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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33
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rhead
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THEOR. ARITH.
"
n
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45
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file
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0045
"
xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0045
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numero, verbi gratia .92. præcepit regula detrahi primum numerum ex ſecundo,
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nempe .20. ex .92. cuius reſiduum, ſcilicet .72. conſeruetur, tum detrahi iubet bi
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narium ex primo, ſic in propoſito exemplo remanebunt .18. huius autem .18. dimi
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dium in ſeipſum multiplicari iubet, quod cum ſit .9. datur numerus .81. ex quo .81.
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primum numerum conſeruatum, nempe .72. vult regula detrahi, ſic remanebit .9.
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/>
tum huius .9. quadrata radix detrahenda eſt ex dimidio ipſius .18. quod fuit ante qua
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dratum, ſic ſupererit .6. hoc eſt .9. excepta radice quadrata, qui .6. erit minor pars
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quæſita, maior verò .14. quarum productum .84. coniunctum cum partium differen
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tia præbet exactè .92.</
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<
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<
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xml:space
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">Cuius rei hæc eſt ſpeculatio. </
s
>
<
s
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xml:space
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preserve
">Primus numerus minor, qui proponitur diuiſibilis
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ſignificetur linea
<
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>.q.g.</
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>
maior vero linea
<
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>.x.</
var
>
tum cogitemus
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>.q.g.</
var
>
diuiſam, cuius maior
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/>
pars ſit
<
var
>.q.o.</
var
>
minor
<
var
>.o.g.</
var
>
differentia
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>.q.p.</
var
>
ex quo
<
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>.p.o.</
var
>
æqualis erit
<
var
>.o.g.</
var
>
ſit autem produ-
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/>
ctum
<
var
>.b.o</
var
>
. </
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>
<
s
xml:id
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xml:space
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preserve
">Oportet igitur, ut
<
var
>.b.o.</
var
>
ſimul cum differentia
<
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var
>
æquale ſit numero
<
var
>.x.</
var
>
ſe-
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cundò propoſito, qui notus eſt, </
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<
s
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xml:space
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">quare etiam ſumma producti
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var
>
cum differentia
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<
var
>q.p.</
var
>
cognita erit, ex qua detracto primo numero
<
var
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>
reſiduum cognitum erit, nunc
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igitur quodnam erit hoc reſiduum? </
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>
<
s
xml:id
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xml:space
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">attendamus qua ratione ex ſumma
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var
>.b.o.</
var
>
et
<
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>.q.p.</
var
>
<
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/>
detrahenda ſit
<
var
>.q.g</
var
>
. </
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>
<
s
xml:id
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xml:space
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">In primis ſi ſubtraxerimus ex dicta ſumma
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>
quę pars eſt
<
var
>.q.g.</
var
>
<
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/>
ſupererit detrahenda
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var
>.p.g.</
var
>
ex
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var
>
pars inquam ipſius
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var
>.q.g.</
var
>
quod fiet quotieſcunque
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/>
cogitauerimus
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var
>.q.o.</
var
>
duabus vnitatibus diminutam, et per
<
var
>.o.g.</
var
>
multiplicatam, ſit au-
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tem productum
<
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>.b.e.</
var
>
nam cum
<
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>.o.g.</
var
>
toties
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var
>
ingrediatur, quot ſunt in
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var
>
vnitates
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ex prima ſexti aut .18. vel .19. ſeptimi,
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ſit
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ex
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quæ
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dupla
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eſt
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>
patebit
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>.o.c.</
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>
æqualem eſſe
<
var
>.p.g.</
var
>
fu-
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pererit ita que
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>.b.e.</
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>
productum
<
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>.q.e.</
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>
in
<
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>.e.</
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>
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<
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fig-0045-01
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xlink:href
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fig-0045-01a
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number
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62
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0045-01
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xlink:href
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i. cognitum, erutis autem ex
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ijſdem
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duabus vnitatibus, remanebit
<
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>.q.i.</
var
>
nobis
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nota, ex quo
<
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>.e.i.</
var
>
æqualis erit
<
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>
. </
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<
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xml:space
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">Cum
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igitur productum
<
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>
in
<
var
>.e.i.</
var
>
cognoſcamus
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/>
ſimul cum
<
var
>.q.i</
var
>
: Sivoluerimus partes
<
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>.q.e.</
var
>
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et
<
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>
cognoſcere, vtemur .45. theorema-
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te huius libri, & propoſitum obtinebimus, nam cognoſcemus
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>
& ex conſequen-
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ti
<
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>
eius æqualem.</
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<
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xml:space
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<
num
value
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51
">LI</
num
>
.</
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<
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<
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style
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>
numerum in duas eiuſmodi partes, quæ pro medio proportionali
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alterum numerum propoſitum recipiant, primi dimidio minorem, aliud ni
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hil eſt, quàm binas primi numeri partes inuenire, quæ inter ſe multiplicatæ quadra
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to ſecundi numeri numerum æqualem proferant, ex .16. ſexti aut .20. ſeptimi, quod
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tamen .45. theoremate fuit à nobis ſpeculatum.</
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xml:space
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<
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52
">LII</
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.</
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<
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<
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xml:space
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">CVR pro poſitis tribus numeris quibuſcunque, ſi productum primi in ſecun-
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dum per tertium multiplicetur, atque ſecundum hoc productum
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,
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per primum numerum diuidatur, proueniens erit numerus æqualis producto ſe-
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cundi in tertium.</
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<
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xml:space
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">Exempli cauſa, proponantur hi tres numeri .10. 11. 12.
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.10.
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.</
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