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
251 239
252 240
253 241
254 242
255 243
256 244
257 245
258 246
259 247
260 248
261 249
262 250
263 251
264 252
265 253
266 254
267 255
268 256
269 259
270 258
271 259
272 260
273 261
274 222
275 263
276 264
277 265
278 266
279 267
280 268
< >
page |< < (284) 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-div544" type="section" level="3" n="13">
              <div xml:id="echoid-div544" type="letter" level="4" n="1">
                <pb o="284" rhead="IO. BAPT. BENED." n="296" file="0296" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0296"/>
              </div>
            </div>
            <div xml:id="echoid-div548" type="section" level="3" n="14">
              <div xml:id="echoid-div548" type="letter" level="4" n="1">
                <head xml:id="echoid-head416" xml:space="preserve">DE IVSTITIA COMMVTATIVA.</head>
                <head xml:id="echoid-head417" style="it" xml:space="preserve">Franciſco Ferrario Anciſa Iuriſconſulto
                  <reg norm="ſenatorique" type="simple">ſenatoriq́ꝫ</reg>
                apud
                  <lb/>
                ſubalpinos grauißimo.</head>
                <p>
                  <s xml:id="echoid-s3522" xml:space="preserve">
                    <emph style="sc">SAepivs</emph>
                  inter nos dum oportunitas vicinarum ædium, & amoris mutui
                    <lb/>
                  vis, ad familiaria trahunt colloquia ego de meis mathematicis, tu de tuis
                    <lb/>
                  legibus, in quibus tractandis magnum tibi nomen comparaſti loquuti ſu
                    <lb/>
                  mus. </s>
                  <s xml:id="echoid-s3523" xml:space="preserve">Cum vero nonnunquam de mirabili iuſtitiæ commutatíuæ inſtitu
                    <lb/>
                  to non ingratus incidiſſet ſermo, dixi modum, quo formam ſuam à proportionali-
                    <lb/>
                  tate arithmetica diſiuncta, & non a coniuncta deſumat, à nemine literis proditum
                    <lb/>
                  eſſe, libet autem nunc per otium latius explicare. </s>
                  <s xml:id="echoid-s3524" xml:space="preserve">dixi enim à diſiuncta, & non con-
                    <lb/>
                  iuncta proportionalitate, quia in coniuncta, ſeu continua nullo pacto fieri poteſt
                    <lb/>
                  talis commutatio, cum ſemper quatuor terminos ad minus tranſeat, vt nunc vide-
                    <lb/>
                  bimus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3525" xml:space="preserve">Exempli gratia, Petrus ex ſuis bonis tribuat Ioanni aliquid valoris quinquagin
                    <lb/>
                  ta aureorum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3526" xml:space="preserve">Vnde priuſquam Ioannes aliquid ex ſuis bonis retribuat Petro, bona ipſius Pe-
                    <lb/>
                  tri diminuta erunt per quinquaginta aureos, bona verò ipſius Ioannis, aucta toti-
                    <lb/>
                  dem aureis.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3527" xml:space="preserve">Ecce nunc quo pacto conftituti ſunt .4. termini in proportionalitate aritmetica,
                    <lb/>
                  per quos ſit talis permutatio, ſed nondum æquata, niſi fiat æqualis retributio à Ioan-
                    <lb/>
                  ne ad Petrum, vt videbimus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3528" xml:space="preserve">Cogitentur itaque .4. termini aritmeticè proportionales
                    <var>.C.A.B.D</var>
                  . </s>
                  <s xml:id="echoid-s3529" xml:space="preserve">Ita quod
                    <var>.A.</var>
                    <lb/>
                  mediante ſignificentur bona Ioannis
                    <var>.B.</var>
                  vero Petri, prius quam Petrus aliquid ex bo
                    <lb/>
                  nis ſuis tribuat Ioanni. </s>
                  <s xml:id="echoid-s3530" xml:space="preserve">Tunc Petrus ſecat partem vnam ex
                    <var>.B.</var>
                    <reg norm="eamque" type="simple">eamq́;</reg>
                  dat ipſi Ioan-
                    <lb/>
                  ni, vnde ipſi Petro remanet
                    <var>.D</var>
                  . </s>
                  <s xml:id="echoid-s3531" xml:space="preserve">Ioanni autem
                    <var>.C.</var>
                  quatuor igitur termini conſtituti
                    <lb/>
                  ſunt
                    <var>.B.D.C.A.</var>
                  quorum
                    <var>.B.</var>
                  primus
                    <var>.A.</var>
                  quartus
                    <var>.C.</var>
                  uero tertius
                    <var>.D.</var>
                    <reg norm="autem" type="wordlist">aũt</reg>
                  ſecundus, ſed
                    <lb/>
                  B. et
                    <var>.A.</var>
                  ſunt in ſua naturali mediocritate abſque defectu vel exceſſu ſui ipſius. </s>
                  <s xml:id="echoid-s3532" xml:space="preserve">Non
                    <lb/>
                  ita tamen ſe habet
                    <var>.C.</var>
                  et
                    <var>.D.</var>
                  quia
                    <var>.D.</var>
                  deficit
                    <var>.C.</var>
                  autem excedit à ſua priori quantitate.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s3533" xml:space="preserve">Nihilominus iſti .4. termini conſtituti ſunt in ipſa aritmetica proportionalitate, nam
                    <lb/>
                  eadem quantitate qua
                    <var>.D.</var>
                  diminuta eſt à
                    <var>.B.</var>
                  eadem
                    <var>.C.</var>
                  aucta eſt ſupra
                    <var>.A</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s3534" xml:space="preserve">Sed quia
                    <var>.B.</var>
                  et
                    <var>.A.</var>
                  tantummodo iuſti ſunt termini
                    <var>.C.</var>
                  uerò et
                    <var>.D.</var>
                  iniuſti, vt ad ſuam
                    <lb/>
                  priorem æqualitatem reuertantur, oportebit ex
                    <var>.C.</var>
                  ſecare aliquam partem æqualis
                    <lb/>
                  valoris ei, qua
                    <var>.C.</var>
                  ſuperat
                    <var>.A.</var>
                  vel qua
                    <var>.D.</var>
                  minor eſt
                    <var>.B.</var>
                  & ipſam partem addere ipſi
                    <var>.D.</var>
                    <lb/>
                  vt bona Petri reuertantur ad priorem ſuam quantitatem ipſius
                    <var>.B.</var>
                  & bona Ioannis
                    <lb/>
                  remaneant æqualia
                    <var>.A.</var>
                  vt prius.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3535" xml:space="preserve">Quare neceſſarium non eſt, vt talis proportionalitas ſit coniuncta (vt inquit Eu
                    <lb/>
                  f
                    <gap/>
                  atius ſeu Michael Epheſius,
                    <lb/>
                  ſuper quinto capite libr. quin-
                    <lb/>
                    <figure xlink:label="fig-0296-01" xlink:href="fig-0296-01a" number="319">
                      <image file="0296-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0296-01"/>
                    </figure>
                  ti Ethicorum) tribus terminis
                    <lb/>
                  contenta, imò oportet ut ipſa
                    <lb/>
                  diſiuncta ſit, ut diximus, vbi
                    <lb/>
                  non eſt neceſſe quod
                    <var>.A.</var>
                  æqualis ſit
                    <var>.B.</var>
                  aliquo modo.</s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum