Casati, Paolo, Fabrica, et uso del compasso di proportione, dove insegna à gli artefici il modo di fare in esso le necessarie divisioni, e con varij problemi ...

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          <p>
            <s xml:id="echoid-s237" xml:space="preserve">
              <pb o="12" file="0024" n="25" rhead="CAPO II."/>
            to dire come 150 à 108. </s>
            <s xml:id="echoid-s238" xml:space="preserve">Moltiplico 108 per 100, & </s>
            <s xml:id="echoid-s239" xml:space="preserve">è
              <lb/>
            10800, queſto diuido per 150, ene viene 72. </s>
            <s xml:id="echoid-s240" xml:space="preserve">Applico dun-
              <lb/>
            que la linea data al 100. </s>
            <s xml:id="echoid-s241" xml:space="preserve">100, e la diſtanza 72. </s>
            <s xml:id="echoid-s242" xml:space="preserve">72, mi dà
              <lb/>
            MX, che è quello, che ſi cercaua. </s>
            <s xml:id="echoid-s243" xml:space="preserve">In queſto eſſempio però,
              <lb/>
            perche 150, e 108 ſono a mbidue pari, baſta diuidere ciaſcu-
              <lb/>
            no per metà, e ne’ numeri 75, e 54 s’eſprime la ſteſſa propor-
              <lb/>
            tione; </s>
            <s xml:id="echoid-s244" xml:space="preserve">onde applicando MN à 75. </s>
            <s xml:id="echoid-s245" xml:space="preserve">75. </s>
            <s xml:id="echoid-s246" xml:space="preserve">la diſtanza 54. </s>
            <s xml:id="echoid-s247" xml:space="preserve">54 da-
              <lb/>
            rà l’iſteſſa MX.</s>
            <s xml:id="echoid-s248" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s249" xml:space="preserve">Mà ſe la linea data foſſ@ così lunga, che ò non haueſſimo
              <lb/>
            Compaſſo così grande, che baſtaſſe à prenderla tutta, per ap-
              <lb/>
            plicarla al noſtro stromento, ò lo Stromento foſſe così picco-
              <lb/>
            lo, che allargato non poteſſe capire tutta la linea data; </s>
            <s xml:id="echoid-s250" xml:space="preserve">Al-
              <lb/>
            lhora vna cotal linea ſi diuida per mezo, e ſe ancora riuſciſſe
              <lb/>
            troppo lunga, la metà ſi diuida di nuouo per mezo, e s’haurà
              <lb/>
            la quarta parte, e queſta quarta parte s’applichi allo Stro-
              <lb/>
            mento, come s ella foſſe la linea propoſta, e ſi cerchi la parte
              <lb/>
            determinata come ſopra; </s>
            <s xml:id="echoid-s251" xml:space="preserve">e poi queſta replicata tante volte, in
              <lb/>
            quante parti è ſtata diuiſa la linea data, ſarà la parte, che ſi de-
              <lb/>
            ſidera: </s>
            <s xml:id="echoid-s252" xml:space="preserve">onde ſe ſolo ſi diuiſe in due queſta parte trouata, ſi rad-
              <lb/>
            doppia, e ſe quella fù diuiſa in quattro, queſta ſi replica quat-
              <lb/>
            tro volte, perche le parti con i moltiplici han la ſteſſa pro-
              <lb/>
            portione (per la 15. </s>
            <s xml:id="echoid-s253" xml:space="preserve">del 5.) </s>
            <s xml:id="echoid-s254" xml:space="preserve">Così figurandoci vna linea lunga
              <lb/>
            300 determinate particelle, ſi prende la ſua quarta parte, che
              <lb/>
            ſia 75. </s>
            <s xml:id="echoid-s255" xml:space="preserve">e s’applichi allo Stromento 75. </s>
            <s xml:id="echoid-s256" xml:space="preserve">75, e ſe ſi vogliono
              <lb/>
            due terzi di tutta la data linea (che ſono 200) ſi prendano li
              <lb/>
            due terzi di 75, che ſono 50. </s>
            <s xml:id="echoid-s257" xml:space="preserve">e perche la linea tutta fù diuiſa
              <lb/>
            in quattro, ſi replichi queſta linea trouata tra 50. </s>
            <s xml:id="echoid-s258" xml:space="preserve">50 quat-
              <lb/>
            tro volte, e ſaranno appunto li due terzi della linea data,
              <lb/>
            cioè 200; </s>
            <s xml:id="echoid-s259" xml:space="preserve">poiche come 50 à 75, così 200 à 300.</s>
            <s xml:id="echoid-s260" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s261" xml:space="preserve">Che ſe dalla linea data ſi doueſſe cauar vna parte </s>
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