Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
121 5
122
123 6
124
125 7
126
127 8
128
129 9
130
131 10
132
133 11
134
135 12
136
137 13
138
139 14
140
141 15
142
143 15
144 16
145 17
146
147 18
148
149 19
150
< >
page |< < (43) of 213 > >|
DE I _IS_ QVAE VEH. IN AQVA.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="55">
          <pb o="43" file="0097" n="97" rhead="DE I _IS_ QVAE VEH. IN AQVA."/>
        </div>
        <div type="section" level="1" n="56">
          <head xml:space="preserve">DEMONSTRATIO QVARTAE PARTIS.</head>
          <p>
            <s xml:space="preserve">HABEAT rurſum portio ad humidum in grauitate
              <lb/>
            proportionem quidem maiorem, quàm quadratum f p ad
              <lb/>
            quadratum b d; </s>
            <s xml:space="preserve">minorem uero, quàm quadratum x o ad
              <lb/>
            b d quadratum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam proportionem habet portio ad
              <lb/>
            humidum in grauitate, eandem habeat quadratum, quod
              <lb/>
            fit à linea ψ ad quadratum b d. </s>
            <s xml:space="preserve">erit ψ maior, quàm f p, & </s>
            <s xml:space="preserve">mi
              <lb/>
            nor, quàm x o. </s>
            <s xml:space="preserve">aptetur ergo quæ dam rectalinea i u inter
              <lb/>
            portiones a u q l, a x d interiecta, quæ ſit æqualis ψ, & </s>
            <s xml:space="preserve">ipſi
              <lb/>
            b d æquidiſtans: </s>
            <s xml:space="preserve">occurratq; </s>
            <s xml:space="preserve">reliquæ ſectioni in y. </s>
            <s xml:space="preserve">rurſus
              <lb/>
            u y dupla ipſius y i demonſtrabitur, ſicuti demonſtrata eſt
              <lb/>
            o g ipſius g x dupla. </s>
            <s xml:space="preserve">ducatur autem ab u linea u ο, quæ ſe
              <lb/>
            ctionem a u q l in u contingat: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta a i ad q produca
              <lb/>
            tur. </s>
            <s xml:space="preserve">eodem modo oſtendemus lineam a i ipſi i q æqualem
              <lb/>
            eſſe: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">a q ipſi
              <lb/>
              <anchor type="figure" xlink:label="fig-0097-01a" xlink:href="fig-0097-01"/>
            u ω æquidiſtan-
              <lb/>
            tem. </s>
            <s xml:space="preserve">Demon-
              <lb/>
            ſtrãdum eſt por
              <lb/>
            tionem in humi
              <lb/>
            dum demiſſam,
              <lb/>
            ĩclinatãq; </s>
            <s xml:space="preserve">adeo,
              <lb/>
            ut baſis ipſius
              <lb/>
            non contingat
              <lb/>
            humidũ, ita con
              <lb/>
            ſiſtere, ut baſis
              <lb/>
            in humidũ ma-
              <lb/>
            gis demergatur
              <lb/>
            quam ut in uno
              <lb/>
            puncto eius ſu-
              <lb/>
            perficiem cõtin
              <lb/>
            gat. </s>
            <s xml:space="preserve">Demittatur enim in humidum, ut dictum eſt; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iaceat
              <lb/>
            primo ſic inclinata, ut baſis nullo modo contingat ſuperfi-
              <lb/>
            ciem humidi. </s>
            <s xml:space="preserve">ſecta autem ipſa plano per axem ad humidi</s>
          </p>
        </div>
      </text>
    </echo>