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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rhead
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IO. BAPT. BENED.
"
n
="
418
"
file
="
0418
"
xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0418
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<
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<
s
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xml:space
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preserve
">Similiter multiplicando pedes, vncias, puncta, & attoma per trabucum, produ-
<
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/>
cunt pedes, vncias, puncta, & attoma ſuperficialia rectangula oblonga, quorum lon
<
lb
/>
gitudo eſt ipſius trabuchi, latitudo vero lineæ dictarum ſpecierum.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4851
"
xml:space
="
preserve
">Dum vero multiplicant pedem per pedem, nulli dubium eſt quin producant pe-
<
lb
/>
dem quadratum, ſed apud ipſos non vocatur quadratum, quamuis reuera ita ſit, ſed
<
lb
/>
illud vocant duas vncias, quæ quidem ſunt rectangula oblonga iam hic ſupradicta,
<
lb
/>
quarum vniuſcuiuſque longitudo ſit vnius trabuchi, latitudo vero vnius duodecimæ
<
lb
/>
partis ipſius pedis linearis.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4852
"
xml:space
="
preserve
">Productum autem pedis per vnciam, vocant duo puncta, quæ etiam ſunt duo re-
<
lb
/>
ctangula oblonga, vt ſupra.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4853
"
xml:space
="
preserve
">Productum deinde vnciæ per vnciam, vocant duos attomos, qui
<
reg
norm
="
etiam
"
type
="
context
">etiã</
reg
>
ſunt duo re-
<
lb
/>
ctangula oblonga, vt dictum eſt, quæ omnia ſcientificè videbimus.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4854
"
xml:space
="
preserve
">Pro cuius rei cognitione, ſit, exempli gratia
<
var
>.a.e.</
var
>
vnus Trabuchus linearis
<
var
>.e.i.</
var
>
ve-
<
lb
/>
ro vnus pes
<
var
>.i.o.</
var
>
autem vna vncia,
<
var
>o.u.</
var
>
poſtea vnum punctum, et
<
var
>.u.t.</
var
>
vnus At-
<
lb
/>
tomus.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
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xml:space
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preserve
">Vnde
<
var
>.e.i.</
var
>
erit ſexta pars ipſius
<
var
>.a.e.</
var
>
et
<
var
>.i.o.</
var
>
duodecima ipſius
<
var
>.e.i.</
var
>
et
<
var
>.o.u.</
var
>
duodecima
<
lb
/>
ipſius
<
var
>.i.o.</
var
>
et
<
var
>.u.t.</
var
>
duodecima ipſius
<
var
>.o.u</
var
>
. </
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>
<
s
xml:id
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xml:space
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">Sit etiam
<
var
>.a.b.</
var
>
æqualis
<
var
>.a.e.</
var
>
lineæ & ſic
<
var
>.e.d</
var
>
:
<
var
>i.
<
lb
/>
f</
var
>
:
<
var
>o.g</
var
>
:
<
var
>o.n.</
var
>
& c.
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norm
="
terminenturque
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type
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">terminenturq́;</
reg
>
parallelogramma
<
var
>.b.e</
var
>
:
<
var
>d.i</
var
>
:
<
var
>f.o</
var
>
:
<
var
>g.u.</
var
>
et
<
var
>.c.t.</
var
>
vnde
<
var
>.b.e.</
var
>
erit
<
lb
/>
trabuchum quadratum, et
<
var
>.d.i.</
var
>
pes rectangulus oblongus vt ſupra, et
<
var
>.f.o.</
var
>
vncia rectan
<
lb
/>
gula oblonga, et
<
var
>.g.u.</
var
>
punctum rectangulum oblongum, et
<
var
>.c.t.</
var
>
attomus rectangu-
<
lb
/>
lus oblongus.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
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"
xml:space
="
preserve
">De producto igitur trabuchi per
<
reg
norm
="
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"
type
="
context
">trabuchũ</
reg
>
, nulli dubium eſt quin ſit quadratum
<
var
>.
<
lb
/>
a.d.</
var
>
vt ſuperius diximus.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
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xml:space
="
preserve
">Productum autem trabuchi cum pede erit
<
var
>.d.i.</
var
>
ſexta pars ipſius
<
var
>.a.d.</
var
>
cum
<
var
>.e.i.</
var
>
ſit ſex
<
lb
/>
ta ipſius
<
var
>.a.e.</
var
>
ex prima ſexti vel .18. aut .19. ſeptimi, ſiue etiam ex .15. quinti Eucli.</
s
>
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p
>
<
p
>
<
s
xml:id
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xml:space
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">Productum autem pedis cum pede erit
<
var
>.e.K.</
var
>
quadratum, quod probandum eſt
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fig-0418-01
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fig-0418-01a
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445
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