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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<
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112
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<
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<
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73
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rhead
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THEOREM. ARITH.
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n
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85
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file
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0085
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0085
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nis, ex quo
<
var
>.m.k.</
var
>
prolixior erit
<
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>.e.d.</
var
>
ex præſup poſito. </
s
>
<
s
xml:id
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echoid-s975
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xml:space
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preserve
">Poſtmodum
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>.m.e.</
var
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et
<
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>.k.d.</
var
>
dua-
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lb
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bus lineis rectis coniungantur, quæ productæ concurrentin puncto
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var
>.b.</
var
>
ducatur pari-
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lb
/>
ter
<
var
>.e.g.</
var
>
à puncto
<
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>.e.</
var
>
parallela
<
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var
>
et
<
var
>.m.a</
var
>
:
<
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>e.h.</
var
>
et
<
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>.b.q.</
var
>
parallelæ
<
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>.f.n.</
var
>
ex quo
<
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>.f.m.</
var
>
æqua-
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/>
lis erit
<
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>.n.a.</
var
>
et
<
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>.m.h</
var
>
:
<
var
>a.e.</
var
>
et
<
var
>.h.q</
var
>
:
<
var
>e.o.</
var
>
et
<
var
>.g.k</
var
>
:
<
var
>e.d.</
var
>
et
<
var
>.f.q</
var
>
:
<
var
>n.o.</
var
>
ex .34. primi Eucli. </
s
>
<
s
xml:id
="
echoid-s976
"
xml:space
="
preserve
">vnde pro
<
lb
/>
portio
<
var
>.m.h.</
var
>
ad
<
var
>.h.q.</
var
>
erit vt
<
var
>.m.g.</
var
>
ad
<
var
>.g.k.</
var
>
quandoquidem vtraque æqualis eſt propor-
<
lb
/>
tioni
<
var
>.m.e.</
var
>
ad
<
var
>.e.b.</
var
>
ex .2. ſexti, ſed cum
<
var
>.m.k.</
var
>
et
<
var
>.g.k.</
var
>
notæ ſint, pariter cognoſcetur
<
var
>.m.
<
lb
/>
g.</
var
>
ſecundum reſiduum, cum etiam notæ ſint
<
var
>.n.e.</
var
>
et
<
var
>.n.a</
var
>
. </
s
>
<
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xml:id
="
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"
xml:space
="
preserve
">Itaque cognoſcemus
<
var
>.a.e.</
var
>
hoc
<
lb
/>
eſt
<
var
>.m.h.</
var
>
cognitis verò
<
var
>.m.g</
var
>
:
<
var
>g.k.</
var
>
et
<
var
>.m.h.</
var
>
ex .15. ſexti aut .20. ſeptimi cognoſcetur
<
var
>.h.
<
lb
/>
q.</
var
>
erit igitur
<
var
>.a.e.</
var
>
aut quod idem eſt
<
var
>.m.</
var
>
hprimum reſiduum, et
<
var
>.m.g.</
var
>
ſecundum, et
<
var
>.h.
<
lb
/>
q.</
var
>
aut
<
var
>.e.o.</
var
>
proueniens, et
<
var
>.n.o.</
var
>
et
<
var
>.f.q.</
var
>
itinera vtriuſque viatoris inter ſe æqualia.
<
lb
/>
</
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">Nec verò prætermittenda eſt ſpeculatio vltimæ rationis inueniendæ quantitatis
<
lb
/>
diei, quæ conſtat ope diuiſionis producti
<
var
>.m.h.</
var
>
in .24. per
<
var
>.m.g</
var
>
. </
s
>
<
s
xml:id
="
echoid-s979
"
xml:space
="
preserve
">Ea autem eiuſmodi
<
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eſt. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Probatum fuit ſic ſe habere
<
var
>.m.h.</
var
>
ad
<
var
>.h.q.</
var
>
ut
<
var
>.m.g.</
var
>
ad
<
var
>.g.k</
var
>
. </
s
>
<
s
xml:id
="
echoid-s981
"
xml:space
="
preserve
">Itaque componendo
<
lb
/>
ſic ſe habebit
<
var
>.m.q.</
var
>
ad
<
var
>.h.q.</
var
>
vt
<
var
>.m.k.</
var
>
ad
<
var
>.g.k.</
var
>
& permutando
<
var
>.m.q.</
var
>
ad
<
var
>.m.k.</
var
>
vt
<
var
>.h.q.</
var
>
ad
<
var
>.g.
<
lb
/>
k</
var
>
. </
s
>
<
s
xml:id
="
echoid-s982
"
xml:space
="
preserve
">Sed cum ſic ſe habeat
<
var
>.m.h.</
var
>
ad
<
var
>.h.q.</
var
>
vt
<
var
>.m.g.</
var
>
ad
<
var
>.g.k.</
var
>
permutando ſic ſe habebit
<
var
>.m.
