Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
81 35
82
83 36
84
85 37
86
87 38
88
89 39
90
91 40
92
93 41
94
95 42
96
97 43
98
99 44
100
101 43
102
103
104
105
106
107
108
109
110
< >
page |< < (24) of 213 > >|
DE IIS QVAE VEH. IN AQVA.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="36">
          <p>
            <s xml:space="preserve">
              <pb o="24" file="0059" n="59" rhead="DE IIS QVAE VEH. IN AQVA."/>
            humidum ſecundum perpendicularem, quæ per z ad hu-
              <lb/>
            midi ſuperficiem ducta fuerit: </s>
            <s xml:space="preserve">quæ autem eſt extra humi-
              <lb/>
            dum ſecundum eam, quæ per gintra humidum feretur. </s>
            <s xml:space="preserve">nõ
              <lb/>
            ergo manebit portio ſic inclinata, ut ponitur: </s>
            <s xml:space="preserve">ſed neque re
              <lb/>
            ſtituecur recta: </s>
            <s xml:space="preserve">quoniam perpendicularium per z g ducta
              <lb/>
            rum, quæ quidem per z ducitur ad eas partes cadit, in qui
              <lb/>
            bus eſt l; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quæ per g ad eas, in quibus eſt a. </s>
            <s xml:space="preserve">quare ſequi-
              <lb/>
            tur centrum z ſurſum ferri: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">g deorſum. </s>
            <s xml:space="preserve">ergo partes to
              <lb/>
            tius ſolidi, quæ ſunt ad a deorſum, quæ uero ad l ſurſum
              <lb/>
            ferentur. </s>
            <s xml:space="preserve">Rurſus alia eadem ponantur: </s>
            <s xml:space="preserve">axis autem
              <lb/>
            portionis cum ſuperficie humidi angulum faciat minorẽ
              <lb/>
            eo, qui eſt ad b. </s>
            <s xml:space="preserve">minorem igitur proportionem habet qua
              <lb/>
              <anchor type="note" xlink:label="note-0059-01a" xlink:href="note-0059-01"/>
            dratum p i ad quadratum i y, quàm quadratum e ψ ad
              <lb/>
            ψ b quadratum: </s>
            <s xml:space="preserve">quare k r ad i y minorem proportionẽ
              <lb/>
            habet, quàm dimidium k r ad ψ b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">propterea i y maior
              <lb/>
            eſt, quam dupla ψ b. </s>
            <s xml:space="preserve">eſt autem ipſius o i dupla. </s>
            <s xml:space="preserve">ergo o i
              <lb/>
            ipſa ψ b maior e-
              <lb/>
              <anchor type="figure" xlink:label="fig-0059-01a" xlink:href="fig-0059-01"/>
            rit. </s>
            <s xml:space="preserve">ſed tota o ω eſt
              <lb/>
            æqualis ipſi r b:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">reliqua ω i mi-
              <lb/>
            nor quàm ψ r. </s>
            <s xml:space="preserve">qua
              <lb/>
            re & </s>
            <s xml:space="preserve">p h minor e-
              <lb/>
            rit, quàm f. </s>
            <s xml:space="preserve">Quòd
              <lb/>
            cum m p ipſi f q
              <lb/>
            ſit æqualis, cõſtat
              <lb/>
            p m maiorẽ eſſe,
              <lb/>
            quàm ſeſquialterã
              <lb/>
            ipſius p h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">p h
              <lb/>
            minorem, quam
              <lb/>
            duplam h m. </s>
            <s xml:space="preserve">Sit
              <lb/>
            p z ipſius z m du
              <lb/>
            pla. </s>
            <s xml:space="preserve">Rurſus to-
              <lb/>
            tius quidem ſolidi centrum grauitatis erit pũctum t; </s>
            <s xml:space="preserve">eius
              <lb/>
            uero partis, quæ intra humidum z: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta z t inuenia-</s>
          </p>
        </div>
      </text>
    </echo>