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

Table of figures

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              <s>
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              Cicloide. </s>
              <s>“ Pour décrire cette ligne, dice l'Autore, ayant tiré des point de la
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              Roulette des lignes paralleles à AC (fig. </s>
              <s>297), si dans chacune de ces lignes,
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              a commencer aux points de la Roulette, l'on prend une ligne égale à la por­
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              tion de la mesme ligne comprise entre la demi-circonference du cercle et
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              son axe, l'on avra les points par lesquels cette ligne est décrite. </s>
              <s>Ainsi tirant
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              comme nous avons dit la ligne GHI, si dans la mesme ligne vous prenez GN
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                <figure id="id.020.01.2818.1.jpg" xlink:href="020/01/2818/1.jpg" number="802"/>
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              <s>Figura 297.
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              égale a HI, vous avrez le point N, par lequel passe la compagne de la Tro­
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              choide. </s>
              <s>De mesme prenant dans KLM la ligne KO égale à LM, vous avrez
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              un autre point O de la mesme ligne. </s>
              <s>Et si par le centre E vous tirez EF
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              perpendiculaire a BD, et si vous la prolongez en P, jusqu'à la Roulette,
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              ayant pris de P vers F la ligne PQ égale à EF, dans la mesme ligne PF
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              vous avrez le point Q, qui est le milieu de cette ligne-cy, et auquel elle
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              change de courbure ” (pag. </s>
              <s>64). </s>
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              <s>Apparisce in primo luogo da una tal descrizione che lo spazio rinchiuso
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              fra la cicloide e la comite è diviso dalla linea PQ in due parti uguali, come
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              quelle che sono intessute de'seni retti di due quadranti del medesimo cir­
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              colo, con transiti, non equabili, ma simili qua e là nelle due figure, ond'è
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              che tutto il detto spazio è uguale a quello dello stesso mezzo cerchio. </s>
              <s>2.o Dai
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              punti N, O, Q abbassando perpendicolari sulla base AD, saranno queste linee
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              i seni versi corrispondenti ai seni retti già presi. </s>
              <s>3.o La parte superiore QB
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              della comite sarà uguale all'inferiore ANQ, perchè tutte le linee condotte
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              parallelamente alla base son tagliate in parti contrariamente uguali, e di qui
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              è ch'essa comite divide il rettangolo nel mezzo, come l'AB diagonale. </s>
              <s>Con­
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              segue in ultimo dalla fatta costruzione che i due bilinei ANQA, QBQ sono
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              uguali, e che perciò uguale spazio rinchiudono dentro l'angolo retto ADB la
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              comite e la diagonale. </s>
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              <s>La superficie dunque, che si propone a quadrare, è composta di quella
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              compresa tra la cicloide e la comite, e dell'altra occupata dal triangolo mi­
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              stilineo AQBD, uguale al rettilineo ABD, che ha per misura AD.BD/2=
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                <foreign lang="grc">π</foreign>
              DB/2.DB/2=
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              DB2/4, ossia uguale al circolo di diametro BD. </s>
              <s>Aggiunta a
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              questa l'altra superficie, compresa tra la linea cicloidale e la comite, e che </s>
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