Valerio, Luca, De centro gravitatis solidorvm libri tres

List of thumbnails

< >
221
221 		222
222
223
223 		224
224
225
225 		226
226
227
227 		228
228
229
229 		230
230
< >
page |< < of 283 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/221.jpg" pagenum="42"/>
              quadrupla igitur BC ipſius DK: cum igitur BC ſit
                <lb/>
              dupla ipſius KH, erit DK dimidia eiuſdem KH, & ſecta
                <lb/>
              bifariam KH in puncto D: ſed recta AG ſecabat eandem
                <lb/>
              KH bi fariam; per punctum igitur D tranſibit AG. </s>
              <s>Quo­
                <lb/>
              niam igitur parabola ADC, cuius vertex D, ſeſquiter­
                <lb/>
              tia eſt per Archimedem trianguli ADB, cuius duplum
                <lb/>
              eſt triangulum ABG, ſicut & huius triangulum ABC;
                <lb/>
              triangulum ABC quadruplum erit trianguli ADB: qua­
                <lb/>
              lium igitur partium æqualium eſt triangulum ABC duo­
                <lb/>
              decim, talium erit triangulum ADB trium, & parabola
                <lb/>
              ADB, cuius ver­
                <lb/>
              tex D quatuor: du
                <lb/>
              plum igitur erit tri­
                <lb/>
              angulum ABC
                <lb/>
              mixtum parabolæ
                <lb/>
              ADB, cuius ver­
                <lb/>
              tex D, & cen­
                <lb/>
              trum grauitatis M:
                <lb/>
              ſed trianguli ABC
                <lb/>
              rectilinei eſt cen­
                <lb/>
              trum grauitatis N,
                <lb/>
              & F
                <expan abbr="triãguli">trianguli</expan>
              ABC
                <lb/>
              mixti; dupla igitur
                <lb/>
              erit MN ipſius N
                <lb/>
              F, & MD ipſius
                <lb/>
                <figure id="id.043.01.221.1.jpg" xlink:href="043/01/221/1.jpg" number="163"/>
                <lb/>
              OF, & DN ipſius NO, propter ſimilitudinem triangulo­
                <lb/>
              rum: ſed & tota AN dupla eſt totius NG, ob centrum
                <lb/>
              grauitatis N rectilinei trianguli ABC; reliqua igitur AD
                <lb/>
              dupla eſt reliquæ GO. cum igitur AG ſit dupla ipſius
                <lb/>
              AD, quadrupla erit AG ipſiuſque GO. quare & quadru
                <lb/>
              pla AE ipſius FE ob parallelas: tripla igitur AF ipſius FE.
                <lb/>
              </s>
              <s>Rurſus quoniam ex Archimede ſeſquialtera eſt DM ipſius
                <lb/>
              MH, erit tota DH ad DM vt quinque ad tria, hoc eſt
                <lb/>
              vt decem ad ſex: ſed MD erat dupla ipſius OF; tota igi-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum