Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
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
111
112
113 1
114
115 2
116
117 3
118
119 4
120
< >
page |< < of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div268" type="section" level="1" n="91">
          <p>
            <s xml:id="echoid-s4528" xml:space="preserve">
              <pb file="0182" n="182" rhead="FED. COMMANDINI"/>
            nis, quouſque in unum punctum r conueniant; </s>
            <s xml:id="echoid-s4529" xml:space="preserve">erit pyra-
              <lb/>
            midis a b c r, & </s>
            <s xml:id="echoid-s4530" xml:space="preserve">pyramidis d e f r grauitatis centrum in li-
              <lb/>
            nea r h. </s>
            <s xml:id="echoid-s4531" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s4532" xml:space="preserve">reliquæ magnitudinis, uidelicet fruſti cen-
              <lb/>
            trum in eadem linea neceſſario comperietur. </s>
            <s xml:id="echoid-s4533" xml:space="preserve">Iungantur
              <lb/>
            d b, d c, d h, d m: </s>
            <s xml:id="echoid-s4534" xml:space="preserve">& </s>
            <s xml:id="echoid-s4535" xml:space="preserve">per lineas d b, d c ducto altero plano
              <lb/>
            intelligatur fruſtum in duas pyramides diuiſum: </s>
            <s xml:id="echoid-s4536" xml:space="preserve">in pyra-
              <lb/>
            midem quidem, cuius baſis eſt triangulum a b c, uertex d:
              <lb/>
            </s>
            <s xml:id="echoid-s4537" xml:space="preserve">& </s>
            <s xml:id="echoid-s4538" xml:space="preserve">in eam, cuius idem uertex, & </s>
            <s xml:id="echoid-s4539" xml:space="preserve">baſis trapezium b c f e. </s>
            <s xml:id="echoid-s4540" xml:space="preserve">erit
              <lb/>
            igitur pyramidis a b c d axis d h, & </s>
            <s xml:id="echoid-s4541" xml:space="preserve">pyramidis b c f e d axis
              <lb/>
            d m: </s>
            <s xml:id="echoid-s4542" xml:space="preserve">atque erunt tres axes g h, d h, d m in eodem plano
              <lb/>
            d a K l. </s>
            <s xml:id="echoid-s4543" xml:space="preserve">ducatur præterea per o linea ſt ip ſi a K æquidiſtãs,
              <lb/>
            quæ lineam d h in u ſecet: </s>
            <s xml:id="echoid-s4544" xml:space="preserve">per p uero ducatur x y æquidi-
              <lb/>
            ſtans eidem, ſecansque d m in
              <lb/>
              <figure xlink:label="fig-0182-01" xlink:href="fig-0182-01a" number="135">
                <image file="0182-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0182-01"/>
              </figure>
            z: </s>
            <s xml:id="echoid-s4545" xml:space="preserve">& </s>
            <s xml:id="echoid-s4546" xml:space="preserve">iungatur z u, quæ ſecet
              <lb/>
            g h in φ. </s>
            <s xml:id="echoid-s4547" xml:space="preserve">tranſibit ea per q: </s>
            <s xml:id="echoid-s4548" xml:space="preserve">& </s>
            <s xml:id="echoid-s4549" xml:space="preserve">
              <lb/>
            erunt φ q unum, atque idem
              <lb/>
            pun ctum; </s>
            <s xml:id="echoid-s4550" xml:space="preserve">ut inferius appare-
              <lb/>
            bit. </s>
            <s xml:id="echoid-s4551" xml:space="preserve">Quoniam igitur linea u o
              <lb/>
            æ quidiſtat ipſi d g, erit d u ad
              <lb/>
              <note position="left" xlink:label="note-0182-01" xlink:href="note-0182-01a" xml:space="preserve">2. ſexti.</note>
            u h, ut g o ad o h. </s>
            <s xml:id="echoid-s4552" xml:space="preserve">Sed g o tri-
              <lb/>
            pla eſt o h. </s>
            <s xml:id="echoid-s4553" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s4554" xml:space="preserve">d u ipſius
              <lb/>
            u h eſt tripla: </s>
            <s xml:id="echoid-s4555" xml:space="preserve">& </s>
            <s xml:id="echoid-s4556" xml:space="preserve">ideo pyrami-
              <lb/>
            dis a b c d centrum grauitatis
              <lb/>
            erit punctum 11. </s>
            <s xml:id="echoid-s4557" xml:space="preserve">Rurſus quo-
              <lb/>
            niam z y ipſi d l æquidiſtat, d z
              <lb/>
            a d z m eſt, utly ad y m: </s>
            <s xml:id="echoid-s4558" xml:space="preserve">eſtque
              <lb/>
            ly ad y m, ut g p ad p n. </s>
            <s xml:id="echoid-s4559" xml:space="preserve">ergo
              <lb/>
            d z ad z m eſt, ut g p ad p n.
              <lb/>
            </s>
            <s xml:id="echoid-s4560" xml:space="preserve">Quòd cum g p ſit tripla p n; </s>
            <s xml:id="echoid-s4561" xml:space="preserve">
              <lb/>
            erit etiam d z ipſius z m tri-
              <lb/>
            pla. </s>
            <s xml:id="echoid-s4562" xml:space="preserve">atque ob eandem cauſ-
              <lb/>
            ſam punctum z eſt centrũ gra-
              <lb/>
            uitatis pyramidis b c f e d. </s>
            <s xml:id="echoid-s4563" xml:space="preserve">iun
              <lb/>
            ctaigitur z u, in ea erit </s>
          </p>
        </div>
      </text>
    </echo>
Impressum