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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THEOR. ARITH.
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æqualis .e: et
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æqualis
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. </
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gitemus abſolui corpus
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ita ut
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o.c.</
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ſit vnica recta linea, ex quo ex .25.
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vndecimi proportio
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ad
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ea-
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dem eſt quæ
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ad
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ſed ſic ſe ha-
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bet
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ad
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vt
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>.h.b.</
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ad
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ex prima ſexti aut .18. vel .19. ſe-
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ptimi itaque
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ad
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ex .11.
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quinti ſic ſe habebit. vt
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ad
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ſed
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ad
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ex eiſdem ſic ſe habet
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ut
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ad
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et
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ad
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ita ut
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>.h.
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b.</
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ad
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ex præſuppoſito. </
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xml:space
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11. prædicta
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ad
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eadem erit
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proportio quæ
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ad
<
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>.n.d</
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>
. </
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xml:space
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ex .9. quinti
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æqualis erit
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Quod erat propoſitum.</
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</
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<
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<
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xml:space
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.</
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">CVR quadrato vnius quantitatis radice proportionalis, per ſingulos tres termi
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nos diuiſo, prouenientia, ſingulis dictis terminis ſint æqualia.</
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<
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Exempli
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type
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gratia, datis tribus terminis continuis proportionalibus .9. 6. 4. qua
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dratum medij erit .36. quod per .9. diuiſum dabit .4: per .6: 6. per .4: 9.</
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<
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xml:space
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">Cuius gratia, ſint tres termini
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continui
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type
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<
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proportionales
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type
="
simple
">ꝓportionales</
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>
<
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>.a.o</
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>
:
<
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>o.c.</
var
>
et
<
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>.c.q.</
var
>
<
reg
norm
="
quadratum
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type
="
context
">quadratũ</
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>
<
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norm
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autem
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type
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reg
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<
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medij ſit
<
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>.e.c</
var
>
. </
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<
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xml:space
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type
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<
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>.a.d.</
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æquale quadrato
<
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>.e.c.</
var
>
ipſi
<
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>.a.o.</
var
>
& re-
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ctangulum
<
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>.q.p.</
var
>
æquale eidem quadrato
<
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>.e.c.</
var
>
ipſi
<
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>.c.q.</
var
>
ſi quadratum
<
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>.e.c.</
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>
per
<
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>.a.o.</
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>
diui
<
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ſerimus, proueniens erit
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var
>
<
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diuiſoque
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type
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per
<
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>.c.q.</
var
>
proueniens erit
<
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>.c.p.</
var
>
quod ſi per ſuam
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radicem
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>.o.c.</
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>
diuidatur, proueniens erit
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>.o.</
var
>
<
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<
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>
e. quod ſine dubio æquale eſt
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ſed dico
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o.d.</
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æqualem eſſe
<
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. </
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<
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xml:space
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">Nam ex .16. ſexti aut
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20. ſeptimi eadem eſt proportio
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ad
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>.o.
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c.</
var
>
quę
<
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>.o.e.</
var
>
ad
<
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>.o.d.</
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nempe
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>.o.c.</
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>
ad
<
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>.o.d.</
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itaque
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<
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>o.d.</
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>
ex .9. quinti æqualis eſt
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quandoqui
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dem ex .11. ſic ſe habet
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ad
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ſicut
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>.o.
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c.</
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ad
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. </
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<
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xml:space
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p.c.</
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probabimus
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æqualem eſſe
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>
cum
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<
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>o.c.</
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>
media ſit proportionalis,
<
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tam
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type
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inter
<
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>.c.p.</
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et
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<
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>c.q.</
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quam inter
<
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>.a.o.</
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et
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>.c.q.</
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itaque
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>.c.p.</
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>
æqua-
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lis eſt
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>.a.o</
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.</
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</
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</
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type
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<
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xml:id
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xml:space
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">THEOREMA
<
num
value
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85
">LXXXV</
num
>
.</
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>
<
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<
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xml:space
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">CVR propoſitis tribus quantitatibus continuis proportionalibus proportione
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aliarum duarum nobis datarum, multiplicata maiori poſtremarum dua-
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rum in ſummam mediæ cum minima trium primarum, productum æqua-
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le ſit producto minoris duarum in ſummam maximæ cum media trium.</
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<
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<
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xml:space
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