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
|<
<
(407)
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-div477
"
type
="
chapter
"
level
="
2
"
n
="
6
">
<
div
xml:id
="
echoid-div758
"
type
="
section
"
level
="
3
"
n
="
44
">
<
div
xml:id
="
echoid-div758
"
type
="
letter
"
level
="
4
"
n
="
1
">
<
p
>
<
s
xml:id
="
echoid-s4859
"
xml:space
="
preserve
">
<
pb
o
="
407
"
rhead
="
EPISTOL AE.
"
n
="
419
"
file
="
0419
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0419
"/>
duplum eſſe rectangulo
<
var
>.f.o.</
var
>
<
reg
norm
="
Nam
"
type
="
context
">Nã</
reg
>
<
var
>.K.i.</
var
>
ſexta pars eſt ipſius
<
var
>.f.i.</
var
>
ex ſuppoſito, et
<
var
>.i.o.</
var
>
duo-
<
lb
/>
decima ipſius
<
var
>.e.i.</
var
>
proportio igitur
<
var
>.e.i.</
var
>
ad
<
var
>.o.i.</
var
>
dupla eſt proportioni ipſius
<
var
>.f.i.</
var
>
ad
<
var
>.K.i</
var
>
.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4860
"
xml:space
="
preserve
">quare
<
var
>.K.e.</
var
>
duplo maius eſt ipſius
<
var
>.f.o.</
var
>
eo quod ſi
<
var
>.i.o.</
var
>
vel
<
var
>.f.g.</
var
>
(quod idem eſt) duplo
<
lb
/>
maius eſſet ipſo latere pręſenti
<
var
>.o.i.</
var
>
vel
<
var
>.f.g.</
var
>
</
s
>
<
s
xml:id
="
echoid-s4861
"
xml:space
="
preserve
">tunc
<
var
>.f.o.</
var
>
æquale eſſet ipſi
<
var
>.K.e.</
var
>
ex .15. ſexti
<
lb
/>
vel .20. ſeptimi quod quidem
<
var
>.f.o.</
var
>
duplo maius eſſet ipſo præſenti
<
var
>.f.o</
var
>
. </
s
>
<
s
xml:id
="
echoid-s4862
"
xml:space
="
preserve
">Rectè igitur
<
lb
/>
inquiunt dicentes productum pedis cum pede eſſe duas vncias, vel ſi mauis, ita dicas
<
lb
/>
<
var
>e.K.</
var
>
ſexta pars eſt ipſius
<
var
>.d.i.</
var
>
ex iam dictis propoſitionibus
<
var
>.f.o.</
var
>
autem eſt duodecima
<
lb
/>
ipſius
<
var
>.d.i.</
var
>
ex ijſdem, cum exſuppoſito
<
var
>.i.o.</
var
>
duodecima ſit ipſius
<
var
>.e.i.</
var
>
</
s
>
<
s
xml:id
="
echoid-s4863
"
xml:space
="
preserve
">quare
<
var
>.e.K.</
var
>
<
reg
norm
="
duplum
"
type
="
context
">duplũ</
reg
>
<
lb
/>
erit ipſius
<
var
>.f.o.</
var
>
ex commu ni notione.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4864
"
xml:space
="
preserve
">Productum verò pedis cum vncia. ſit
<
var
>.K.o.</
var
>
quod probabimus ex ijſdem rationibus
<
lb
/>
duplum eſſe ipſius
<
var
>.g.u.</
var
>
puncti rectanguli oblongi. </
s
>
<
s
xml:id
="
echoid-s4865
"
xml:space
="
preserve
">Nam
<
var
>.l.o.</
var
>
ſexta pars ſimiliter eſt
<
lb
/>
ipſius
<
var
>.g.o.</
var
>
et
<
var
>.o.u.</
var
>
duodecima ipſius
<
var
>.o.i.</
var
>
</
s
>
<
s
xml:id
="
echoid-s4866
"
xml:space
="
preserve
">quare proportio
<
var
>.i.o.</
var
>
ad
<
var
>.o.n.</
var
>
dupla eſt propor
<
lb
/>
tioni
<
var
>.g.o.</
var
>
ad
<
var
>.o.l.</
var
>
ſequitur ergo ex prædictis rationibus
<
var
>.k.o.</
var
>
duplum eſſe ipſius
<
var
>.g.u.</
var
>
<
lb
/>
vel ſic, vtlin præcedenti, cum
<
var
>.K.o.</
var
>
ſit ſexta pars ipſius
<
var
>.f.o.</
var
>
ex dictis propoſitionibus
<
var
>.
