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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407
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EPISTOL AE.
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419
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0419
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0419
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duplum eſſe rectangulo
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>.f.o.</
var
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Nam
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type
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context
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>.K.i.</
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ſexta pars eſt ipſius
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ex ſuppoſito, et
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var
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duo-
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decima ipſius
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>
proportio igitur
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var
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ad
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dupla eſt proportioni ipſius
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ad
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var
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.
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</
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<
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xml:id
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xml:space
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var
>
duplo maius eſt ipſius
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>.f.o.</
var
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eo quod ſi
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>.i.o.</
var
>
vel
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>
(quod idem eſt) duplo
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maius eſſet ipſo latere pręſenti
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vel
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>.f.g.</
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</
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>
<
s
xml:id
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xml:space
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æquale eſſet ipſi
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ex .15. ſexti
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vel .20. ſeptimi quod quidem
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duplo maius eſſet ipſo præſenti
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var
>
. </
s
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<
s
xml:id
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xml:space
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inquiunt dicentes productum pedis cum pede eſſe duas vncias, vel ſi mauis, ita dicas
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<
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>e.K.</
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>
ſexta pars eſt ipſius
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>
ex iam dictis propoſitionibus
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var
>
autem eſt duodecima
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ipſius
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>
ex ijſdem, cum exſuppoſito
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>.i.o.</
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>
duodecima ſit ipſius
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var
>.e.i.</
var
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</
s
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<
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xml:id
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xml:space
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>
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norm
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type
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erit ipſius
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ex commu ni notione.</
s
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</
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<
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<
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xml:id
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xml:space
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>
quod probabimus ex ijſdem rationibus
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duplum eſſe ipſius
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var
>
puncti rectanguli oblongi. </
s
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<
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xml:id
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xml:space
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var
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var
>
ſexta pars ſimiliter eſt
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ipſius
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>.g.o.</
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>
et
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>.o.u.</
var
>
duodecima ipſius
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>.o.i.</
var
>
</
s
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<
s
xml:id
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xml:space
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ad
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>
dupla eſt propor
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tioni
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>
ad
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>.o.l.</
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>
ſequitur ergo ex prædictis rationibus
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>.k.o.</
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duplum eſſe ipſius
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>.g.u.</
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vel ſic, vtlin præcedenti, cum
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ſit ſexta pars ipſius
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ex dictis propoſitionibus
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g.u.</
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>
verò duodecima eiuſdem
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>
ex ijſdem, nam
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duodecima eſt ipſius
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ergo
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duplo maius eſt ipſo
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>.g.u</
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.</
s
>
</
p
>
<
p
>
<
s
xml:id
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xml:space
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preserve
">Ex ijſdemmet rationibus productum
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var
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>
pedis cum puncto duplum eſt ipſius
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var
>.c.t.</
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>
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attomi rectanguli oblongi.</
s
>
</
p
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<
p
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<
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xml:id
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xml:space
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preserve
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>
vnciæ cum vncia, quod eſt quadra-
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tum, duplum eſſe ipſius
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var
>
attomi rectanguli oblongi. </
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<
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xml:id
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xml:space
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preserve
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<
var
>.i.n.</
var
>
eſt pars vna ex .72.
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ipſius
<
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var
>
et
<
var
>.u.t.</
var
>
pars vna ex .144. ipſius
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var
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var
>
ex ſuppoſito, </
s
>
<
s
xml:id
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xml:space
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<
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
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xml:space
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<
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var
>
eſt vna pars ex .72. ipſius
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var
>
exſupradictis, eo
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/>
quod
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var
>.n.i.</
var
>
ita ſe habet ad
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var
>.f.i.</
var
>
vt vnitas ad .72. ſed ex ijſdem rationibus
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var
>.c.t.</
var
>
pars vna ex
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144. eſt ipſius
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>
eo quod ita ſe habet
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ad
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>
</
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<
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xml:space
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duplo maius erit ipſo
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>.
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c.t</
var
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.</
s
>
</
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<
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<
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xml:space
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">Propoſitum ſit nobis nunc, exercitij gratia, quærere ſuperficiem alicuius rectan
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guli, cuius vnum latus ſit
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.3. pedum .2. & vnciarum .3. aliud vero latus ſit
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trabuchorum .2. pedum .3. vnciarum vero .2.</
s
>
</
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<
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<
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xml:space
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">Huiuſmodi autem methodo mediante, multiplicando primum latus
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.3. 2. 3.
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per numerum trabucorum ſecundi lateris .2. ſcilicet producentur nobis primò trabu
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cha ſuperficialia .6. pedes .4. & vnciæ .6. omnia rectagula, vt dictum eſt. </
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xml:space
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do deinde idem primum latus .3. 2. 3. per pedes .3. ſecundi lateris. </
s
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<
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xml:space
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<
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primi lateris cum .3. pedibus ſecundi, producentur .9. pedes rectanguli, hoc eſt
<
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vnus trabuchus cum tribus pedibus rectangulis. </
s
>
<
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xml:id
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xml:space
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">Ex pedibus autem huius .2. cum
<
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ijſdem alterius lateris .3. producentur .12. vnciæ rectangulæ ideſt vnus pes rectangu-
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lus. </
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<
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xml:space
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">Exijſdem pedibus .3. ſecundi lateris, cum .3. vncijs primi lateris producentur
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<
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table-0419-01
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table-0419-01a
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<
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<
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">pedes.</
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<
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">vnciæ.</
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</
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<
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<
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<
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</
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<
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<
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">2.</
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<
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xml:space
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<
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</
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<
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<
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<
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<
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</
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<
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<
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<
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<
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<
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<
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<
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<
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<
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<
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<
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<
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<
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<
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</
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<
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<
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<
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<
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<
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</
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</
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