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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<
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xml:space
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">DE IVSTITIA COMMVTATIVA.</
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<
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">Franciſco Ferrario Anciſa Iuriſconſulto
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apud
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ſubalpinos grauißimo.</
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<
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inter nos dum oportunitas vicinarum ædium, & amoris mutui
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vis, ad familiaria trahunt colloquia ego de meis mathematicis, tu de tuis
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legibus, in quibus tractandis magnum tibi nomen comparaſti loquuti ſu
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mus. </
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>
<
s
xml:id
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xml:space
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">Cum vero nonnunquam de mirabili iuſtitiæ commutatíuæ inſtitu
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to non ingratus incidiſſet ſermo, dixi modum, quo formam ſuam à proportionali-
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tate arithmetica diſiuncta, & non a coniuncta deſumat, à nemine literis proditum
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eſſe, libet autem nunc per otium latius explicare. </
s
>
<
s
xml:id
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xml:space
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">dixi enim à diſiuncta, & non con-
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iuncta proportionalitate, quia in coniuncta, ſeu continua nullo pacto fieri poteſt
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talis commutatio, cum ſemper quatuor terminos ad minus tranſeat, vt nunc vide-
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bimus.</
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</
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<
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<
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xml:space
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">Exempli gratia, Petrus ex ſuis bonis tribuat Ioanni aliquid valoris quinquagin
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ta aureorum.</
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</
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<
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xml:space
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">Vnde priuſquam Ioannes aliquid ex ſuis bonis retribuat Petro, bona ipſius Pe-
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tri diminuta erunt per quinquaginta aureos, bona verò ipſius Ioannis, aucta toti-
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dem aureis.</
s
>
</
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<
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<
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">Ecce nunc quo pacto conftituti ſunt .4. termini in proportionalitate aritmetica,
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per quos ſit talis permutatio, ſed nondum æquata, niſi fiat æqualis retributio à Ioan-
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ne ad Petrum, vt videbimus.</
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<
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<
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. </
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>.A.</
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mediante ſignificentur bona Ioannis
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vero Petri, prius quam Petrus aliquid ex bo
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nis ſuis tribuat Ioanni. </
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dat ipſi Ioan-
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ni, vnde ipſi Petro remanet
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>
. </
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<
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">Ioanni autem
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>.C.</
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quatuor igitur termini conſtituti
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ſunt
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>.B.D.C.A.</
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>
quorum
<
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>.B.</
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>
primus
<
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>.A.</
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>
quartus
<
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>.C.</
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>
uero tertius
<
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>.D.</
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>
<
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type
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ſecundus, ſed
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B. et
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ſunt in ſua naturali mediocritate abſque defectu vel exceſſu ſui ipſius. </
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<
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ita tamen ſe habet
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et
<
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>.D.</
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quia
<
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>.D.</
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>
deficit
<
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>.C.</
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>
autem excedit à ſua priori quantitate.
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</
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<
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xml:space
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">Nihilominus iſti .4. termini conſtituti ſunt in ipſa aritmetica proportionalitate, nam
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eadem quantitate qua
<
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>.D.</
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diminuta eſt à
<
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>.B.</
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>
eadem
<
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>.C.</
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>
aucta eſt ſupra
<
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>.A</
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>
.</
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</
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<
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<
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et
<
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tantummodo iuſti ſunt termini
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>.C.</
var
>
uerò et
<
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>.D.</
var
>
iniuſti, vt ad ſuam
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priorem æqualitatem reuertantur, oportebit ex
<
var
>.C.</
var
>
ſecare aliquam partem æqualis
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valoris ei, qua
<
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>.C.</
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>
ſuperat
<
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>.A.</
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>
vel qua
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>.D.</
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>
minor eſt
<
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>.B.</
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>
& ipſam partem addere ipſi
<
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>.D.</
var
>
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vt bona Petri reuertantur ad priorem ſuam quantitatem ipſius
<
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>.B.</
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>
& bona Ioannis
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remaneant æqualia
<
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>.A.</
var
>
vt prius.</
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<
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">Quare neceſſarium non eſt, vt talis proportionalitas ſit coniuncta (vt inquit Eu
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f
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atius ſeu Michael Epheſius,
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ſuper quinto capite libr. quin-
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</
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ti Ethicorum) tribus terminis
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contenta, imò oportet ut ipſa
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diſiuncta ſit, ut diximus, vbi
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non eſt neceſſe quod
<
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>.A.</
var
>
æqualis ſit
<
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>.B.</
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>
aliquo modo.</
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