<
lb
/>
g.u.</
var
>
verò duodecima eiuſdem
<
var
>.f.o.</
var
>
ex ijſdem, nam
<
var
>.o.u.</
var
>
duodecima eſt ipſius
<
var
>.o.i.</
var
>
ergo
<
lb
/>
<
var
>K.o.</
var
>
duplo maius eſt ipſo
<
var
>.g.u</
var
>
.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4867
"
xml:space
="
preserve
">Ex ijſdemmet rationibus productum
<
var
>.l.u.</
var
>
pedis cum puncto duplum eſt ipſius
<
var
>.c.t.</
var
>
<
lb
/>
attomi rectanguli oblongi.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4868
"
xml:space
="
preserve
">Probandum nunc relinquitur productum
<
var
>.o.n.</
var
>
vnciæ cum vncia, quod eſt quadra-
<
lb
/>
tum, duplum eſſe ipſius
<
var
>.c.t.</
var
>
attomi rectanguli oblongi. </
s
>
<
s
xml:id
="
echoid-s4869
"
xml:space
="
preserve
">Nam
<
var
>.i.n.</
var
>
eſt pars vna ex .72.
<
lb
/>
ipſius
<
var
>.c.u.</
var
>
et
<
var
>.u.t.</
var
>
pars vna ex .144. ipſius
<
var
>.o.i.</
var
>
ex ſuppoſito, </
s
>
<
s
xml:id
="
echoid-s4870
"
xml:space
="
preserve
">quare proportio
<
var
>.i.o.</
var
>
ad
<
var
>.u.t.</
var
>
<
lb
/>
dupla eſt proportioni ipſius
<
var
>.c.u.</
var
>
ad
<
var
>.n.i.</
var
>
ex dictis igitur rationibus
<
var
>.o.n.</
var
>
duplo maius
<
lb
/>
eſt ipſo
<
var
>.c.t</
var
>
. </
s
>
<
s
xml:id
="
echoid-s4871
"
xml:space
="
preserve
">Vel ſi placet dicas
<
var
>.n.o.</
var
>
eſt vna pars ex .72. ipſius
<
var
>.f.o.</
var
>
exſupradictis, eo
<
lb
/>
quod
<
var
>.n.i.</
var
>
ita ſe habet ad
<
var
>.f.i.</
var
>
vt vnitas ad .72. ſed ex ijſdem rationibus
<
var
>.c.t.</
var
>
pars vna ex
<
lb
/>
144. eſt ipſius
<
var
>.f.o.</
var
>
eo quod ita ſe habet
<
var
>.u.t.</
var
>
ad
<
var
>.o.i.</
var
>
</
s
>
<
s
xml:id
="
echoid-s4872
"
xml:space
="
preserve
">quare
<
var
>.o.n.</
var
>
duplo maius erit ipſo
<
var
>.
<
lb
/>
c.t</
var
>
.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4873
"
xml:space
="
preserve
">Propoſitum ſit nobis nunc, exercitij gratia, quærere ſuperficiem alicuius rectan
<
lb
/>
guli, cuius vnum latus ſit
<
reg
norm
="
trabuchorum
"
type
="
context
">trabuchorũ</
reg
>
.3. pedum .2. & vnciarum .3. aliud vero latus ſit
<
lb
/>
trabuchorum .2. pedum .3. vnciarum vero .2.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4874
"
xml:space
="
preserve
">Huiuſmodi autem methodo mediante, multiplicando primum latus
<
reg
norm
="
dictum
"
type
="
context
">dictũ</
reg
>
.3. 2. 3.
