Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
41 15
42
43 16
44
45 17
46
47 18
48
49 19
50
51 20
52
53 21
54
55 22
56
57 23
58
59 24
60
61 25
62
63 26
64
65 27
66
67 22
68
69 29
70
< >
page |< < of 213 > >|
FED. COMMANDINI
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="87">
          <p>
            <s xml:space="preserve">
              <pb file="0168" n="168" rhead="FED. COMMANDINI"/>
            ſunt uertice, eandem proportionem habent, quam ipſarũ
              <lb/>
            baſes. </s>
            <s xml:space="preserve">eadem ratione pyramis a c l k pyramidi b c l k: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">py
              <lb/>
            ramis a d l k ipſi b d l k pyramidi æqualis erit. </s>
            <s xml:space="preserve">Itaque ſi a py
              <lb/>
            ramide a c l d auferantur pyramides a clk, a d l k: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">à pyra
              <lb/>
            mide b c l d auferãtur pyramides b c l k, d b l K: </s>
            <s xml:space="preserve">quæ relin-
              <lb/>
            quuntur erunt æqualia. </s>
            <s xml:space="preserve">æqualis igitur eſt pyramis a c d k
              <lb/>
            pyramidi b c d _K_. </s>
            <s xml:space="preserve">Rurſus ſi per lineas a d, d e ducatur pla-
              <lb/>
            num quod pyramidem ſecet: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">eius & </s>
            <s xml:space="preserve">baſis communis
              <lb/>
            ſectio a e m: </s>
            <s xml:space="preserve">ſimiliter oſtendetur pyramis a b d K æqualis
              <lb/>
            pyramidi a c d
              <emph style="sc">K</emph>
            . </s>
            <s xml:space="preserve">ducto denique alio piano per lineas c a,
              <lb/>
            a f: </s>
            <s xml:space="preserve">ut eius, & </s>
            <s xml:space="preserve">trianguli c d b communis ſectio ſit c fn, py-
              <lb/>
            ramis a b c k pyramidi a c d
              <emph style="sc">K</emph>
            æqualis demonſtrabitur. </s>
            <s xml:space="preserve">cũ
              <lb/>
            ergo tres pyramides b c d _k_, a b d k, a b c k uni, & </s>
            <s xml:space="preserve">eidem py
              <lb/>
            ramidia c d k ſint æquales, omnes inter ſe ſe æquales erũt.
              <lb/>
            </s>
            <s xml:space="preserve">Sed ut pyramis a b c d ad pyramidem a b c k, ita d e axis ad
              <lb/>
            axem k e, ex uigeſima propoſitione huius: </s>
            <s xml:space="preserve">ſunt enim hæ
              <lb/>
            pyramides in eadem baſi, & </s>
            <s xml:space="preserve">axes cum baſibus æquales con
              <lb/>
            tinent angulos, quòd in eadem recta linea conſtituantur. </s>
            <s xml:space="preserve">
              <lb/>
            quare diuidendo, ut tres pyramides a c d k, b c d _K_, a b d _K_
              <lb/>
            ad pyramidem a b c _K_, ita d _k_ ad _K_ e. </s>
            <s xml:space="preserve">conſtat igitur lineam
              <lb/>
            d K ipſius _K_ e triplam eſſe. </s>
            <s xml:space="preserve">ſed & </s>
            <s xml:space="preserve">a k tripla eſt K f: </s>
            <s xml:space="preserve">itemque
              <lb/>
            b K ipſius _K_ g: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">c
              <emph style="sc">K</emph>
            ipſius
              <emph style="sc">K</emph>
            l tripla. </s>
            <s xml:space="preserve">quod eodem modo
              <lb/>
            demonſtrabimus.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <note position="right" xlink:label="note-0167-01" xlink:href="note-0167-01a" xml:space="preserve">17. huíus</note>
            <handwritten xlink:label="hd-0167-01" xlink:href="hd-0167-01a"/>
            <figure xlink:label="fig-0167-01" xlink:href="fig-0167-01a">
              <image file="0167-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0167-01"/>
            </figure>
            <note position="right" xlink:label="note-0167-02" xlink:href="note-0167-02a" xml:space="preserve">1. ſexti.</note>
            <note position="right" xlink:label="note-0167-03" xlink:href="note-0167-03a" xml:space="preserve">5. duode-
              <lb/>
            cimi.</note>
          </div>
          <p>
            <s xml:space="preserve">Sit pyramis, cuius baſis quadrilaterum a b c d; </s>
            <s xml:space="preserve">axis e f:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">diuidatur e fin g, ita ut e g ipſius g f ſit tripla. </s>
            <s xml:space="preserve">Dico cen-
              <lb/>
            trum grauitatis pyramidis eſſe punctum g. </s>
            <s xml:space="preserve">ducatur enim
              <lb/>
            linea b d diuidens baſim in duo triangula a b d, b c d: </s>
            <s xml:space="preserve">ex
              <lb/>
            quibus intelligãtur cõſtitui duæ pyramides a b d e, b c d e: </s>
            <s xml:space="preserve">
              <lb/>
            ſitque pyramidis a b d e axis e h; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">pyramidis b c d e axis
              <lb/>
            e K: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iungatur h _K_, quæ per ftranſibit: </s>
            <s xml:space="preserve">eſt enim in ipſa h K
              <lb/>
            centrum grauitatis magnitudinis compoſitæ ex triangulis
              <lb/>
            a b d, b c d, hoc eſt ipſius quadrilateri. </s>
            <s xml:space="preserve">Itaque centrum gra
              <lb/>
            uitatis pyramidis a b d e ſit punctum l: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">pyramidis b c d e
              <lb/>
            ſit m. </s>
            <s xml:space="preserve">ductaigitur l m ipſi h m lineæ æquidiſtabit: </s>
            <s xml:space="preserve">nam el ad
              <lb/>
              <anchor type="note" xlink:label="note-0168-01a" xlink:href="note-0168-01"/>
            </s>
          </p>
        </div>
      </text>
    </echo>