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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7
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rhead
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THEOR. ARITH.
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19
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file
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0019
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0019
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<
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<
s
xml:id
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xml:space
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>.a.i.</
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diuifa in partes octo, & ei æqualis in longitudine
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>
in qua-
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tuor, productum verò vnius in alteram
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<
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xlink:label
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fig-0019-01
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xlink:href
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fig-0019-01a
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number
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12
">
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file
="
0019-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0019-01
"/>
</
figure
>
ſit
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var
>.u.i.</
var
>
trigintaduarum particularum
<
lb
/>
fuperficialium fimilium &
<
reg
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="
æqualium
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type
="
context
">æqualiũ</
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>
ad-
<
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inuicem. </
s
>
<
s
xml:id
="
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"
xml:space
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">fit deinde
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>.a.e.</
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ſeptem
<
reg
norm
="
partium
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type
="
context
">partiũ</
reg
>
<
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/>
lineæ
<
var
>.a.i.</
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>
&
<
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>.a.o.</
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>
trium partium
<
var
>.a.u</
var
>
.
<
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/>
</
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<
s
xml:id
="
echoid-s100
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xml:space
="
preserve
">tunc productum
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>.a.e.</
var
>
in
<
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>.a.u.</
var
>
erit
<
var
>.u.e.</
var
>
<
lb
/>
particularum ſuperficialium vigintiocto
<
lb
/>
& productum
<
var
>.a.o.</
var
>
in
<
var
>.a.i.</
var
>
erit
<
var
>.o.i.</
var
>
par
<
lb
/>
ticularum
<
reg
norm
="
ſuperficialium
"
type
="
context
">ſuperficialiũ</
reg
>
vigintiquatuor
<
lb
/>
eiuſdem naturæ cum partibus triginta-
<
lb
/>
duabus totius denominantis communis.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s101
"
xml:space
="
preserve
">vnde diuifo numerante vigintiocto per-
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/>
numerantem vigintiquatuor, dabitur
<
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/>
vnum cum fexta parte illius vnius.</
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>
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<
head
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xml:space
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">THEOREMA
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num
value
="
10
">X</
num
>
.</
head
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<
s
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xml:space
="
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<
emph
style
="
sc
">PArtiri</
emph
>
ſeu diuidere vno numero alium numerum, eſt etiam quodammodo
<
lb
/>
eiuſmodi partem numeri diuifibilis inuenire refpectu totius numeri diuifibilis,
<
lb
/>
cuiuſmodi eſt vnitas in diuidente refpectu totius diuidentis, partem inquam numeri
<
lb
/>
diuiſibilis ſic ſe habentem ad totum numerum diuiſibilem ſicut vnitas ad totum di-
<
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/>
uidentem, quod ſimiliter ex regula de tribus præſtamus dicentes, ſi tantus numerus
<
lb
/>
diuidens dat
<
reg
norm
="
vnitatem
"
type
="
context
">vnitatẽ</
reg
>
, quid dabit numerus diuifibilis, quemadmodum ex
<
ref
id
="
ref-0006
">.15. ſexti</
ref
>
<
lb
/>
ſeu
<
ref
id
="
ref-0007
">.20. ſeptimi</
ref
>
licet ſpeculari, Idcircò quotieſcunque minorem numerum per
<
lb
/>
maiorem diuidimus, ſemper qui prouenit fractus eſt.</
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>
</
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>
<
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>
<
s
xml:id
="
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xml:space
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">Exempli gratia, ſi cogitaremus lineam
<
var
>.a.e.</
var
>
diuiſam in octo partes æquales, qua
<
lb
/>
rum vna ſcilicet vnitas effet
<
var
>.a.i.</
var
>
& cupere-
<
lb
/>
mus eam diuidere in nouem partes, ac ſcire
<
lb
/>
<
figure
xlink:label
="
fig-0019-02
"
xlink:href
="
fig-0019-02a
"
number
="
13
">
<
image
file
="
0019-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0019-02
"/>
</
figure
>
quan a ſit nona illius pars; </
s
>
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xml:id
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xml:space
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">manifeſtum eſſet,
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/>
nonam partem ipſius
<
var
>.a.e.</
var
>
minorem futuram
<
lb
/>
ipſa
<
var
>.a.i.</
var
>
cum
<
var
>.a.i.</
var
>
diminui debeat à ſua inte-
<
lb
/>
gritate eadem proportione, qua
<
var
>.a.e.</
var
>
minor
<
lb
/>
reperitur vna linea nouem partium æqualium
<
lb
/>
fingularum
<
var
>.a.i</
var
>
.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s105
"
xml:space
="
preserve
">Quod vt dilucidè cuiuis innoteſcat, hoc
<
lb
/>
etiam modo licebit videre ſitlinea
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>.n.c.</
var
>
no-
<
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/>
nupla ad
<
var
>.a.i.</
var
>
& parallela ad
<
var
>.a.e.</
var
>
dubium non
<
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/>
eſt quin
<
var
>.n.c.</
var
>
maior futura ſit ipſa
<
var
>.a.e.</
var
>
iam ſi
<
lb
/>
earum extrema congiungantur medijs duabus
<
lb
/>
lineis
<
var
>.n.a.</
var
>
et
<
var
>.c.e.</
var
>
quæ ſimul concurrant in
<
lb
/>
puncto
<
var
>.o.</
var
>
(quod eſt probatu facillimum) da-
<
lb
/>
buntur certe duo trianguli fimiles
<
var
>.a.o.e.</
var
>
et
<
var
>.n.o.c</
var
>
. </
s
>
<
s
xml:id
="
echoid-s106
"
xml:space
="
preserve
">Sit deinde
<
var
>.n.t.</
var
>
vna è partibus
<
lb
/>
ipſius
<
var
>.n.c.</
var
>
quæ
<
var
>.n.t.</
var
>
æqualis erit
<
var
>.a.i.</
var
>
ex præſuppoſito. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">ducatur deinde
<
var
>.o.t.</
var
>
quę
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/>
interſecet
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var
>.a.e.</
var
>
in puncto
<
var
>.x.</
var
>
dico
<
var
>.a.x.</
var
>
tanto minorem futuram
<
var
>.a.i.</
var
>
quanto
<
var
>.a.e.</
var
>
<
lb
/>
minor eſt
<
var
>.n.c.</
var
>
neque enim dubium eſſe poteſt quin proportiones
<
var
>.n.t.</
var
>
ad
<
var
>.a.x.</
var
>
et
<
var
>. </
var
>
</
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