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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THEOREM. ARIT.
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93
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file
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0093
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0093
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componitur ex
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dupla .ad
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pri-
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mam partem, & ex
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numero dato.
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<
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compoſita eſt ex
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e.f.</
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æquali
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hoc eſt æquali compoſi-
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to ex prima, & ſe cunda parte, & ex
<
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b.</
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numero dato vt proponebatur.</
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<
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xml:space
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">THEOREMA
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value
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119
">CXIX</
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<
s
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">INter alia problemata ab antiquis inuenta, hoc etiam ponitur. </
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<
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">Aliquis inter-
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rogat quot ſint horæ, alius verò reſpondit tot eſſe, quot duæ tertiæ præteriti
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temporis ſimul iuncta cum tribus quintis futuri temporis totius dieri naturalis effi-
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ciunt. </
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<
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xml:space
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">Nunc quæritur quot ſint horę.</
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<
s
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xml:space
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">Antiqui, hoc etiam problema ſoluebant mediante regula falſi, ſed mihi alio mo
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do ſoluendum eſſe dictum problema videtur. </
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<
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xml:space
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">Accipio enim ex quinque, tres vni-
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tates, pro parte futuri temporis, quas quidem in tres vnitates præteriti temporis
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duco, vnde proueniunt mihi nouem vnitates, quod productum coniungo
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type
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quin-
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que futuri temporis, vnde veniunt .14. vnitates, ex regula poftea de tribus ita dico
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ſi ex .14. mihi prouenit .9. quid reſultabit ex .24. & prouenient mihi horæ .15. cum
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tribus ſeptimis vnius horæ, hoc eſt minuta ferè .26.</
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<
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xml:space
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">Pro cuius ratione, quinque vnitates, feu partes temporis futuri ſignificentur à
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linea
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>.e.u.</
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quarum trium ſigniſicentur a linea
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ſumpta deinde ſit linea
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æqualis
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lineæ
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et
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>.e.a.</
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tripla ſit ad
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vel ad
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quod idem eſt, vnde
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>.a.e.</
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>
compoſita erit
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ex
<
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>.a.o.</
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(hoc eſt ex duabus tertijs ip ſius
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) & ex
<
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>o.e.</
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(hoc eſt ex. tribus quintis ip-
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ſius
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>.e.u.</
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>
) vnde
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>.a.u.</
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ad
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>.a.e.</
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eandem rationem obtinebit, quæ .14. ad .9. </
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<
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xml:space
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">propterea igi
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tur poſſumus recte ratiotinari
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xlink:label
="
fig-0093-02
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xlink:href
="
fig-0093-02a
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number
="
127
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file
="
0093-02
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0093-02
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fi .14. nobis dat .9. quid dabit .24.
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qui quidem .24. nobis dabit .15.
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cum min .26. quod rectè factum
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erit ex
<
ref
id
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">.20. ſeptimi Euclidis</
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>
.</
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<
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type
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n
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<
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xml:space
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">THEOREMA
<
num
value
="
120
">CXX</
num
>
.</
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<
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<
s
xml:id
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xml:space
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">SVpponunt etiam antiqui tres ſocios nummos habere, quorum ſumma primi &
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ſecundi cognita ſit, item ſumma primi & tertij cognita & ſumma ſecundi &
<
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tertij item cognita, at que ex huiuſmodi tribus aggregatis veniunt in cognitionem
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particularem vniuſcuiuſque illorum.</
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<
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<
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xml:id
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xml:space
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">Gemafriſius ſoluit hoc problema ex regula ſalſi. </
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>
<
s
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xml:space
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">At ego tali ordine progredior.
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<
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xml:space
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">Sit verbi gratia, ſumma primi cum ſecundo .50. & ſecundi cum tertio .70. & primi
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cum tertio .60. harum trium ſummarum accipiantur duæ quæuis, vt puta .50. & .70
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quæ coniunctæ ſimul dabunt .120. à qua ſumma detrahatur reliqua, ideſt .60. &
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reſtabit nobis .60. cuius medietas erit .30. hoc eſt numerus nummorum ſecundi
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ſocij quo numero detracto à .70. hoc eſt à ſumma ſecundi cum tertio remanebit .40.
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hoc eſt numerus tertij ſocij, & hic numerus deſumptus à .60. reſiduus erit nume-
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rus primi ſocij.</
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