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
301 289
302 290
303 291
304 292
305 293
306 294
307 295
308 296
309 297
310 298
311 299
312 300
313 301
314 302
315 303
316 304
317 305
318 306
319 307
320 308
321 309
322 310
323 311
324 312
325 313
326 314
327 315
328 316
329 317
330 318
< >
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