<
lb
/>
per numerum trabucorum ſecundi lateris .2. ſcilicet producentur nobis primò trabu
<
lb
/>
cha ſuperficialia .6. pedes .4. & vnciæ .6. omnia rectagula, vt dictum eſt. </
s
>
<
s
xml:id
="
echoid-s4875
"
xml:space
="
preserve
">Multiplican-
<
lb
/>
do deinde idem primum latus .3. 2. 3. per pedes .3. ſecundi lateris. </
s
>
<
s
xml:id
="
echoid-s4876
"
xml:space
="
preserve
">Ex trabuchis .3.
<
lb
/>
primi lateris cum .3. pedibus ſecundi, producentur .9. pedes rectanguli, hoc eſt
<
lb
/>
vnus trabuchus cum tribus pedibus rectangulis. </
s
>
<
s
xml:id
="
echoid-s4877
"
xml:space
="
preserve
">Ex pedibus autem huius .2. cum
<
lb
/>
ijſdem alterius lateris .3. producentur .12. vnciæ rectangulæ ideſt vnus pes rectangu-
<
lb
/>
lus. </
s
>
<
s
xml:id
="
echoid-s4878
"
xml:space
="
preserve
">Exijſdem pedibus .3. ſecundi lateris, cum .3. vncijs primi lateris producentur
<
num
value
="
18
">.
<
lb
/>
<
xhtml:table
xlink:label
="
table-0419-01
"
xlink:href
="
table-0419-01a
">
<
xhtml:tr
>
<
xhtml:th
xml:space
="
preserve
">Trabucha.</
xhtml:th
>
<
xhtml:th
xml:space
="
preserve
">pedes.</
xhtml:th
>
<
xhtml:th
xml:space
="
preserve
">vnciæ.</
xhtml:th
>
</
xhtml:tr
>
<
xhtml:tr
>
<
xhtml:td
xml:space
="
preserve
">3.</
xhtml:td
>
<
xhtml:td
xml:space
="
preserve
">2.</
xhtml:td
>
<
xhtml:td
xml:space
="
preserve
">3.</
xhtml:td
>
</
xhtml:tr
>
<
xhtml:tr
>
<
xhtml:td
xml:space
="
preserve
">2.</
xhtml:td
>
<
xhtml:td
xml:space
="
preserve
">3.</
xhtml:td
>
<
xhtml:td
xml:space
="
preserve
">2.</
xhtml:td
>
</
xhtml:tr
>
<
xhtml:tr
>
<
xhtml:td
xml:space
="
preserve
">6.</
xhtml:td
>
<
xhtml:td
xml:space
="
preserve
">4.</
xhtml:td
>
<
xhtml:td
xml:space
="
preserve
">6.</
xhtml:td
>
</
xhtml:tr
>
<
xhtml:tr
>
<
xhtml:td
xml:space
="
preserve
">1.</
xhtml:td
>
<
xhtml:td
xml:space
="
preserve
">3.</
xhtml:td
>
<
xhtml:td
xml:space
="
preserve
">1.</
xhtml:td
>
<
xhtml:td
xml:space
="
preserve
">6.</
xhtml:td
>
</
xhtml:tr
>
<
xhtml:tr
>
<
xhtml:td
xml:space
="
preserve
"> </
xhtml:td
>
<
xhtml:td
xml:space
="
preserve
">1.</
xhtml:td
>
<
xhtml:td
xml:space
="
preserve
">6.</
xhtml:td
>
<
xhtml:td
xml:space
="
preserve
">8.</
xhtml:td
>
</
xhtml:tr
>
<
xhtml:tr
>
<
xhtml:td
xml:space
="
preserve
"> </
xhtml:td
>
<
xhtml:td
xml:space
="
preserve
"> </
xhtml:td
>
<
xhtml:td
xml:space
="
preserve
"> </
xhtml:td
>
<
xhtml:td
xml:space
="
preserve
">1.</
xhtml:td
>
</
xhtml:tr
>
<
xhtml:tr
>
<
xhtml:td
xml:space
="
preserve
">8.</
xhtml:td
>
<
xhtml:td
xml:space
="
preserve
">3.</
xhtml:td
>
<
xhtml:td
xml:space
="
preserve
">2.</
xhtml:td
>
<
xhtml:td
xml:space
="
preserve
">3.</
xhtml:td
>
</
xhtml:tr
>
</
xhtml:table
>
</
num
>
</
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>