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
|<
<
(117)
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-div293
"
type
="
appendix
"
level
="
3
"
n
="
1
">
<
p
>
<
s
xml:id
="
echoid-s1471
"
xml:space
="
preserve
">
<
pb
o
="
117
"
rhead
="
THEOR. ARITH.
"
n
="
129
"
file
="
0129
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0129
"/>
do ſe inuicem habentes, vt .24. et .16. quæ ſunt .21. cum tribus quintis, et .14.
<
reg
norm
="
cum
"
type
="
context
">cũ</
reg
>
dua
<
lb
/>
bus quintis, ex quo ſequitur, vt quod fit ex .21. cum tribus quintis, in 16. ęquale ſit ei
<
lb
/>
quod fit ex .14 cum duabus quintis, in .24. & ita reperiuntur duo producta æqualia,
<
lb
/>
vnum lucri, reliquum vero perditionis, vt in figura
<
var
>.M.</
var
>
clarè videtur.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1472
"
xml:space
="
preserve
">A Liud verò exemplum eſt .39. quod quidem à ſuperiori non differt, niſi quod
<
lb
/>
in fine operationis, operarius dictus lucratus eſt ſolidos .60: </
s
>
<
s
xml:id
="
echoid-s1473
"
xml:space
="
preserve
">quęritur
<
reg
norm
="
nunc
"
type
="
context
">nũc</
reg
>
vt ſu-
<
lb
/>
pra, quot fuerunt dies lucri, & quot perditionis.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1474
"
xml:space
="
preserve
">Hoc etiam abſque vlla falſa poſitione dicto citius poteſt ſolui, hoc modo,
<
reg
norm
="
diuidem
"
type
="
context
">diuidẽ</
reg
>
<
lb
/>
do ſcilicet illos .60 ſolidos per .40. ideſt per aggregatum .24. cum .16. proueniens
<
lb
/>
autem, quod erit .1. cum dimidio, adde ad latus ſuperius inuentum, hoc eſt .21. cum
<
lb
/>
tribus quintis, & ſunima erit .23. cum decima parte pro numero dierum lucri, dein-
<
lb
/>
de idem prouentum deme ex alio latere ſuperius reperto .14. cum duabus quintis, &
<
lb
/>
refiduum erit .12. cum nouem decimis, vnde habebis numerum dierum perdi-
<
lb
/>
tionis.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1475
"
xml:space
="
preserve
">Pro cuius rei ſpeculatione cogitemus in figura
<
var
>.N.</
var
>
duo dicta producta inuicem
<
lb
/>
æqualia
<
var
>.o.b.</
var
>
et
<
var
>.n.c.</
var
>
exiſtente latere
<
var
>.u.c.</
var
>
vt .24.
<
var
>u.o.</
var
>
ut .16: </
s
>
<
s
xml:id
="
echoid-s1476
"
xml:space
="
preserve
">b.u. vt .21. cum tribus quin
<
lb
/>
tis, et
<
var
>.u.n.</
var
>
vt .14. cum duabus quintis. </
s
>
<
s
xml:id
="
echoid-s1477
"
xml:space
="
preserve
">Nunc verò ſi mente concepta fuerit recta
<
var
>.e.
<
lb
/>
a.t.</
var
>
æquidiſtans
<
var
>.o.c.</
var
>
ita vt rectangulum
<
var
>.o.e.</
var
>
ſit .60. </
s
>
<
s
xml:id
="
echoid-s1478
"
xml:space
="
preserve
">tunc rectangulum, ſeu productum
<
lb
/>
<
var
>b.t.</
var
>
ſuperabit rectangulum ſeu productum
<
var
>.n.e.</
var
>
per idem .60. ex communi conceptu,
<
lb
/>
eo quòd ex producto
<
var
>.n.c.</
var
>
ſublatum eſt productum
<
var
>.a.c.</
var
>
24. & producto
<
var
>.o.b.</
var
>
additum
<
lb
/>
eſt productum
<
var
>e.a.</
var
>
16. rectè igitur feci cum diuiſerim .60 per .40. vnde prouenit mi
<
lb
/>
hi
<
var
>.u.a.</
var
>
ideſt .1. cum dimidio, quod additum ipſi
<
var
>.b.u.</
var
>
compoſuit
<
var
>.b.a.</
var
>
& dempto ex
<
var
>.u.
<
lb
/>
n.</
var
>
relinquit
<
var
>.a.n.</
var
>
pro lateribus duorum productorum
<
var
>.b.t.</
var
>
et
<
var
>.n.e</
var
>
.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1479
"
xml:space
="
preserve
">Sed ſi idem operator perdidiſſet .60. tunc cogitaremus parallelam dictam
<
var
>.e.a.</
var
>
t
<
lb
/>
ſuperius ductam eſſe ita vt ſecaret
<
var
>.b.u.</
var
>
& non
<
var
>.u.n.</
var
>
vnde adderet .24. ipſi producto
<
var
>.n.
<
lb
/>
c.</
var
>
& d@meret .16. à producto
<
var
>.b.o</
var
>
.</
s
>
</
p
>
<
figure
position
="
here
"
number
="
177
">
<
image
file
="
0129-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0129-01
"/>
</
figure
>
<
p
>
<
s
xml:id
="
echoid-s1480
"
xml:space
="
preserve
">CIRCA verò talia quæſita videtur mihi non inutile fore ſi aliquid notatu di-
<
lb
/>
gnum aduerterim, hoc eſt quod ſæpe accidere poterit ut caſus impoſſibiles
<
lb
/>
proponantur. </
s
>
<
s
xml:id
="
echoid-s1481
"
xml:space
="
preserve
">Quemadmodum ſi aliquis diceret, cupio mihi ueſtimentum con-
<
lb
/>
ficere ex duobus pannis colore & pretio differentibus, quorum unus exempli gra- </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>