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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0015
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<
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xml:space
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.</
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<
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<
emph
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reperturi qualis ſit fractus aliquis numerus reſpectu alterius; </
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xml:space
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debeant numeratores adinuicem & ita etiam denominatores, ex quo produ-
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ctum ex numeratoribus nomen capiat à producto denominatorum.</
s
>
</
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<
p
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<
s
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xml:space
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">Huius ſi cauſam noſce vis, ſume
<
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>.o.i.</
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>
&
<
var
>.o.u.</
var
>
pro totis denominatoribus, tum
<
var
>.o.e.</
var
>
<
lb
/>
&
<
var
>.o.a.</
var
>
pro numeratoribus (exempli cauſa) ſit
<
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>.o.i.</
var
>
ſenarius
<
var
>.o.u.</
var
>
quaternarius
<
var
>.o.e.</
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>
<
lb
/>
quinarius
<
var
>.o.a.</
var
>
ternarius. </
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>
<
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xml:space
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preserve
">Si noſce vis quæ ſint tres quartę partes quinque ſextarum,
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patet ex regulis practicis oriri quindecim vigeſimaſquartas. </
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>
<
s
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xml:space
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ſubſcripta ſigura depræhendetur, memores tamen eſſe oportet, quodlibet
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type
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conſiderari
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type
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ſuperficiem, producentia
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type
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tan-
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quam lineas. </
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<
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xml:space
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<
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xlink:href
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number
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<
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0015-01
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xlink:href
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linearibus eſt
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>.u.i.</
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>
aggregatum ex .24. partibus, &
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>.u.e.</
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>
<
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productum aggregatum ex .20. </
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xml:space
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ad productum totale
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ſicut
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>
ad
<
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>o.i.</
var
>
ex prima
<
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/>
ſexti aut .18. ſeptimi, ita
<
var
>.u.e.</
var
>
erunt quinque ſextæ par
<
lb
/>
tes
<
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>.u.i.</
var
>
quarum in propoſito exemplo, tres quartæ
<
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<
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type
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. </
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<
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xml:space
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multiplicabitur
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<
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type
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<
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orietur
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productum
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ita
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proportionatum
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type
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ad
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ſicut
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>.o.a.</
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>
ad
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<
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>o.u.</
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>
reperitur, ex prædictis rationibus. </
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<
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xml:space
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eſt
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tres quartas partes eſſe ipſius
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<
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type
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<
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tres
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quartæ partes
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erunt
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type
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<
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ſed
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>
quinque ſextæ ſunt ip-
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ſius
<
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>.u.i.</
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>
ex quo ſequitur bonum eſſe huiuſmodi opus.</
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<
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xml:space
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<
num
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num
>
.</
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<
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<
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<
emph
style
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">CVr</
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>
multiplicaturi fractos cum integris, rectè multiplicent numerantem fra-
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cti per numerum integrorum, partianturq́ue productum per
<
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<
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fracti, ex quo numerus quæſitus colligitur.</
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<
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<
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xml:space
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">Propter quod mente concipiamus in ſubſequenti figura, numerum integrorum
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tanquam lineam
<
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var
>
qui, verbigratia, ſit denarius, quorum vnuſquiſque ſit æqualis
<
lb
/>
<
var
>a.i.</
var
>
cogiteturq́ue productum ipſius
<
var
>.a.e.</
var
>
in
<
var
>.a.i.</
var
>
ſitq́ue
<
var
>.u.e.</
var
>
quod quidem erit dena-
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lb
/>
rius ſuperficialis, conſtituta prius
<
var
>.a.u.</
var
>
æqualis
<
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>.a.i.</
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>
&
<
var
>.a.o.</
var
>
ſint duæ tertiæ
<
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>.a.u.</
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>
<
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quarum
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type
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<
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duarum tertiarum productum in numerum
<
var
>.a.e.</
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>
ſit
<
var
>.o.e.</
var
>
pariter
<
var
>.u.i.</
var
>
vnitas ſit ſuper-
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ficialis prout
<
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>
vnitas eſt linearis, quam
<
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var
>
reſpicere debet productum
<
var
>.o.e.</
var
>
ex
<
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quo integer ſuperficialis
<
var
>.u.i.</
var
>
erit tanquam ternarius, & productum
<
var
>.o.i.</
var
>
tanquam bi
<
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/>
narius, & quia quælibet pars è viginti ipſius
<
var
>.o.e.</
var
>
æqualis eſt tertiæ parti
<
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>.u.i.</
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>
vnita-
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tis ſuperficialis; </
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<
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conſul-
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tum eſt eaſdem diuidere per denominantem
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>
compoſitum ex tribus partibus ſu
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perficialibus, & cum tam linea
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>u.a.</
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>
quam ſuperficies
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>
diuidatur in 3. partes
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les</
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noſce peroportunum eſt eiuſmodi partitionem numeri
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>
fieri per numerum
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ipſius
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>
non
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>
ex prædictis cauſis.</
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