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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IO. BAPT. BENED.
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116
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file
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0116
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0116
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producitur ex
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differentia in
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aggregatum amborum numerorum, ſed hoc pro
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ductum excedit productum
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>e.c</
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: partem gnomonis dicti per
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quod quidem
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n.</
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æquatur ipſi
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reliquæ ſcilicet parti ipſius gnomonis,
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nam
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type
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æqualis eft
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qua
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re et
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ſed
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ęquatur
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vnde
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æqualis erit
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</
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<
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">quare et
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: at cum
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æqua
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lis ſit ipſi
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erit etiam æqualis ipſi
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>.
<
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o.t</
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>
. </
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<
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">quare
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æqualis erit ipſi
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>.u.o.</
var
>
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& tunc intellectus quieſcit, &
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<
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fig-0116-01
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number
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159
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0116-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0116-01
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</
figure
>
aliqua alia experientia verè ſcientifi
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ceque
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dicere poteft, quòd.</
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<
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<
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xml:space
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">Quorumcumque duorum nume-
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rorum differentia, fi fuerit multipli-
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cata in aggregatum eorum, producit
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ipſam
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differentiam
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type
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">differentiã</
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, quæ eftinter qua-
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drata eorum.</
s
>
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<
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<
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xml:space
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">Hæcautem propoſitio à me ipſo
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etiam in .60. </
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<
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xml:space
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">Theoremate huius libri
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aliter demonftrata fuit.</
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<
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<
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xml:space
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">DE ſpeculatione autem, etſcientia ſecundi exempli, in ſecunda hic ſubſcripta
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figura
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>.ω.</
var
>
cogitemus lineam
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var
>
tribusin partibus arithmeticè diuiſam, qua
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rum maxima ſit
<
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>.u.o.</
var
>
media. ſit
<
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>.o.e.</
var
>
minima verò ſit
<
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>.e.a.</
var
>
multiplicatio autem mediæ
<
var
>.
<
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/>
o.e.</
var
>
in ſe ſit quadratum
<
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>.o.t.</
var
>
abſcindatur deinde ex
<
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>.o.e</
var
>
:
<
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>e.i.</
var
>
æqualis
<
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>.e.a.</
var
>
</
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>
<
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xml:space
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">tunc
<
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>.o.i.</
var
>
erit
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differentia inter
<
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>.o.e.</
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>
et
<
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>.e.a.</
var
>
& æqualis differentiæ inter
<
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>.o.e.</
var
>
et
<
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>.o.u.</
var
>
ex hypotefi, quæ
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/>
quidem
<
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>.o.i.</
var
>
in ſe ducta procreabit quadratum
<
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>.o.c.</
var
>
quod erit productum ex differen
<
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/>
tijs ipſarum partium, & erit pars quadrati
<
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>.o.t.</
var
>
ſuperius dicti, vt exſe patet. </
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>
<
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xml:space
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">Nunc
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autem dico gnomonem
<
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>.i.t.n.</
var
>
æqualem eſſe ei quod fit ex
<
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>.a.e.</
var
>
in
<
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>.o.u</
var
>
. </
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>
<
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xml:space
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">Producatur igi
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tur
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quouſque
<
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>.t.r.</
var
>
æqualis ſit ipſi
<
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>.o.i</
var
>
. </
s
>
<
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xml:id
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xml:space
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">tunc
<
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>.e.r.</
var
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erit æqualis
<
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>.o.u.</
var
>
quod etiam clarum
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eſt. </
s
>
<
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xml:space
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">Claudatur ergo rectangulum
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quod erit æquale producto ipſius
<
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>.e.a.</
var
>
in
<
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>.o.u.</
var
>
<
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/>
Nam
<
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>.e.i.</
var
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ſumpta fuit
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/>
æqualis
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>.e.a.</
var
>
ſed ex ra
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<
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fig-0116-02
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xlink:href
="
fig-0116-02a
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number
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160
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file
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0116-02
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0116-02
"/>
</
figure
>
tionibus in priori
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plo allatis,
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type
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>.
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i.r.</
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æquale erit gno-
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moni
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>
. </
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<
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tem verè, ſcientifice-
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q́ue poſſumus affirma
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re, quòd. </
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<
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numeris
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pro
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greffionem arithme-
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ticam diſpofitis, fa-
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cit multiplicatio me-
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dij in ſe quantum mul
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tiplicatio extremorum inter ſe, cum multiplicatione differentiarum inter ſe.</
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<
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<
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xml:space
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">Et ſic de alijs huiuſmodi inuentionibus infero.</
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<
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<
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">DIcturus igitur aliquid circa
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falſi, videtur mihi nullam oportere facere
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mentionem de origine huiuſcæ regulæ, cum in hoc Stifelius ſatisfecerit, ſed </
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