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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377
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EPISTOLAE.
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389
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0389
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0389
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a. ſeſquialter erit angulo
<
var
>.t.</
var
>
quod vt clarius videas cogita lineam
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cuius medietas
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ſit
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>.c.d.</
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tertia verò pars illius ſit
<
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>.g.d.</
var
>
</
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<
s
xml:id
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xml:space
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<
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var
>
ſeſquialteram eſſe ipſi
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>.g.d.</
var
>
ſit enim
<
lb
/>
<
var
>f.d.</
var
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duplum ipſius
<
var
>.g.d.</
var
>
</
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<
s
xml:id
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xml:space
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<
var
>.f.d.</
var
>
erunt duæ tertiæ totius lineę
<
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>.b.d.</
var
>
& quia eadem pro
<
lb
/>
portio eſt totius
<
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>.b.d.</
var
>
ad
<
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>.c.d.</
var
>
quæ
<
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>.f.d.</
var
>
ad
<
var
>.g.d.</
var
>
ergo permutando eadem erit totius
<
var
>.b.
<
lb
/>
d.</
var
>
ad
<
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>.f.d.</
var
>
quæ
<
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>.c.d.</
var
>
ad
<
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>.g.d</
var
>
. </
s
>
<
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xml:id
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xml:space
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">Sed
<
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>.b.d.</
var
>
ad
<
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>.f.d.</
var
>
ſeſquialtera eſt, verum igitur erit quod an-
<
lb
/>
gulus
<
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>.a.</
var
>
ſeſquialter ſit ipſi
<
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>.t.</
var
>
deinde
<
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>.t.n.</
var
>
eſt ſeſquitertia ipſi
<
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>.a.u.</
var
>
vt ſuperius vidimus .
<
lb
/>
in eorum duplis. </
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<
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xml:space
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var
>
eſſe dimidium ipſius
<
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>.t.e.</
var
>
co quod cum
<
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>.e.t.n.</
var
>
ſit
<
lb
/>
tertia pars vnius recti, angulus,
<
var
>t.e.n.</
var
>
erit duo tertia vnius recti, vnde
<
var
>.e.n.</
var
>
erit latus.
<
lb
/>
exagoni æquilateris inſcriptibilis circulo cuius diameter ſit
<
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>.e.t.</
var
>
</
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>
<
s
xml:id
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xml:space
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<
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>.e.t.</
var
>
dupla erit
<
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ipſi
<
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>.e.n.</
var
>
in longitudine, ſed quadrupla in potentia: </
s
>
<
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xml:space
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">t.n. vero tripla in potentia ipſi
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<
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/>
e.</
var
>
ex penultima primi, quæ omnia etiam ex .8. tertijdecimi. Eucli. elicere potes, ſed
<
lb
/>
<
var
>c.n.</
var
>
erat ſexquitertia ipſi
<
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>.a.u.</
var
>
in longitudine, hoc eſt ipſi
<
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>.o.u.</
var
>
nam
<
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>.o.u.</
var
>
æqualis eſt ipſi
<
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/>
<
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>a.u</
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>
. </
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>
<
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xml:id
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xml:space
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<
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erit minus quam dupla in potentia ipſi
<
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>.o.u.</
var
>
hoc eſt, vt .16. ad .9. ergo
<
lb
/>
maior proportio erit ipſius
<
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>.t.n.</
var
>
in potentia ad
<
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>.n.e.</
var
>
quam ad
<
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>.o.u.</
var
>
</
s
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<
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xml:id
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xml:space
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">quare etiam in lon
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/>
gitudine, maior proportio erit ipſius
<
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>.t.n.</
var
>
ad
<
var
>.n.e.</
var
>
quam ad
<
var
>.o.u.</
var
>
vnde
<
var
>.o.u.</
var
>
longior erit
<
lb
/>
ipſa
<
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>.n.e.</
var
>
quod eſt propoſitum.</
s
>
</
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<
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<
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xml:space
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">Sed ſi
<
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var
>
eſſet pentagonus æquilaterus & æquiangulus, ſimiliter probabo per-
<
lb
/>
pendicularem
<
var
>.o.u.</
var
>
longiorem eſſe
<
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>.n.e.</
var
>
ipſius trianguli æquilateri, dummodo ſint iſo-
<
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perimetrę. </
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>
<
s
xml:id
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xml:space
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">Sit enim
<
var
>.a.u.</
var
>
dimidium lateris pentagoni ex ſuppoſito, cuius centrum ſit
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o. </
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>
<
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xml:id
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xml:space
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">tunc proportio
<
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>.t.n.</
var
>
ad
<
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>.a.u.</
var
>
erit ſuperbipartienstertias, vt ex ordine iam hic ſupradi
<
lb
/>
cto à te facillimè elicere potes, hoc eſt, vt .5. ad .3. et
<
var
>.a.u.</
var
>
minor erit
<
var
>.o.u.</
var
>
eo quod
<
lb
/>
angulus
<
var
>.o.</
var
>
minor erit angulo
<
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>.a.</
var
>
nam angulus
<
var
>.o.</
var
>
erit quinta pars
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type
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rectorum, hoc
<
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/>
eſt duæ quintæ vnius recti, vnde angulus
<
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>.a.</
var
>
reſiduum vnius recti erit tres quin-
<
lb
/>
tæ vnius recti, </
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>
<
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xml:space
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">quare angulus
<
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>.a.</
var
>
maior ericangulo
<
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>.o.</
var
>
& conſequenter latus
<
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>.o.u.</
var
>
ma-
<
lb
/>
ius latere
<
var
>.a.u.</
var
>
ſed
<
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>.t.n.</
var
>
minor eſt quam tripla in potentia ad
<
var
>.a.u.</
var
>
eo quod erit vt .25.
<
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/>
ad .9. cum in longitudine ſit vt .5. ad .3. ſed dicta
<
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>.t.n.</
var
>
tripla eſt in potentia ad
<
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>.e.n.</
var
>
qua-
<
lb
/>
re
<
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>.a.u.</
var
>
maior erit ipſa
<
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>.e.n.</
var
>
ſed
<
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>.o.u.</
var
>
maior eſt ipſa
<
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>.a.u.</
var
>
vt diximus, igitur multo magis
<
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>.
<
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/>
o.u.</
var
>
maior eſt ipſa
<
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>.a.u.</
var
>
vt
<
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type
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">diximꝰ</
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&
<
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conſequenter
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type
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">cõſequẽter</
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multo magis
<
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>.o.u.</
var
>
maior erit ipſa
<
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>.n.e</
var
>
.</
s
>
</
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<
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>
<
s
xml:id
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xml:space
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">Quotieſcunque enim cognoſcimus proportionem anguli
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>.o.</
var
>
ad angulum
<
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>.a.</
var
>
quod
<
lb
/>
quidem facillimum eſt, nec non proportionem
<
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>.t.n.</
var
>
ad
<
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>.a.u.</
var
>
quod, etiam illico cogno-
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ſcitur, </
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>
<
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xml:space
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">tunc exſcientia cordarum & arcuum omnia etiam facillimè innueniuntur.
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</
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<
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xml:space
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">Verum circa
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triangulum
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type
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">triangulũ</
reg
>
æquilaterum, & pentagonum, alium
<
reg
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modum
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type
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">modũ</
reg
>
inueni, ſed aliquan
<
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tulum prolixiorem.</
s
>
</
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<
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<
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0389-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0389-01
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