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]
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
page
|<
<
(47)
of 445
>
>|
<
echo
version
="
1.0
">
<
text
type
="
book
"
xml:lang
="
la
">
<
div
xml:id
="
echoid-div7
"
type
="
body
"
level
="
1
"
n
="
1
">
<
div
xml:id
="
echoid-div7
"
type
="
chapter
"
level
="
2
"
n
="
1
">
<
div
xml:id
="
echoid-div140
"
type
="
math:theorem
"
level
="
3
"
n
="
71
">
<
pb
o
="
47
"
rhead
="
THEOR. ARITH.
"
n
="
59
"
file
="
0059
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0059
"/>
<
p
>
<
s
xml:id
="
echoid-s618
"
xml:space
="
preserve
">Cuius rationem ſi quæris, ſignificentur .4. numeri lineis,
<
var
>a.e.o.u.</
var
>
<
reg
norm
="
diuidaturque
"
type
="
simple
">diuidaturq́;</
reg
>
.2.
<
lb
/>
per
<
var
>.o.</
var
>
&
<
reg
norm
="
oriatur
"
type
="
simple
">oriat̃</
reg
>
. s. & per
<
var
>.u.</
var
>
<
reg
norm
="
oriatur
"
type
="
simple
">oriat̃</
reg
>
<
var
>.y.</
var
>
et
<
var
>.
<
lb
/>
<
figure
xlink:label
="
fig-0059-01
"
xlink:href
="
fig-0059-01a
"
number
="
80
">
<
image
file
="
0059-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0059-01
"/>
</
figure
>
e.</
var
>
diuiſo per
<
var
>.o.</
var
>
oriatur
<
var
>.z.</
var
>
& per
<
var
>.u.</
var
>
<
lb
/>
proueniat
<
var
>.f.</
var
>
tum
<
var
>.n.</
var
>
ſit productum
<
var
>.z.</
var
>
<
lb
/>
in
<
var
>.y.</
var
>
et
<
var
>.m.</
var
>
productum
<
var
>.s.</
var
>
in
<
var
>.f</
var
>
. </
s
>
<
s
xml:id
="
echoid-s619
"
xml:space
="
preserve
">Dico
<
lb
/>
n. futurum æquale
<
var
>.m</
var
>
. </
s
>
<
s
xml:id
="
echoid-s620
"
xml:space
="
preserve
">Sit deinde
<
var
>.
<
lb
/>
x.</
var
>
vnitas, quare ex definitione diui-
<
lb
/>
ſionis eadem erit proportio
<
var
>.s.</
var
>
ad
<
var
>.a.</
var
>
<
lb
/>
et
<
var
>.z.</
var
>
ad
<
var
>.e.</
var
>
quæ
<
var
>.x.</
var
>
ad
<
var
>.o</
var
>
. </
s
>
<
s
xml:id
="
echoid-s621
"
xml:space
="
preserve
">Sed ita ſe ha-
<
lb
/>
bet
<
var
>.a.</
var
>
ad
<
var
>.y.</
var
>
et
<
var
>.e.</
var
>
ad
<
var
>.f.</
var
>
ſicut
<
var
>.u.</
var
>
ad
<
var
>.x.</
var
>
ex
<
lb
/>
quo ſic ſe habebit
<
var
>.s.</
var
>
ad
<
var
>.a.</
var
>
ſicut
<
var
>.z.</
var
>
ad
<
lb
/>
e. et
<
var
>.a.</
var
>
ad. y, ſicut
<
var
>.e.</
var
>
ad
<
var
>.f</
var
>
. </
s
>
<
s
xml:id
="
echoid-s622
"
xml:space
="
preserve
">Itaque ex
<
lb
/>
æqualitate proportionum ſic ſe ha-
<
lb
/>
bebit s. ad
<
var
>.y.</
var
>
ſicut
<
var
>.z.</
var
>
ad
<
var
>.f</
var
>
. </
s
>
<
s
xml:id
="
echoid-s623
"
xml:space
="
preserve
">Igitur ex
<
lb
/>
15. ſexti aut .20. ſeptimi productum
<
var
>.
