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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DE PERSPECT.
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xlink:href
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<
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xml:space
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">Ad habendam deinde quantitatem diſtantiæ, aut interualli ſimul cum ſitu, in fa-
<
lb
/>
cie
<
var
>.q.d.k.</
var
>
quem latus
<
var
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var
>
perpendiculariter reſpicit. </
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<
s
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xml:space
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preserve
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var
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var
>
ſuper
<
lb
/>
<
var
>q.a.</
var
>
cad ere lineam perpendicularem
<
var
>.u.o.</
var
>
quæ illico reperitur cum triangulum
<
var
>.a.
<
lb
/>
u.q.</
var
>
ex lateribus datis & cognitis conſtet,
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type
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triangulum, medietas eſt qua-
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drilateri, ſeu. rumbi
<
var
>.q.a.b.u.</
var
>
cui vnaquæque dictarum quatuor facierum perpendi-
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lb
/>
cularis exiſtit ex .4. ct .18. lib. 11. & ob id linea
<
var
>.u.o.</
var
>
extenſa in ſuperficie dicti quadri-
<
lb
/>
lateri, & perpendicularis lineæ
<
var
>.q.a.</
var
>
perpendicularis erit faciei
<
var
>.q.d.k.</
var
>
& ex .29.
<
lb
/>
primi, angulus
<
var
>.b.u.o.</
var
>
rectus erit, ut
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type
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angulus
<
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>.o.u.l.</
var
>
ex .2. definitione lib. 11. vnde
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ex .4. eiuſdem lib
<
var
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var
>
perpendicularis erit faciei
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>
. </
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>
<
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xml:space
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cie
<
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>
qui reſpicietur ad angulos rectos à linea
<
var
>.p.l.</
var
>
quiquidem erit in perpendi-
<
lb
/>
culari à puncto
<
var
>.o.</
var
>
ad
<
var
>.q.a.</
var
>
ducta.</
s
>
</
p
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<
p
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<
s
xml:id
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xml:space
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">Quòd autem
<
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>
ſit latus exagoni æquilateris circumſcrip tibilis ab eodem circu
<
lb
/>
lo, qui vnam ex faciebus triangularibus æquilateribus propoſiti corporis circunſcri-
<
lb
/>
bere pot eſt, ita oſtenditur. ſit
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type
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imaginatione, triangulum
<
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>
ſepara
<
lb
/>
tim, cuius latus
<
var
>.a.u.</
var
>
æquale eſt vni ex lateribus
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norm
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triangulorum
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type
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eiuſdem corporis ex .33.
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lb
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primi, quo dlibet verò aliorum duorum æquale perpendicularibus dictorum trian-
<
lb
/>
gulorum, in quo triangulo
<
var
>.a.u.q.</
var
>
ducta ſit perpendicularis
<
var
>.u.o.</
var
>
ab vna
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type
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<
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lateris maioris, ad vnum ex minoribus lateribus, quę perpendicularis intra triangu-
<
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lum cadet, quia dictum triangulum oxigonium eſt. </
s
>
<
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xml:space
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">quod autem attinet ad duos angu
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los
<
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>.a.</
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>
et
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>.u.</
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>
cum æquales ſint ex quinta lib. primi; </
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<
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xml:space
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">17. nos certiores facit; </
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<
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xml:space
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">quod verò an
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gulus
<
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>.q.</
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>
ſit
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type
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acutus: </
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<
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xml:space
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">30. lib. tertii nos cer-
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tos reddit,
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type
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<
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>
minor eſt diametro
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norm
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ſphae ræ
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type
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xlink:href
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ræ</
reg
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datum corpus circumſcribentis, cum
<
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var
>
<
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dictæ ſphęrę ſuperficiem tangat.</
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>
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<
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<
s
xml:id
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xml:space
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">Ad probandum
<
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>.a.o.</
var
>
ęqualem eſſe lateri
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lb
/>
exagoni dicti, ſatis erit probare
<
var
>.a.q.</
var
>
ſeſqui
<
lb
/>
alteram eſſe ad
<
var
>.a.o.</
var
>
quia ſi in ſubſcripto
<
lb
/>
hîc circulo ducemus duas ſemidiametros
<
var
>.
<
lb
/>
n.p.</
var
>
et
<
var
>.n.l.</
var
>
ad. angulos
<
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="
trianguli
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type
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ęquilateri
<
var
>.p.</
var
>
<
lb
/>
et
<
var
>.l.</
var
>
& cum quodlibet laterum ipſius exago
<
lb
/>
ni, ęquale ſit ſemidiametro circuli ex .15.
<
lb
/>
lib. 4. habebimus ex .8. primi, angulum
<
var
>.n.
<
lb
/>
p.l.</
var
>
æqualem angulo
<
var
>.q.p.l</
var
>
. </
s
>
<
s
xml:id
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xml:space
="
preserve
">Vnde ex .4. eiuſ
<
lb
/>
dem
<
var
>.o.n.</
var
>
ęqualiserit ipſi
<
var
>.o.q.</
var
>
ideſt
<
var
>.q.a.</
var
>
ſeſ
<
lb
/>
quialtera erit ad
<
var
>.a.o</
var
>
.</
s
>
</
p
>
<
p
>
<
s
xml:id
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xml:space
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">Ad probandum nunc in triangulo
<
var
>.a.q.
<
lb
/>
u</
var
>
:
<
var
>a.q.</
var
>
ſeſquialteram eſſe ad
<
var
>.a.o.</
var
>
eſt
<
reg
norm
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quoque
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type
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">quoq;</
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>
<
lb
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ſciendum primò omne latus trianguli ęquilateri in potentia ſeſquitertium eſſe ad
<
lb
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perpendicularem eiuſdem trianguli, quod vndecima lib. 14. Eucli. breuiter demon
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ſtratum eſt.</
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