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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EPISTOLAE.
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387
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file
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0387
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0387
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Alexander Piccolhomineus in libro primo de mundi ſphæra vbi tractat de
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tunditate</
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, ita inquit.</
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<
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it
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<
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xml:space
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">Oltre di queſto, douendo il decimo cielo contenere & in ſe chiudere tutte le co-
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ſe, è conueneuol coſa il penſare, che foſſe fatto di quella più capace figura che eſ-
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ſer poſſa, la qual è la figura rotunda, però che ſi può trar da molti luoghi d'Euclide
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che ſi come ſe noi ciimmagineremo più figure ſuperficiali talmente che tutte le li-
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nee de l'vna congionte inſieme, ſieno vguali à tutte le linee pur inſiememente com
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poſte di qual ſi voglia de l'altre figure, ne ſeguirà, che quella figura ſarà più capa-
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ce la qual haurà manco angoli, & quella capaciſſima che ſarà ſenza alcuno come è
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la figura circolare, & c.</
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<
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xml:space
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">Cogitemus igitur primò de triangulo æquilate-
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ro & quadrato iſoperimetris, ſit enim triangulus æ-
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quilaterus
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>.o.b.g.</
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quadratum verò
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>.b.l.</
var
>
quorum pe-
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riferiæ inuicem æquales ſint. </
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<
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xml:space
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0387-01
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xlink:href
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figure
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ioris ſuperficiei eſſe ipſo triangulo. </
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>
<
s
xml:id
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xml:space
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">Accipio pri-
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mum lineam
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>.f.h.</
var
>
eiuſdem longitudinis quæ vnius
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/>
periferiæ dictarum figurarum, quam punctis
<
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>.r.K.</
var
>
<
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/>
mediantibus diuido in tres ęquas partes, in quatuor
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/>
verò mediantibus punctis
<
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>.l.x.i.</
var
>
vnde proportio to-
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tius
<
var
>.f.h.</
var
>
ad
<
var
>.K.h.</
var
>
erit vt
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>.l.h.</
var
>
ad
<
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>.i.h.</
var
>
ideſt tripla, & per
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/>
16. quinti erit
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>.f.h.</
var
>
ad
<
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>.l.h.</
var
>
vt
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>.k.h.</
var
>
ad
<
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>.i.h.</
var
>
per .19. verò
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/>
<
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>f.h.</
var
>
ad
<
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>.f.l.</
var
>
vt
<
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>.K.h.</
var
>
ad
<
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>.K.i.</
var
>
ſed
<
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>.f.l.</
var
>
eſt quarta pars ip-
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/>
ſius
<
var
>.f.h.</
var
>
ergo
<
var
>.k.i.</
var
>
erit quarta pars ipſius
<
var
>.k.h</
var
>
. </
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>
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>
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gantur enim ambo iſtæ figuræ vt hic inferius vides,
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lb
/>
vnde
<
var
>.a.g.</
var
>
erit quarta pars ipſius
<
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>.b.g.</
var
>
diuiſa poſtea
<
var
>.
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/>
b.g.</
var
>
per æqualia in
<
var
>.c.</
var
>
erit
<
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>.a.c.</
var
>
æqualis
<
var
>.a.g</
var
>
. </
s
>
<
s
xml:id
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xml:space
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">Ducatur
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deinde
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>.o.c.</
var
>
quę per .8. primi, nec
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type
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">nõ</
reg
>
ex definitione,
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/>
perpendicularis erit ipſi
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>.b.g.</
var
>
ergo etiam
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norm
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type
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>
<
lb
/>
b q. ſupra
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>.b.g.</
var
>
<
reg
norm
="
producoque
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type
="
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">producoq́;</
reg
>
<
var
>.o.c.</
var
>
vſque ad
<
var
>.m.</
var
>
nam nul
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/>
li dubium eſt quin
<
var
>.o.c.</
var
>
breuior ſit
<
var
>.o.g.</
var
>
ex .18. vel .48
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/>
primi cui æquatur
<
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>.q.g.</
var
>
diuido etiam
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var
>.c.m.</
var
>
per æqua
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/>
lia in puncto
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>.e.</
var
>
<
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type
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>
<
var
>t.e.p.</
var
>
æquidiſtantem
<
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>.b.g.</
var
>
<
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/>
vnde habebimus duo quadrata
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>.e.g.</
var
>
et
<
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>.e.b.</
var
>
ſed
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/>
quadratum
<
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>.b.l.</
var
>
æquatur quadrato ipſius
<
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>.c.a.</
var
>
<
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/>
cum duplo illius quod fit ex
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>.b.c.</
var
>
in
<
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>.c.g.</
var
>
vt patet
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/>
ex .9. ſecundi, hoc eſt æquatur quadrato
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var
>.c.a.</
var
>
& re-
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ctangulo
<
var
>.t.g</
var
>
. </
s
>
<
s
xml:id
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xml:space
="
preserve
">Deinde vt ſe habet
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>.p.g.</
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ad
<
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>.o.e.</
var
>
ita ſe habet
<
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>.u.p.</
var
>
ad
<
var
>.u.e.</
var
>
ex ſimilitudine
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triangulorum. </
s
>
<
s
xml:id
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xml:space
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">Sed
<
var
>.p.g.</
var
>
maior eſt ipſa
<
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>.o.e.</
var
>
cum
<
var
>.p.g.</
var
>
æqualis ſit
<
var
>.e.m.</
var
>
</
s
>
<
s
xml:id
="
echoid-s4445
"
xml:space
="
preserve
">quare triangu-
<
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lus
<
var
>.u.g.p.</
var
>
maior erit triangulo
<
var
>.o.e.u.</
var
>
ex .17. ſexti. </
s
>
<
s
xml:id
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echoid-s4446
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xml:space
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preserve
">Similiter dico maiorem eſſe trian
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gulum
<
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>.b.d.t.</
var
>
triangulo
<
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>.e.o.d.</
var
>
vnde ſequitur rectangulum
<
var
>.t.g.</
var
>
maiorem eſſe triangu-
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lb
/>
lo
<
var
>.b.o.g.</
var
>
ſed quadratum
<
var
>.b.l.</
var
>
eſt etiam maior ipſo rectangulo
<
var
>.t.g.</
var
>
ex quadrato ipſius
<
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/>
<
var
>c.a.</
var
>
vt diximus, tanto igitur maior erit triangulo
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>.b.o.g</
var
>
.</
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>
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