Caverni, Raffaello, Storia del metodo sperimentale in Italia, 1891-1900

Table of figures

< >
[Figure 711]
Page: 2714
[Figure 712]
Page: 2714
[Figure 713]
Page: 2715
[Figure 714]
Page: 2716
[Figure 715]
Page: 2716
[Figure 716]
Page: 2718
[Figure 717]
Page: 2719
[Figure 718]
Page: 2719
[Figure 719]
Page: 2721
[Figure 720]
Page: 2722
[Figure 721]
Page: 2722
[Figure 722]
Page: 2723
[Figure 723]
Page: 2725
[Figure 724]
Page: 2727
[Figure 725]
Page: 2727
[Figure 726]
Page: 2728
[Figure 727]
Page: 2730
[Figure 728]
Page: 2730
[Figure 729]
Page: 2731
[Figure 730]
Page: 2732
[Figure 731]
Page: 2732
[Figure 732]
Page: 2733
[Figure 733]
Page: 2734
[Figure 734]
Page: 2736
[Figure 735]
Page: 2737
[Figure 736]
Page: 2738
[Figure 737]
Page: 2739
[Figure 738]
Page: 2744
[Figure 739]
Page: 2745
[Figure 740]
Page: 2745
< >
page |< < of 3504 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="020/01/2736.jpg" pagenum="361"/>
              reliquum BRD, ad reliquum ERD, est ut 3 ad 2 etc. </s>
              <s>Si denique ab hoc
                <lb/>
              communi concursu R producatur recta quaedam linea per O usque ad rectam
                <lb/>
              DI; habebitur centrum reliqui frusti ” (ibid., fol. </s>
              <s>240). </s>
            </p>
            <p type="main">
              <s>Dop'aver raccontatò in che modo, e a quale occasione gli proponesse il
                <lb/>
              Cavalieri il problema, risoluto così nella sua generalità e ne'suoi particolari,
                <lb/>
              soggiungeva il Torricelli in tal guisa nella scrittura sopra citata: “ Il me­
                <lb/>
              desimo padre fra Bonaventura mi ha fatto istanza più di una volta, in diversi
                <lb/>
              tempi, acciò che io volessi trovare la dimostrazione di un altro quesito, che
                <lb/>
              neanco egli sapeva, ed è così definito: ” </s>
            </p>
            <p type="main">
              <s>“ Se sarà un solido, nato e segato come il precedente, ma che le basi
                <lb/>
              opposte siano figure composte di due mezze parabole ABC, ABF (fig. </s>
              <s>229),
                <lb/>
              congiunte con la base comune AB, e che le cime siano C ed F; si cerca il
                <lb/>
              centro di gravità delle due parti del solido. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>“ Io dimostrai che, facendosi DA alla DB come 8 a 7, nel caso propo­
                <lb/>
              stomi, e tirando la DE parallela alla BI, e di nuovo facendo OD alla OE
                <lb/>
                <figure id="id.020.01.2736.1.jpg" xlink:href="020/01/2736/1.jpg" number="734"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 229.
                <lb/>
              come 8 a 7; il punto Q, cioè il mezzo della retta
                <lb/>
              OD, era centro della parte di sopra del solido se­
                <lb/>
              gato. </s>
              <s>Ma la mia dimostrazione essendo univer­
                <lb/>
              sale, provavo che, se il solido nasceva dalla prima
                <lb/>
              parabola, che è il triangolo, la retta BD alla DA
                <lb/>
              era come 6 a 6. Se della seconda parabola, era
                <lb/>
              come 8 a 7; se della terza, come 9 a 8; se della
                <lb/>
              quarta, come 10 a 9, et sic semper. </s>
              <s>La retta poi
                <lb/>
              ED va segata nella medesima proporzione che
                <lb/>
              la BA, e si troverà il punto O. </s>
              <s>E segando per
                <lb/>
              mezzo la OD in Q, sarà Q centro della parte su­
                <lb/>
              periore del solido segato. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>“ Quanto al centro della parte inferiore non
                <lb/>
              soggiungerò altro, poichè, essendo dato il centro
                <lb/>
              di tutto, e di una parte, con la proporzione delle
                <lb/>
              parti, è dato ancora il centro della parte rima­
                <lb/>
              nente, per la VIII del primo degli Equiponde­
                <lb/>
              ranti. </s>
              <s>La dimostrazione di questo è stata da me
                <lb/>
              conferita solo al medesimo fra Bonaventura, il
                <lb/>
              quale me l'ha chiesta ” (ivi, T. XXXII, fol. </s>
              <s>42).
                <lb/>
              E allo stesso fra Bonaventura fu da questa sug­
                <lb/>
              gerita la dimostrazione della XXI della sua quinta Esercitazione geometrica,
                <lb/>
              ma la originale proposizione torricelliana è, per quel che da noi si sappia, al
                <lb/>
              pubblico ignota, per cui ci sentiamo tanto più fortemente invogliati di pub­
                <lb/>
              blicarla, come corona e fastigio delle precedenti. </s>
              <s>Ciò facciamo altresì perchè
                <lb/>
              quella si tira dietro queste altre due proposizioni, che le servon per lemmi,
                <lb/>
              il secondo dei quali specialmente è, per la sua universalità, nella Baricentrica
                <lb/>
              di non lieve importanza. </s>
            </p>
            <p type="main">
              <s>PROPOSIZIONE LIII. —
                <emph type="italics"/>
              Di due mezze parabole simili e uguali, con-
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum