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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201
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IN QVINT. LIB. EVCLI.
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0213
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0213
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b.</
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et
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& ſimiliter proportio
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ex eis quæſunt
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<
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<
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5. et .6. theorema nihil notandum occurrit.</
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<
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xml:space
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">THeoremata à .6. in .13. cum ſint de obiectis intelligibilibus, ſine vllo medio,
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ab intellectu cognitis, inter axiomata à me relata fuerunt .7. inquam quinti
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Euclid. fecimus tertium Poſtulatum, .8. quintum, .9. quartum, .10. ſextum, .11. ſepti
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mum, .12. octauum, .13. nonum.</
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theorematibus ab interprete notatis, ita vt loco .7. 8. noni, & decimi citetur
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tertium .5. 4. et .6. poſtulatum à me propoſitum.</
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nus antecedens. et
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conſequens, qui-
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bus duo multiplices ſumantur
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et
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. </
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fig-0213-01a
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0213-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0213-01
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</
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eandem proportionem habiturum
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ad
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quam
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>.a.</
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ad
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habet. </
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ſtè patet quamlibet partem ipſius
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habitu-
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ram eandem proportionem cum qualibet par
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te
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quam habet
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ad
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quare ex .7. et .8. po
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ſtulato propoſitum eluceſcet.</
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xml:space
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">Sit, exempli cauſa, eadem pro
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portio
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ad
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quæ eſt
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ad
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. </
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ita ſe habebit
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ad
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ſicut
<
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>.b.</
var
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ad
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. </
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<
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xml:space
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temus itaque alterum iſtorum terminorum
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aut
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medium inter
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>.a.</
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et
<
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>.d</
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. </
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<
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">quare
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primum intelligamus
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inter
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et. d proportio ipſius
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>.a.</
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ad
<
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>.d.</
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componetur ex ea quę
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eſt
<
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>.a.</
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ad
<
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>.b.</
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& ea quæ eſt
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>.b.</
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ad
<
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ex .12. poſtulato. </
s
>
<
s
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xml:space
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">Et ex eodem, illa ipſa proportio
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a.</
var
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ad
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pariter componetur ex ea quæ eſt
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>.a.</
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ad
<
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>.c.</
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& ea quæ eſt
<
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>.c.</
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ad
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>.d.</
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ſumpto
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>.c.</
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pro
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medio termino. </
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<
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">Ex quo ſequitur, aggregatum duarum proportionum, videlicet
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ad
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et
<
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ad
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æquale eſſe aggregato
<
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>.a.</
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ad
<
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>.c.</
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et
<
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>.c.</
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ad
<
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>.d.</
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ex quibus aggregatis æqua-
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libus ſi duas proportiones æquales ſubtraxerimus, eam videlicet quæ eſt
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ad
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& il
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lam quæ eſt
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ad
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ſupererunt duæ proportiones
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inter ſe æquales. </
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>
<
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xml:space
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">erit enim proportio
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>.a.</
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ad
<
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æqua
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<
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xlink:label
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fig-0213-02
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xlink:href
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fig-0213-02a
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number
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264
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<
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="
0213-02
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xlink:href
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"/>
</
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>
lis proportioni
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ad
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ex prima parte ſecundi po
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ſtulati diuiſim.</
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</
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<
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<
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poteſt,
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ſumpto
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>.b.</
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pro medio termino inter
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et .c: et
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>.c.</
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>
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pro termino medio inter
<
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>.b.</
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et
<
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>.d</
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. </
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<
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xml:space
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">quare propor-
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tio
<
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>.a.</
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ad
<
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>.c.</
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>
componetur ex
<
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>.a.</
var
>
ad
<
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>.b.</
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>
et
<
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>.b.</
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>
ad
<
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>.c.</
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>
illa
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verò quæ eſt
<
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>.b.</
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>
ad
<
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>.d.</
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>
ex
<
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>.b.</
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>
ad
<
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>.c.</
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>
et
<
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>.c.</
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>
ad
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>.d.</
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ex .12. </
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