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]

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IO. BAPT. BENED.
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                <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>
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                <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/>
                    <anchor type="figure" xlink:label="fig-0296-01a" xlink:href="fig-0296-01"/>
                  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>
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