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
171 159
172 160
173 161
174 162
175 163
176 164
177 165
178 166
179 167
180 168
181 169
182 170
183 171
184 172
185 173
186 174
187 175
188 176
189 177
190 178
191 179
192 180
193 181
194 182
195 183
196 184
197 185
198 186
199 187
200 188
< >
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