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]

Page concordance

< >
Scan Original
341 329
342 330
343 331
344 332
345 333
346 334
347 335
348 336
349 337
350 338
351 339
352 340
353 341
354 342
355 343
356 344
357 345
358 346
359 347
360 348
361 349
362 350
363 351
364 352
365 353
366 354
367 355
368 356
369 357
370 358
< >
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>
Impressum