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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28. Floreni æquantur Blancis .48. tot Groſſi erunt in .28. Florenis quot in .48. Blan-
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cis. </
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<
s
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xml:space
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">Fingamus igitur, mente, noſtram figuram .79. Theorematis Arithmetici
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e.n.</
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ſupponendo ambo producta
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et
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>.n.e.</
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inuicem ęqualia exiſtere, & vnumquod-
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que eſſe groſſorum .336. ſit etiam
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>
vnus Florenus .12. groſſorum
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>.o.n.</
var
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verò Blan-
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cus .7. eorundem groſſorum
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>.o.e.</
var
>
autem Blancorum .48. </
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<
s
xml:id
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xml:space
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">Nunc certi erimus ex .15.
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ſexti vel .20. ſeptimi Euclidis eandem fore proportionem
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ad
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quæ
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var
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ad
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>.o.
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x.</
var
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ſed
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eſt ſumma medietatis ipſius
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cum ſexta parte dictæ medietatis, ita igi-
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tur erit
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var
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ipſius
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hoc eſt ſumma medietatis
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<
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type
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ſexta parte medietatis eiuſ-
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dem, quæ ſumma in præſenti exemplo erit .28.</
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>
</
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<
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<
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xml:space
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preserve
">Hac enim ſpeculatione mediante, poteris methodum inuenire conuertendi Flo-
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renos in Blancos. </
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>
<
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xml:space
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">Vt ſi nobis propoſiti fuerint Floreni .28. </
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xml:space
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">Voluerimusq́ue inuenire
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quot Blancos faciant, ſuppoſita menſura communi, iam ſupradicta. </
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>
<
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xml:id
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xml:space
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preserve
">Nam duplica-
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bimus numerum Florenorum, à quo duplo detrahemus ſeptimam partem,
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type
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verò erit numerus quæſitus.</
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<
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<
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xml:space
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">Huiuſmodi autem rei ratio eſt, quia, cum in ſupradicta figura, proportio
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ad
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<
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>o.u.</
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ęqualis exiſtat ei, quæ
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var
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ad
<
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>.o.n.</
var
>
atque etiam
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ſit minor duplo ipſius
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>
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per ſeptimam partem ipſius dupli
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>
minor erit
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>
duplo ipſius
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>
per
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norm
="
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type
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partem eiuſdem dupli ipſius
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.</
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<
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xml:space
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">Idem affirmo de quauis conuerſione aliorum numiſmatum, quorum ſemper
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maior ſit
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verò minor. </
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<
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xml:space
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">Vt ſi
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æquiualeret .7: et
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valeret .4. et
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valeret
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42. quæ quidem
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menſuraretur ab
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.</
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<
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xml:space
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">Si cuperemus ſcire quot
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ſint in
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>
. </
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<
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xml:space
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">Primo dicemus in
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reperiri ſummam
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medietatis ſex ſeptimorum ipſius
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>
collectæ cum vna ſeptima parte ipſius
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ſeu
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(vt ita dicam) cum tertia ipſius medietatis. </
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<
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quæ eſt .6.
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cum medietate reſidui, quæ eſt .18. habebimus .24. res, quarum
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vnaquæque æqualis erit ipſi
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.</
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<
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xml:space
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">Sed ſi quis cupiat reperire
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dato
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duplicet
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à quo demat quartam
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type
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tẽ</
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ipſius
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& habebit propoſitum. </
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<
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">Nam ita ſe habere oportet
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ad
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quemad
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modum
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ad
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>.o.n</
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>
.</
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<
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style
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xml:space
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">AD EVNDEM.</
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demum ſcire à me deſideras, eſt, quod cum vendideris libram vnam
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mercis pro .4. ſolidis, & lucratus fueris .2. cum quarta parte vnius pro ſingu-
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lis decem libris, ſcire velles quantum lucri facturus eſſes in libris
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dan-
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do ſingulam libram pro .6. ſolidis.</
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<
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xml:space
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">Nulli dubium eſt quin decima pars de .2. cum quarta vnius ſit lucrum libræ vnius.
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<
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xml:space
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">Quæ decima pars ſunt
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quadrageſimæ partes, & hæc ſubducta à ſolidis .4. reli-
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qui erunt ſolidi .3. cum .31. quadrageſimis partibus pro ſorte vnius libræ. </
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>
<
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xml:space
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">Quę ſors
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ſubtracta à ſolidis .6. remanebunt ſol .2. cum .9. quadrageſimis lucri pro libra, quod
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multiplicatum per .10. proueniunt ſol .22. cum quarta parte vnius, & tantum aſcen-
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deret lucrum, quod fieri poſſet in libris decem ſi quamlibet, ſol .3. cum .31. quadra
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geſimis nobis conſtaret.</
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<
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<
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xml:space
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">Vel ſic multiplicemus ſortem vnius libræ per .10. productum erit .37. cum tribus </
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