Zanotti, Francesco Maria, Della forza de' corpi che chiamano viva libri tre, 1752

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            <s xml:id="echoid-s4112" xml:space="preserve">
              <pb o="284" file="0308" n="308" rhead="DELLA FORZA DE’ CORPI"/>
            le potenze laterali ſteſſe. </s>
            <s xml:id="echoid-s4113" xml:space="preserve">E certo le potenze non
              <lb/>
            pajono di lor natura ordinate a produrre altre po-
              <lb/>
            tenze. </s>
            <s xml:id="echoid-s4114" xml:space="preserve">E’ dunque la potenza diagonale, ſecondo lui,
              <lb/>
            non prodotta nel corpo, ma finta e immaginata.
              <lb/>
            </s>
            <s xml:id="echoid-s4115" xml:space="preserve">nell’ animo dei matematici; </s>
            <s xml:id="echoid-s4116" xml:space="preserve">i quali non volendo
              <lb/>
            valerſi di due potenze, che ſono nella natura, amano
              <lb/>
            meglio di ricorrere ad’ una ſola, che eſſi ſi fingo. </s>
            <s xml:id="echoid-s4117" xml:space="preserve">
              <lb/>
            no; </s>
            <s xml:id="echoid-s4118" xml:space="preserve">la qual ſe foſſe, farebbe lo ſteſſo effetto, che
              <lb/>
            quelle due. </s>
            <s xml:id="echoid-s4119" xml:space="preserve">Quindiè, che a conſervar l’ uguaglian-
              <lb/>
            za tra l’ azione e l’ effetto, non altro fa d’uopo ſe
              <lb/>
            non dimoſtrare, che l’azione, che fanno le due po-
              <lb/>
            tenze laterali congiunte inſieme, ſia eguale a quella
              <lb/>
            azione, che farebbe la potenza diagonale da ſe
              <lb/>
            ſola, ſe vi foſſe. </s>
            <s xml:id="echoid-s4120" xml:space="preserve">E queſto ſi è quello, che il
              <lb/>
            Padre Riccati prende a dimoſtrare, e il fa di
              <lb/>
            maniera, che la dimoſtrazione ſteſſa lo con-
              <lb/>
            duce nell’ opinione della forza viva. </s>
            <s xml:id="echoid-s4121" xml:space="preserve">Come ciò
              <lb/>
            ſia, vi ſpiegherò brevemente, proponendovi prima
              <lb/>
            un teorema di geometria aſſai bello, e non men faci-
              <lb/>
            le, ſopra cui non dovrà naſcere niuna conteſa. </s>
            <s xml:id="echoid-s4122" xml:space="preserve">Ec-
              <lb/>
            covi il teorema. </s>
            <s xml:id="echoid-s4123" xml:space="preserve">Nella diagonale AD di un paralle-
              <lb/>
            logrammo BC ſi prenda un punto
              <emph style="it">r</emph>
            , e quindi ſi guidi-
              <lb/>
            n
              <unsure/>
            o le due rette
              <emph style="it">rp, rq</emph>
            , perpendicolari ai lati AB, AC. </s>
            <s xml:id="echoid-s4124" xml:space="preserve">
              <lb/>
            Dico, che il rettangolo di AB, et A
              <emph style="it">p</emph>
            , e il rettan-
              <lb/>
            golo di AC et A
              <emph style="it">q</emph>
            , preſi inſieme, ſono eguali al
              <lb/>
            rettangolo di AD et A
              <emph style="it">r</emph>
            . </s>
            <s xml:id="echoid-s4125" xml:space="preserve">Volete voi, che io il vi
              <lb/>
            dimoſtri? </s>
            <s xml:id="echoid-s4126" xml:space="preserve">Fermoſſi quì un poco il Signor D. </s>
            <s xml:id="echoid-s4127" xml:space="preserve">Felice. </s>
            <s xml:id="echoid-s4128" xml:space="preserve">
              <lb/>
            Allora la Signora Principeſſa, quelli, diſſe, che ne
              <lb/>
            deſiderano la dimoſtrazione, deſidereranno anche. </s>
            <s xml:id="echoid-s4129" xml:space="preserve">
              <lb/>
            di trovarſela da loro ſteſſi. </s>
            <s xml:id="echoid-s4130" xml:space="preserve">Quanto a me, io ſon </s>
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