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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112
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file
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0112
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0112
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xml:space
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:
<
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et
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quorum
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et
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nobis tantummodo cogniti ſint,
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imagina
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tione deſcriptus cubus
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primi termini,
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ſecundi rermini, conſidere-
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mus etiam baſim
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quadratam ipſius cubi
<
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hoc eſt præcedentem dignitatem ip
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ſius cubi eiuſdem radicis, quæ quidem baſis
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multiplicetur per quartum
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<
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productum autem ſit
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vnde eadem proportio erit
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ad
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quæ
<
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>.b.q.</
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ad
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>.b.
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g.</
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per .25. vndecimi, ſed per primam ſexti, vel .18. aut .19. ſeptimi ita eſt
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ad
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>.i.g.</
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vt
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>.b.q.</
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ad
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xml:space
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">quare per .11. quinti
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ita erit
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ad
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vt
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ad
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ideſt
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number
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0112-01
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</
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vt
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ad
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ſed vt eſt
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ad
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ſic eſt
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ad
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per .36. vndecimi,
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ſeu per .11. octaui, vnde per .11. quin
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ti ſic erit
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>.a.q.</
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ad
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vt ad
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>.k.d</
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. </
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xml:space
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re per .9. eiuſdem
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ęqualis erit
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>.k.
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d</
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. </
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xml:space
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">Vnde rectè erit accipere radicem
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cubam
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pro
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termino
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id, quod nobis inſeruit ad inueniendam tertiam partem vnius propoſitæ propor-
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tionis.</
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<
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n
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<
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xml:space
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">THEOREMA
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.</
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vt ſpeculatio iſta ita vniuerſalis fiat vt ad
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dignitates applicari poſſit;
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</
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<
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xml:space
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">Supponamus
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et
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eſſe duas dignitates quas volueris vnius, ſed eiuſdem
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ſpeciei, et
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>.a.i.</
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dignitas præcedens dignitatem
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>.a.q.a.</
var
>
cuius multiplicatione in
<
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>.a.b.</
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>
<
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eius radix producitur dignitas
<
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>.a.q.</
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>
& ab ipſius
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>.a.i.</
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multiplicatione in
<
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reſultet
<
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>.a.
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g.</
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vnde ex .18. vel .19. ſeptimi eadem proportio erit
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>
ad
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quæ
<
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>.a.b.</
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>
ad
<
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>.g.h.</
var
>
ſed
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eadem etiam eſt
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>.a.q.</
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>
ad
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>.k.d.</
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ex ijs, quæ in .17. theoremare dixi, vnde ex .11. quinti,
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ita erit
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>.a.q.</
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ad
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vt ad
<
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>.k.d</
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>
. </
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<
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xml:space
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">Quapropter
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æqualis erit
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& ideo cum inuenta
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fuerit radix huiuſmodi dignitatis ex quantitate
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habebimus
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>.c.d.</
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ſecundum ter-
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minum quæſitum.</
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<
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xml:space
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">CLI</
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.</
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<
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<
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verò fiat, quòd cum quis voluerit dimidium alicuius datæ proportio-
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nis inuenire, rectè faciat, ſi accipiat radices quadratas illorum datorum rer-
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minorum, etſi voluerit tertiam partem, accipiat radices cubas: </
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<
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">ſi autem quartam,
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accipereradices cenſicas cenſicas ipſorum, & ſic de ſingulis in .17. </
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<
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nia patent.</
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<
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<
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xml:space
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">THEOREMA
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.</
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<
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<
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autem fiat, vt cum quis voluerit multiplicare aliquam proportionem
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per fractos, rectè faciat prius multiplicando eam per numeratorem, dein-
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de productum diuiſerit per denominationem ipſorum fractorum.</
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<
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xml:space
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">Vt exempli gratia, cum aliquis voluerit multiplicare proportionem ſeſquiquar-
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tam per duo tertia, multiplicabit prius ipſam proportionem per numeratorem .2.
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& productum, erit proportio .25. ad .16. qua poſtea diuiſa per .3. denominatorem,
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prouentus erit proportio radicis cubæ .25. ad radicem cubam .16. vel vt proportio.</
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