Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
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
151 20
152
153 21
154
155 22
156
157 23
158
159 24
160
< >
page |< < of 213 > >|
FED. COMMANDINI
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="95">
          <pb file="0202" n="202" rhead="FED. COMMANDINI"/>
          <p>
            <s xml:space="preserve">ABSCINDATVR à portione conoidis rectanguli
              <lb/>
            a b c alia portio e b f, plano baſi æquidiſtante: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">eadem
              <lb/>
            portio ſecetur alio plano per axem; </s>
            <s xml:space="preserve">ut ſuperficiei ſectio ſit
              <lb/>
            parabole a b c: </s>
            <s xml:space="preserve">planorũ portiones abſcindentium rectæ
              <lb/>
            lineæ a c, e f: </s>
            <s xml:space="preserve">axis autem portionis, & </s>
            <s xml:space="preserve">ſectionis diameter
              <lb/>
            b d; </s>
            <s xml:space="preserve">quam linea e fin puncto g ſecet. </s>
            <s xml:space="preserve">Dico portionem co-
              <lb/>
            noidis a b c ad portionem e b f duplam proportionem ha-
              <lb/>
            bere eius, quæ eſt baſis a c ad baſim e f; </s>
            <s xml:space="preserve">uel axis d b ad b g
              <lb/>
            axem. </s>
            <s xml:space="preserve">Intelligantur enim duo coni, ſeu coni portiones
              <lb/>
            a b c, e b f, eãdem baſim, quam portiones conoidis, & </s>
            <s xml:space="preserve">æqua
              <lb/>
            lem habentes altitudinem. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam a b c portio conoi
              <lb/>
            dis ſeſquialtera eſt coni, ſeu portionis coni a b c; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">portio
              <lb/>
            e b f coniſeu portionis coni e b feſt ſeſquialtera, quod de-
              <lb/>
              <anchor type="figure" xlink:label="fig-0202-01a" xlink:href="fig-0202-01"/>
            monſtrauit Archimedes in propoſitionibus 23, & </s>
            <s xml:space="preserve">24 libri
              <lb/>
            de conoidibus, & </s>
            <s xml:space="preserve">ſphæroidibus: </s>
            <s xml:space="preserve">erit conoidis portio ad
              <lb/>
            conoidis portionem, ut conus ad conum, uel ut coni por-
              <lb/>
            tio ad coni portionem. </s>
            <s xml:space="preserve">Sed conus, uel coni portio a b c ad
              <lb/>
            conum, uel coni portionem e b f compoſitam proportio-
              <lb/>
            nem habet ex proportione baſis a c ad baſim e f, & </s>
            <s xml:space="preserve">ex pro-
              <lb/>
            portione altitudinis coni, uel coni portionis a b c ad alti-
              <lb/>
            tudinem ipſius e b f, ut nos demonſtrauimus in com men-
              <lb/>
            tariis in undecimam propoſitionem eiuſdem libri A rchi-
              <lb/>
            medis: </s>
            <s xml:space="preserve">altitudo autem ad altitudinem eſt, ut axis ad axem.
              <lb/>
            </s>
            <s xml:space="preserve">quod quidem in conis rectis perſpicuum eſt, in ſcalenis ue</s>
          </p>
        </div>
      </text>
    </echo>