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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1 - 30
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383
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EPISTOLAE.
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395
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file
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0395
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0395
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cum ſit
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æqualis ipſi
<
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>.u.i.</
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vt tibi probaui, & inuicem parallelæ ideo
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>.f.i.</
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parallela
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erit ipſi
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ex .33. primi Euclidis. </
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<
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xml:space
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">Vnde ex .30. eiuſdem, parallela erit etiam ipſi
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c.</
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ſed cum
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diuiſa ſit ab
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>.d.b.</
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per æqualia, eo quod diuidit
<
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>.a.c.</
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eodem modo, quę
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ipſi parallela eſt ex .2. ſexti. </
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<
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xml:space
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<
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xml:space
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x.</
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et
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parallelæ ſint ipſi
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ſequitur quod cum ex .34. primi
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et
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i.</
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æqualis ſit medietati ipſius
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erunt inuicem æquales.</
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<
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xml:space
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">Minime dubitabam tibi non ſatisfacere Eutocium in .3. propoſitione ſecundi
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lib. de centris Grauium Archimedis, cum citet .6. librum de elementis conicis, ad-
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de quod ſi aliud in ipſo .6. libro ab eo citato non eſſet magis ad propoſitum, quàm
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ca quæ ab ipſo citata ſunt, nihilominus adhuc irreſolutus maneres.</
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<
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<
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xml:space
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">Conſidera igitur eandem ipſam figuram præcedentem; </
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xml:space
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mili dictæ, accipe ſecundam figuram ipſius tertiæ dictæ propoſitionis. </
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<
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xml:space
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ginabis duo latera
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>
et
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var
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diuiſa eſſe per æqualia in punct is
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var
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et
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var
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diametris
<
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et
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quæ, vt in præcedenti probaui, ſunt inuicem æquales, ſcire
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debes quod ſimiles parabolæ inuicem aliæ non poſſunt eſſe, niſi eæ quæ diametros
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proportionales ſuis baſibus habeant,
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poſitæ, hoc eſt, ut proportio ipſius
<
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<
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>b.d.</
var
>
ad
<
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>
ſit eadem quæ ipſius
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>
ad
<
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>.x.p.</
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>
& quod anguli ad
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>.r.</
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ſint æquales angulis
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circa
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>
. </
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>
<
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xml:space
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cum
<
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>
& ipſius
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var
>
x
<
lb
/>
cum
<
var
>.f.m.</
var
>
characteribus. ω
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unsure
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. et
<
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>
. </
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<
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xml:space
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æqualem eſſe
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tota
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type
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reg
>
<
var
>.f.
<
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i.</
var
>
parallelam eſſe ipſi
<
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>
. </
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<
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xml:space
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<
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triangulique
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<
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et
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ω
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. eſſe ſimiles
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triangulis
<
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>
et. ω
<
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/>
<
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>
quod ita probatur, nam ex .15. primi Euclid. anguli ad
<
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var
>
<
lb
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ſunt inuicem æquales, ex .29. verò eiuſdem anguli
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var
>
et
<
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>
ſimiliter æquales
<
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ita etiam
<
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var
>
et
<
var
>.n.m.b</
var
>
.</
s
>
</
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<
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<
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xml:space
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">Idem dico in ſecunda figura, vnde ex .4. ſexti Eucli. proportio
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var
>
ad
<
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>.m.n.</
var
>
erit ea
<
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/>
dem quę
<
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>.f.x.</
var
>
ad
<
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>.b.m.</
var
>
& ipſius
<
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>.n.f.</
var
>
ad
<
var
>.x.f.</
var
>
vt
<
var
>.n.m.</
var
>
ad
<
var
>.m.b.</
var
>
ex .16. quinti. </
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<
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">Quare ex .11.
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