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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IO. BAPT. BENED.
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92
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file
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0092
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0092
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coniunctis denotetur, et
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ſit tertia pars ipſius
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prioris numeri im aginati, et. b
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c. tertia pars ipſius,
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ſecundi numeri propoſiti, vnde coniunctum vnius harum ter
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tiarum
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alia ſit
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quod quidem
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eſſe tertiam partem ſummæ duorum
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primorum ideſt
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aſſero. </
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<
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xml:space
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">Iam manifeſtum eſt ipſius
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ad
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eſſe quemadmo
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dum ipſius
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ad
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vnde viciſſim ipſius
<
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>.d.b.</
var
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ad
<
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>.b.a.</
var
>
erit quemadmodum ipſius
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>.b.
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c.</
var
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ad
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& coniunctim ipſius
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>.d.a.</
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ad
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>.a.b.</
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quemadmodum ipſius
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>.c.e.</
var
>
ad
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>.e.b.</
var
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& viciſ-
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ſim ipſius
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>.d.a.</
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ad
<
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>.c.e.</
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quemadmodum ipſius
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>.b.a.</
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ad
<
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>.b.e.</
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ſed proportio ipſius
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ad
<
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>.
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b.e.</
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eſt tripla, ergo ea quæ eſt ipſius
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>.a.d.</
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ad
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>.e.c.</
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erit quoque tripla; </
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<
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xml:space
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">vnde ſumendo
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>.e.
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c.</
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pro tertia parte ipſius
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>.a.d.</
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& ab ipſa
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>.e.c.</
var
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ſubtrahendo tertiam partem ipſius
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>.a.b.</
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tertia pars ipſius
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>.b.d.</
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remanebit
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>.b.c</
var
>
.</
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<
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xml:space
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">Aut alio hoc modo, ſupponendo
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tertiam partem ipſius
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et
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ipſius
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>.a.
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b.</
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exiſter. </
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xml:space
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">Dico
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tertiam partem ipſius
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futuram:</
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xml:space
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">quia ſi totius
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ad totum
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<
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ita ſe habet, quemadmodum
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à toto
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>.a.d.</
var
>
diffecti atque diuulſi ad
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à toto
<
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>.
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e.c.</
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diſractum, ergo ex
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number
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0092-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0092-01
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</
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clid.</
ref
>
reſidui
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totius
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ad reſiduum
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>.b.c.</
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totius
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>.e.c.</
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erit, vt totius
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ad
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at-
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que hic quidem modus rem
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ſpe-
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culandi mihi aptior & commodior eſſe videtur.</
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<
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xml:space
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">THEOREMA
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xml:space
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">PErmulta ac varia problemata inuenerunt antiqui, longioribus verò vijs reſolu-
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ta, proptereà quòd
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ſemper nobis ſuccurrit breuiſſima in vnaquaque re ex-
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plicatio. </
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xml:space
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">Vt exempli gratia, proponitur numerus .50. diuidendus in tres tales par-
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tes, quod ſecunda dupla ſit primę, & adhuc eam ſuperet tribus vnitatibus, tertia ve
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rò æqualis ſit aggregato primæ cum ſecunda, & amplius ipſum aggregatum ſuperet
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quinque vnitatibus.</
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<
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<
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xml:space
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">Ad hoc autem quæſitum ſoluendum antiqui vtebantur regula falſi, quod reuera
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breuiori modo poteſt ſolui, videlicet detra hendo illud ſecundum exceſſum, quin-
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que ſcilicet ex .50. ita vt nobis .45. remaneret, cui medietati hoc eſt .22. cum dimidia
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vnitate, ſi addiderimus illud quinque habebimus .27. cum dimidia vnitate pro ter-
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tia parte quæſita ipſius numeri .50. deinde ſi ab eodem numero .22. cum dimidia
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vnitate detractum fuerit illud .3. primus exceſſus datus, remanebit .19. cum dimi-
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dia vnitate, cuius tertia pars, hoc eſt .6. cum dimidia vnitate, prima pars, ex tri-
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bus quæſita erit, quæ quidem ſi detraxerimus ex .19. cum dimidia vnitate, reli-
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quum erit .13. cui
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additus fuerit primus exceſſus ideſt .3. </
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<
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xml:space
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">Iam propoſitum re-
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ſultabit nobis .16. pro ſecunda parte quæſita.</
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<
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<
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xml:space
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">Ratio verò huiuſmodi operationis talis eſt, ſit verbi gratia totalis numerus pro-
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poſitus ſignificatus per lineam
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>
cuius ſecundæ partis numerus datus ſignificetur
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per lineam
<
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>.g.</
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>
& numerus tertiæ partis propoſitus per lineam
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. </
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<
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ex
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nobis cognita, remanebit
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qua
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per æqualia imaginatione diuiſa in pun
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cto
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& ipſi
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addita
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>.f.b.</
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>
tota
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>.e.b.</
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>
nobis cognita erit, quæ quidem tertia pars
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quæſita ipſius
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>
erit, proptereà quòd
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>
(quæ æqualis eſt ipſi
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>
) erit ſumma
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primæ, & ſecundæ partis. </
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<
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xml:space
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">Detrahatur poſteà. g. ex
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& remanebit
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>.d.a.</
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>
cuius ter
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tia pars ſit
<
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>.a.c.</
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>
quæ quidem prima pars quæſita erit, & nunc cognita, & ita
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>.c.d.</
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>
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cognita, cui cum addita fuerit
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habebimus ſecundam partem quæſitam, quæ
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compo- </
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