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

Table of figures

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            <p type="main">
              <s>
                <pb xlink:href="020/01/2708.jpg" pagenum="333"/>
              ad sphaeroidem praedictam, sive ad reliquum solidum, dempto cono ABC,
                <lb/>
              est ut 4 ad 1. Ergo hemisphaerium, vel hemisphaeroides, ad dictum solidum,
                <lb/>
              est ut 2 ad 1, et, per conversionem rationis, ad conum inscriptum erit ut
                <lb/>
              2 ad 1,
                <expan abbr="q.">que</expan>
              e. </s>
              <s>d. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>“ Che il quadrato AD sia sempre doppio del rettangolo patet, perchè il
                <lb/>
              quadrato FE al quadrato AD sta come il rettangolo BEO al rettangolo BDO,
                <lb/>
              cioè come 3 a 4, ed il quadrato AD, al quadrato GE, sta come 4 a 1. Ergo
                <lb/>
              ex aequo il quadrato FE, all'EG, sta come 3 a 1. E, dividendo, il rettan­
                <lb/>
              golo FGH, al quadrato GE, sta come 2 a 1, ed al quadrato AD come 2 a 4,
                <lb/>
                <expan abbr="q.">que</expan>
              e. </s>
              <s>d. </s>
              <s>” (ivi, fol. </s>
              <s>175). </s>
            </p>
            <p type="main">
              <s>Sia ora CM, nella stessa figura 195, il cilindro circoscritto: se di lui si
                <lb/>
              tolga la scodella esterna, il rimanente è l'emisferoide nuda, della quale si
                <lb/>
              può ritrovare il centro, perch'essendo E quello del tutto, N quello della parte
                <lb/>
              tolta, che si sa essere uguale al cono MDP; avremo in Q il centro dell'emi­
                <lb/>
              sferoide che si voleva, se faremo EQ a EN reciprocamente come il cono
                <lb/>
              inscritto alla stessa emisferoide, o, per le cose ora dimostrate, come uno a
                <lb/>
              due, d'onde è manifesto che BQ è cinque delle parti, delle quali QD è tre
                <lb/>
              solamente. </s>
            </p>
            <p type="main">
              <s>Ma, per tornare all'argomento dei solidi scavati, e per mostrare la va­
                <lb/>
              rietà dell'aspetto e delle forme, sotto le quali gli con­
                <lb/>
                <figure id="id.020.01.2708.1.jpg" xlink:href="020/01/2708/1.jpg" number="701"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 196.
                <lb/>
              siderava il Torricelli, trascriveremo dal manoscritto di
                <lb/>
              lui quest'altre proposizioni. </s>
            </p>
            <p type="main">
              <s>“ PROPOSIZIONE XXXVII. —
                <emph type="italics"/>
              Esto portio circuli
                <lb/>
              ABC
                <emph.end type="italics"/>
              (fig. </s>
              <s>196)
                <emph type="italics"/>
              sive minor, sive maior semicirculi:
                <lb/>
              duae tangentes AD, DB, axis BM, et convertatur. </s>
              <s>Dico
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              solidum vasiforme, genitum a trilineo ADB, aequale esse cono DMO. ”
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>“ Ducta enim EI, erit rectangulum EFI, sive FEL, aequale quadrato EA,
                <lb/>
              per penultimam Tertii, vel quadrato GH (quadratum enim EA, ad quadra­
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              tum AD, est ut quadratum HM ad MB, sive GH ad DB, et consequentia
                <lb/>
              sunt aequalia). Quare armilla EF aequalis est circulo GH, propterea solidum
                <lb/>
              vasiforme aequalis erit cono DMO ” (ibid. </s>
              <s>T. XXX, fol. </s>
              <s>71).
                <lb/>
                <figure id="id.020.01.2708.2.jpg" xlink:href="020/01/2708/2.jpg" number="702"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 197.</s>
            </p>
            <p type="main">
              <s>“ PROPOSIZIONE XXXVIII. —
                <emph type="italics"/>
              Se la parabola
                <lb/>
              ABC
                <emph.end type="italics"/>
              (fig. </s>
              <s>197),
                <emph type="italics"/>
              il cui diametro BF, averà la tan­
                <lb/>
              gente DBE per la cima, e le tangenti AD, CE alla
                <lb/>
              base, e prodotta FD si giri la figura; sarà la sco­
                <lb/>
              della del triangolo ADF eguale al conoide, e lo
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              scodellino del trilineo DAB eguale al cono DFE,
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              e perciò medesimo sarà il centro di gravità della
                <lb/>
              scodella e del conoide; dello scodellino e del cono. </s>
              <s>”
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>“ Tirisi l'applicata GL: averà il rettangolo GIL, al quadralo AF, ra­
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              gion composta di GI ad AF, ovvero di ID a DF, ovvero di OB a BF, e di
                <lb/>
              IL a FC, e, perchè sono uguali, diremo di BF alla BF. </s>
              <s>Sta dunque il ret­
                <lb/>
              tangolo GIL, al quadrato AF, come la OB alla BF, ovvero come il quadrato
                <lb/>
              OR al quadrato FA, e però sono uguali il rettangolo GIL e il quadrato RO, </s>
            </p>
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