Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

List of thumbnails

< >
411
411 (399)
412
412 (400)
413
413 (401)
414
414 (402)
415
415 (403)
416
416 (404)
417
417 (405)
418
418 (406)
419
419 (407)
420
420 (408)
< >
page |< < (408) of 445 > >|
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div758" type="section" level="3" n="44">
              <div xml:id="echoid-div758" type="letter" level="4" n="1">
                <p>
                  <s xml:id="echoid-s4878" xml:space="preserve">
                    <num value="18">
                      <pb o="408" rhead="IO. BAPT. BENED." n="420" file="0420" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0420"/>
                    18.</num>
                  puncta rectangula, hoc eſt vna vncia cum .6. punctis rectangulis. </s>
                  <s xml:id="echoid-s4879" xml:space="preserve">Deinde ex
                    <lb/>
                  multiplicatione vnciarum .2. ſecundi lateris, cum .3. trabuchis primi lateris, produ-
                    <lb/>
                  centur .6. vnciæ. </s>
                  <s xml:id="echoid-s4880" xml:space="preserve">Ex multiplicatione poſtea dictarum .2. vnciarum ſecundi lateris
                    <lb/>
                  cum .2. pedibus primi, producentur .8. puncta.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4881" xml:space="preserve">Demum ex ijſdem .2. vncijs ſecundi lateris cum .3. primi, producentur .12. atto-
                    <lb/>
                  mi, ideſt vnum punctum. </s>
                  <s xml:id="echoid-s4882" xml:space="preserve">Quæ omnia collecta facient trabucha .8. pedes .3. uncias
                    <lb/>
                  2. & attomi .3. omnes rectanguli oblongi. </s>
                  <s xml:id="echoid-s4883" xml:space="preserve">Pulcherrima profecto operatio.</s>
                </p>
                <xhtml:table>
                  <xhtml:tr>
                    <xhtml:th xml:space="preserve">Trabucha.</xhtml:th>
                    <xhtml:th xml:space="preserve">pedes.</xhtml:th>
                    <xhtml:th xml:space="preserve">vnciæ.</xhtml:th>
                  </xhtml:tr>
                  <xhtml:tr>
                    <xhtml:td xml:space="preserve">3.</xhtml:td>
                    <xhtml:td xml:space="preserve">2.</xhtml:td>
                    <xhtml:td xml:space="preserve">3.</xhtml:td>
                  </xhtml:tr>
                  <xhtml:tr>
                    <xhtml:td xml:space="preserve">2.</xhtml:td>
                    <xhtml:td xml:space="preserve">3.</xhtml:td>
                    <xhtml:td xml:space="preserve">2.</xhtml:td>
                  </xhtml:tr>
                  <xhtml:tr>
                    <xhtml:td xml:space="preserve">6.</xhtml:td>
                    <xhtml:td xml:space="preserve">4.</xhtml:td>
                    <xhtml:td xml:space="preserve">6.</xhtml:td>
                  </xhtml:tr>
                  <xhtml:tr>
                    <xhtml:td xml:space="preserve">1.</xhtml:td>
                    <xhtml:td xml:space="preserve">3.</xhtml:td>
                    <xhtml:td xml:space="preserve">1.</xhtml:td>
                    <xhtml:td xml:space="preserve">6.</xhtml:td>
                  </xhtml:tr>
                  <xhtml:tr>
                    <xhtml:td xml:space="preserve"> </xhtml:td>
                    <xhtml:td xml:space="preserve">1.</xhtml:td>
                    <xhtml:td xml:space="preserve">6.</xhtml:td>
                    <xhtml:td xml:space="preserve">8.</xhtml:td>
                  </xhtml:tr>
                  <xhtml:tr>
                    <xhtml:td xml:space="preserve"> </xhtml:td>
                    <xhtml:td xml:space="preserve"> </xhtml:td>
                    <xhtml:td xml:space="preserve"> </xhtml:td>
                    <xhtml:td xml:space="preserve">1.</xhtml:td>
                  </xhtml:tr>
                  <xhtml:tr>
                    <xhtml:td xml:space="preserve">8.</xhtml:td>
                    <xhtml:td xml:space="preserve">3.</xhtml:td>
                    <xhtml:td xml:space="preserve">2.</xhtml:td>
                    <xhtml:td xml:space="preserve">3.</xhtml:td>
                  </xhtml:tr>
                </xhtml:table>
                <p>
                  <s xml:id="echoid-s4884" xml:space="preserve">Videamus nunc exercitij cauſa, vt dixi, quomodo conueniat calculus iſte cum
                    <lb/>
                  calculo ordinario communi?</s>
                </p>
                <p>
                  <s xml:id="echoid-s4885" xml:space="preserve">Nam quotieſcunque dicta latera, fracta fuerint in vncias, primum latus erit
                    <lb/>
                  vnciarum .243. ſecundum autem .182. productum vero vnius in alterum erit vn-
                    <lb/>
                  ciarum quadratarum .44 226. quod quidem productum cum diuiſum fuerit per
                    <num value="5184">.
                      <lb/>
                    5184.</num>
                  vncias quadratas vnius trabuchi quadrati, prouentus erit .8. trabucho-
                    <lb/>
                  rum, reliquus verò numerus, ſiue fractus, erit vnciarum quadratarum .2754. qui
                    <lb/>
                  cum diuiſus fuerit per numerum .144. vnciarum vnius pedis quadrati, prouenient
                    <lb/>
                  pedes .19. quadrati cum vncijs .18. ſuperabundantibus, dicti autem pedes .19. ſignifi-
                    <lb/>
                  cant tres pedes rectangulos oblongos cum vno pede quadrato, hoc eſt cum duabus
                    <lb/>
                  vncijs rectangulis oblongis, vt ſupra.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4886" xml:space="preserve">Videndum nunc eſt, vtrum illæ .18. vnciæ æquipolleant tribus punctis rectangu-
                    <lb/>
                  lis oblongis: </s>
                  <s xml:id="echoid-s4887" xml:space="preserve">ſed hoc manifeſtè videre eſt, ex hoc, quia quęlibet vncia rectangula
                    <lb/>
                  oblonga componitur ex .72. quadratis, punctum autem rectangulum oblongum,
                    <reg norm="cum" type="context">cũ</reg>
                    <lb/>
                  ſit duodecima pars ipſius vnciæ rectangulæ oblongæ, ipſum componetur ex .6. vn-
                    <lb/>
                  cijs quadratis .18. igitur vncijs quadratis, triplum erit ipſius puncti rectanguli dicti.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4888" xml:space="preserve">Vnde clarè patet, quod, quotieſcunque voluerimus ſcire proportionem ipſarum vn
                    <lb/>
                  ciarum quadratarum ſuperabundantium, ad punctum rectangulum oblongum, ſi
                    <lb/>
                  dixerimus ex regula de tribus, ſi .72. (vncia rectangula oblonga) dat .18. quid
                    <reg norm="dabunt" type="context">dabũt</reg>
                    <lb/>
                  12? </s>
                  <s xml:id="echoid-s4889" xml:space="preserve">puncta rectangula oblonga, quarum vnaquæque eſt duodecima pars ipſius vn-
                    <lb/>
                  ciæ rectangulæ oblongæ, in præſenti autem caſu prouenient .3. pro quarto termino
                    <lb/>
                  quæſito, & habebimus propſitum.</s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>