igitur portio ad humidũ eã in grauitate proportione
              <lb/>
            habere ponitur, quam quadratum x o ad quadratum b d:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">eandem proportionem habet pars ipſius demerſa ad to
              <lb/>
            tam; </s>
            <s xml:space="preserve">hoc eſt quadratum t p ad quadratum b d: </s>
            <s xml:space="preserve">æqualis uti
              <lb/>
            que erit t p ipſi x o: </s>
            <s xml:space="preserve">cumq; </s>
            <s xml:space="preserve">portionum i p m, a o q diame-
              <lb/>
            tri ſint æquales, & </s>
            <s xml:space="preserve">portiones ipſæ æquales erunt. </s>
            <s xml:space="preserve">Rurſus
              <lb/>
              <anchor type="note" xlink:label="note-0091-01a" xlink:href="note-0091-01"/>
            quoniam in por
              <lb/>
              <anchor type="note" xlink:label="note-0091-02a" xlink:href="note-0091-02"/>
              <anchor type="figure" xlink:label="fig-0091-01a" xlink:href="fig-0091-01"/>
            tionibus æquali
              <lb/>
            bus, & </s>
            <s xml:space="preserve">ſimilibus
              <lb/>
            a o q l, a p m l,
              <lb/>
            ductæ ſunt lineæ
              <lb/>
            a q, i m, quæ æ-
              <lb/>
            quales portio-
              <lb/>
            nes auferunt; </s>
            <s xml:space="preserve">il-
              <lb/>
            la quidem ab ex
              <lb/>
            tremitate baſis,
              <lb/>
            hæc autem non
              <lb/>
            ab extremitate:
              <lb/>
            </s>
            <s xml:space="preserve">cõſtat eam, quæ
              <lb/>
            ab extremitate
              <lb/>
            baſis ducta eſt,
              <lb/>
            minorem facere
              <lb/>
            angulum acutũ
              <lb/>
            cum diametro totius portionis. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam angulus, qui
              <lb/>
              <anchor type="note" xlink:label="note-0091-03a" xlink:href="note-0091-03"/>
            ad χ minor eſt angulo, qui ad n; </s>
            <s xml:space="preserve">maior erit b c, quàm b s:
              <lb/>
            </s>
            <s xml:space="preserve">cr autem, quàm ſr minor. </s>
            <s xml:space="preserve">quare & </s>
            <s xml:space="preserve">o g minor, quàm p z: </s>
            <s xml:space="preserve">
              <lb/>
            & </s>
            <s xml:space="preserve">g x maior, quàm z t. </s>
            <s xml:space="preserve">ergo p z maior eſt, quàm dupla z t;</s>
            <s xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>