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-s1912" xml:space="preserve">
              <pb o="100" file="0114" n="116" rhead="CAPO III."/>
            grandeil numero, piglio la metà 48, e prendo nella linea Geo-
              <lb/>
            metrica l’interuallo 48. </s>
            <s xml:id="echoid-s1913" xml:space="preserve">48, e con vn’altro Compaſſo l’inter-
              <lb/>
            uallo per eſſempio 4. </s>
            <s xml:id="echoid-s1914" xml:space="preserve">4, la cui radice è 2, ma per commodità
              <lb/>
            nella linea Aritmetica s’applicherà all’interuallo 20. </s>
            <s xml:id="echoid-s1915" xml:space="preserve">20, onde
              <lb/>
            poi s’hauranno li decimi dell’vnità: </s>
            <s xml:id="echoid-s1916" xml:space="preserve">ſe ſi applicaſſe alla linea
              <lb/>
            Arit metica, l’interuallo preſo 48. </s>
            <s xml:id="echoid-s1917" xml:space="preserve">48 non hauriamo ſe non la
              <lb/>
            radice della metà del quadrato, & </s>
            <s xml:id="echoid-s1918" xml:space="preserve">eſſa caderebbe all’interual-
              <lb/>
            lo 69. </s>
            <s xml:id="echoid-s1919" xml:space="preserve">69, cioè la radice ſaria 6 {9/10}, onde per hauer la radice
              <lb/>
            del doppio quadrato, cioè di 96, conuerrebbe raddoppiare
              <lb/>
            la radice trouata, e tra 69 decime, e 138 decime trouare il
              <lb/>
            medio proportionale 9 {7/10}. </s>
            <s xml:id="echoid-s1920" xml:space="preserve">Mà per trouare ciò ſenza fatica di
              <lb/>
            calcolo in trouar queſto medio proportionale, prendo quell’-
              <lb/>
            apertura di compaſſo, che pigliaua l’interuallo 48. </s>
            <s xml:id="echoid-s1921" xml:space="preserve">48, e l’ap-
              <lb/>
            plico nella linea Geometrica all’interuallo 10. </s>
            <s xml:id="echoid-s1922" xml:space="preserve">10, e poi (per-
              <lb/>
            che 48 è la metà di 96) prendo l’interuallo del doppio di 10,
              <lb/>
            cioè 20. </s>
            <s xml:id="echoid-s1923" xml:space="preserve">20, e queſto applico alla linea Aritmetica, in cuil’a-
              <lb/>
            pertura dell’altro Compaſſo è applicata al 20. </s>
            <s xml:id="echoid-s1924" xml:space="preserve">20, e trouo,
              <lb/>
            che queſt’vltimo interuallo cade nel 97. </s>
            <s xml:id="echoid-s1925" xml:space="preserve">97, e quaſi nel 98.
              <lb/>
            </s>
            <s xml:id="echoid-s1926" xml:space="preserve">98, onde conchiudo, chela radice del numero 96 è 9 {7/10}, e
              <lb/>
            quaſi 9 {8/10}.</s>
            <s xml:id="echoid-s1927" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1928" xml:space="preserve">E perche operando in tal maniera occorrerà, che l’interual-
              <lb/>
            lo vltimo da applicarſi alla linea Aritmetica ſarà tale, che non
              <lb/>
            capirà nell’interuallo dell’a pertura dello ſtromento, perciò ti-
              <lb/>
            riſi vna linea lunga quanto porta queſt’interuallo preſo nella
              <lb/>
            linea Geometrica: </s>
            <s xml:id="echoid-s1929" xml:space="preserve">e poi preſo nell’ Aritmetiche l’interuallo
              <lb/>
            100. </s>
            <s xml:id="echoid-s1930" xml:space="preserve">100, ſi leui dalla linea tirata; </s>
            <s xml:id="echoid-s1931" xml:space="preserve">il reſto della linea s’appli-
              <lb/>
            chi all’interuallo dell’ Aritmetiche, e s’haurà il numero da
              <lb/>
            aggiungerſi al 100: </s>
            <s xml:id="echoid-s1932" xml:space="preserve">tutte le decine ſaranno vnità, il reſto da-
              <lb/>
            rà i decimi dell’vnità. </s>
            <s xml:id="echoid-s1933" xml:space="preserve">Per eſſempio cerco la radice di 156:
              <lb/>
            </s>
            <s xml:id="echoid-s1934" xml:space="preserve">perche è troppo grande, piglio la terza parte, che è 52, e </s>
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