<
lb
/>
n.</
var
>
producto
<
var
>.m.</
var
>
æquale erit.</
s
>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div142
"
type
="
math:theorem
"
level
="
3
"
n
="
72
">
<
head
xml:id
="
echoid-head88
"
xml:space
="
preserve
">THEOREMA
<
num
value
="
72
">LXXII</
num
>
.</
head
>
<
p
>
<
s
xml:id
="
echoid-s624
"
xml:space
="
preserve
">ALIVD quoque problema à me inuentum eſt, nempe vt proponantur .4.
<
lb
/>
numeri qualeſcunque tandem, quorum duo diuiſibiles ſint, tertius diuiſor
<
lb
/>
vnius è duobus pro libito,
<
reg
norm
="
quæramusque
"
type
="
simple
">quæramusq́;</
reg
>
alterius diuidentem, qui ſic ſe habeat vt pro
<
lb
/>
ductum duorum prouenientium quarto numero propoſito ſit æquale.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s625
"
xml:space
="
preserve
">Exempli gratia, proponuntur .4. numeri .20. 48. 5. 12. porrò .20. et .48. numeri
<
lb
/>
ſint diuiſibiles et .5.
<
reg
norm
="
diuidens
"
type
="
context
">diuidẽs</
reg
>
vnius, ut potè .20. </
s
>
<
s
xml:id
="
echoid-s626
"
xml:space
="
preserve
">
<
reg
norm
="
Quærendus
"
type
="
context
">Quærẽdus</
reg
>
nunc erit diuidens alterius
<
lb
/>
nempe .48. eiuſmodi vt productum prouenientium æquale ſit .12. </
s
>
<
s
xml:id
="
echoid-s627
"
xml:space
="
preserve
">Diuidam itaque
<
num
value
="
20
">.
<
lb
/>
20.</
num
>
per .5.
<
reg
norm
="
prouenietque
"
type
="
simple
">prouenietq́;</
reg
>
4. quem per .48. multiplicabo, nempe per alterum diuiſibi-
<
lb
/>
lem,
<
reg
norm
="
ſicque
"
type
="
simple
">ſicq́;</
reg
>
proueniet .192. quod productum per quartum numerum nempe .12. diui-
<
lb
/>
fum dabit .16. qui erit diuidens quæſitus, quo diuiſo .48. proueniet .3. ſecundum ſci
<
lb
/>
licet proueniens, quo per alterum hoc eſt .4. multiplicato producetur quartus nu-
<
lb
/>
merus .12.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s628
"
xml:space
="
preserve
">Quod vt ſciamus, primus nume-
<
lb
/>
rus diuiſibilis ſignificetur
<
reg
norm
="
rectangulo
"
type
="
context
">rectãgulo</
reg
>
<
var
>.
<
lb
/>
<
figure
xlink:label
="
fig-0059-02
"
xlink:href
="
fig-0059-02a
"
number
="
81
">
<
image
file
="
0059-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0059-02
"/>
</
figure
>
a.i.</
var
>
ſecundus rectangulo
<
var
>.o.u.</
var
>
primus
<
lb
/>
diuidens latere
<
var
>.a.e.</
var
>
quartum nume-
<
lb
/>
rum rectangulo
<
var
>.i.o.</
var
>
primum proue-
<
lb
/>
niens latere
<
var
>.e.i.</
var
>
ſecundus diuidens la
<
lb
/>
tere
<
var
>.e.u.</
var
>
(hic autem eſt quem quæri-
<
lb
/>
mus) tum alterum proueniens ſigni
<
lb
/>
ficetur latere
<
var
>.e.o</
var
>
. </
s
>
<
s
xml:id
="
echoid-s629
"
xml:space
="
preserve
">Iam
<
reg
norm
="
eadem
"
type
="
context
">eadẽ</
reg
>
erit pro-
<
lb
/>
portio
<
var
>.e.i.</
var
>
ad
<
var
>.e.u.</
var
>
quæ
<
var
>.o.i.</
var
>
ad
<
var
>.o.u.</
var
>
<
lb
/>
Sed cum cognitæ ſint tres quantita-
<
lb
/>
tes
<
var
>.e.i</
var
>
:
<
var
>i.o</
var
>
: et
<
var
>.o.u.</
var
>
quarta quoque. e
<
unsure
/>
<
var
>.u.</
var
>
exregula de tribus immediatè cognoſcetur,
<
lb
/>
cætera in ſubſcripta figura facillimè patebunt.</
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>