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="84">
          <p>
            <s xml:space="preserve">
              <pb file="0160" n="160" rhead="FED. COMMANDINI"/>
            æqualibus baſibus, quorum axes cum baſibus æquales an
              <lb/>
            gulos faciant. </s>
            <s xml:space="preserve">Dico ſolidum a b adſolidũ c d ita eſſe, ut axis
              <lb/>
            e f ad axem g h: </s>
            <s xml:space="preserve">nam ſi axes ad planum baſis recti ſint, il-
              <lb/>
            lud perſpicue conſtat: </s>
            <s xml:space="preserve">quoniam eadem linea, & </s>
            <s xml:space="preserve">axem & </s>
            <s xml:space="preserve">ſoli
              <lb/>
            di altitudinem determinabit. </s>
            <s xml:space="preserve">Si uero ſintinclinati, à pun-
              <lb/>
            ctis e g ad ſubiectum planum perpendiculares ducantur
              <lb/>
            e k, g l: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iungantur f_k_, h l. </s>
            <s xml:space="preserve">rurſus quoniam axes cum ba
              <lb/>
            ſibus æquales faciunt angulos, eodem modo demonſtrabi
              <lb/>
            tur, triangulum e f K triangulo g h l ſimile eſſe: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">e k ad g l,
              <lb/>
            ut e f ad g h. </s>
            <s xml:space="preserve">Solidum autem a b ad ſolidum c d eſt, ut
              <lb/>
            e K ad g l. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">ut axis e f ad axem g h. </s>
            <s xml:space="preserve">quæ omnia de
              <lb/>
            monſtrare oportebat.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">Ex iis quæ demonſtrata ſunt, facile conſtare
              <lb/>
            poteſt, priſmata omnia & </s>
            <s xml:space="preserve">pyramides, quæ trian-
              <lb/>
            gulares baſes habent, ſiue in eiſdem, ſiue in æqua
              <lb/>
            libus baſibus conſtituantur, eandem proportio-
              <lb/>
              <anchor type="note" xlink:label="note-0160-01a" xlink:href="note-0160-01"/>
            nem habere, quam altitudines: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi axes cum ba
              <lb/>
            ſibus æquales angulos contineant, ſimiliter ean-
              <lb/>
            dem, quam axes, habere proportionem: </s>
            <s xml:space="preserve">ſunt
              <lb/>
              <anchor type="note" xlink:label="note-0160-02a" xlink:href="note-0160-02"/>
            enim ſolida parallelepipeda priſmatum triangula
              <lb/>
            res baſes habentiũ dupla; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">pyramidum ſextupla.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="4">
            <note position="left" xlink:label="note-0160-01" xlink:href="note-0160-01a" xml:space="preserve">15. quinti</note>
            <note position="left" xlink:label="note-0160-02" xlink:href="note-0160-02a" xml:space="preserve">28. unde-
              <lb/>
            cimi.</note>
          </div>
          <note position="left" xml:space="preserve">7. duode-
            <lb/>
          cimi.</note>
        </div>
        <div type="section" level="1" n="85">
          <head xml:space="preserve">THE OREMA XVI. PROPOSITIO XX.</head>
          <p>
            <s xml:space="preserve">Priſmata omnia & </s>
            <s xml:space="preserve">pyramides, quæ in eiſdem,
              <lb/>
            uel æqualibus baſibus conſtituuntur, eam inter
              <lb/>
            ſe proportionem habent, quam altitudines: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi
              <lb/>
            axes cum baſibus faciant angulos æquales, eam
              <lb/>
            etiam, quam axes habent proportionem.</s>
            <s xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>