<
lb
/>
h.</
var
>
ad
<
var
>.m.g.</
var
>
vt
<
var
>.h.q.</
var
>
ad
<
var
>.g.k.</
var
>
itaque
<
lb
/>
ex .11. quinti ita
<
var
>.m.h.</
var
>
ad
<
var
>.m.g.</
var
>
vt
<
var
>.
<
lb
/>
<
figure
xlink:label
="
fig-0085-01
"
xlink:href
="
fig-0085-01a
"
number
="
116
">
<
image
file
="
0085-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0085-01
"/>
</
figure
>
m.q.</
var
>
ad
<
var
>.m.k.</
var
>
ex quo permutando
<
lb
/>
<
var
>m.h.</
var
>
ad
<
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>.m.q.</
var
>
vt
<
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>.m.g.</
var
>
ad
<
var
>.m.k.</
var
>
ſed
<
lb
/>
<
reg
norm
="
cum
"
type
="
context
">cũ</
reg
>
<
var
>.m.k.</
var
>
ſit motus toti diei reſpon
<
lb
/>
dens, ſecurè dicere poterimus, ſi
<
lb
/>
<
var
>m.g.</
var
>
talis eſt reſpectu horarum
<
num
value
="
24
">.
<
lb
/>
24.</
num
>
ſignificatarum per
<
var
>.m.k.</
var
>
qualis
<
lb
/>
<
figure
xlink:label
="
fig-0085-02
"
xlink:href
="
fig-0085-02a
"
number
="
117
">
<
image
file
="
0085-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0085-02
"/>
</
figure
>
erit
<
var
>.m.h.</
var
>
& quo
<
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/>
tæ parti dieire-
<
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/>
ſpondens: </
s
>
<
s
xml:id
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xml:space
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preserve
">quæ
<
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/>
<
reg
norm
="
poſtmodum
"
type
="
context
">poſtmodũ</
reg
>
erit
<
var
>.
<
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/>
m.q.</
var
>
quæ, vt
<
reg
norm
="
di- ctum
"
type
="
context
">di-
<
lb
/>
ctũ</
reg
>
fuit, talis eſt
<
lb
/>
reſpectu
<
var
>.m.k.</
var
>
<
lb
/>
qualis
<
var
>.m.h.</
var
>
re-
<
lb
/>
ſpectu
<
var
>.m.g</
var
>
. </
s
>
<
s
xml:id
="
echoid-s984
"
xml:space
="
preserve
">Reli
<
lb
/>
quę duæ ſpecula
<
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/>
tiones priorum
<
lb
/>
<
reg
norm
="
modorum
"
type
="
context
">modorũ</
reg
>
, vna &
<
lb
/>
eadem eſt,
<
reg
norm
="
facilisque
"
type
="
simple
">facilisq́;</
reg
>
per ſe mediocriter intelligenti. </
s
>
<
s
xml:id
="
echoid-s985
"
xml:space
="
preserve
">Eodem modo reliquæ omnes
<
lb
/>
progreſſiones ſecundi viatoris
<
reg
norm
="
cum
"
type
="
context
">cũ</
reg
>
rectangulo primi conferri ex hoc theoremate
<
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/>
poterunt.</
s
>
</
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>
</
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>
<
div
xml:id
="
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type
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level
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n
="
113
">
<
head
xml:id
="
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"
xml:space
="
preserve
">THEOREMA
<
num
value
="
113
">CXIII</
num
>
.</
head
>
<
p
>
<
s
xml:id
="
echoid-s986
"
xml:space
="
preserve
">PRoponitur & aliud, primum ſcilicet viatorem iter incipere diebus aliquot an-
<
lb
/>
tè ſecundum, primum tamen lentius, quàm ſecundum ambulare, & utrunque
<
lb
/>
eorum certa quædam milliaria conficere. </
s
>
<
s
xml:id
="
echoid-s987
"
xml:space
="
preserve
">Iam ſiſcire voluerimus in quot diebus
<
lb
/>
ſeſe conſequentur, uulgaris regula iubet, inſpici quot milliaria primus ſolus iter a-
<
lb
/>
gens confecerit, tum animaduerti differentiam diurnam motus vnius ab altero,
<
reg
norm
="
atque
"
type
="
simple
">atq;</
reg
>
<
lb
/>
milliarium numerum primi viatoris ſoli abundantis per hanc
<
reg
norm
="
differentiam
"
type
="
context
">differentiã</
reg
>
diuidi, pro
<
lb
/>
ueniens autem erit numerus dierum quæſitus.</
s
>
</
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>
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