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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[Handwritten note 21]
Page: 393
[Handwritten note 22]
Page: 441
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IO. BAPT. BENED.
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n
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36
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file
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0036
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0036
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<
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<
s
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xml:space
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">Hoc ipſum & alia ratione perfici poteſt, nempe, iuncta ſumma
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:
<
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: ec
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unsure
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<
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b.t.</
var
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alteri rectangulo æquali
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>.b.d.</
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>
quod ſit
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>
ex quo totum quadratum lineæ
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var
>
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cognitum erit,
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ita etiam conſequenter eius radicem
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>
cognoſcemus, cuius
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lb
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ope ac producti
<
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>.d.b.</
var
>
cognoſcemus
<
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>.d.p.</
var
>
et
<
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>.p.k.</
var
>
prout ex theoremate quadrageſi-
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moquinto huius libri patebit.</
s
>
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<
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<
s
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xml:space
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">Michael Stifelius, vndecimo cap. tertij libri, problema eiuſmodi proponit,
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quod tamen ipſe via algebræ diſsoluit.</
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50
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0036-01
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xlink:href
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xml:space
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">THEOREMA
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num
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38
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num
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.</
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xml:space
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">CVR ij, qui duos numeros inuenire volunt, quorum productum alicui nu-
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mero propoſito æquetur, & quadratorum eorundem differentia alteri nu-
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mero propoſito æqualis ſir. </
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<
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xml:space
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">Rectè dimidium ſecundi numeri propoſiti in ſeipſum
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multiplicent, cui quidem numero differentia quadratorum æquari debet; </
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>
<
s
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xml:space
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">porrò
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lb
/>
huic quadrato primi propoſiti numeri, cui æquandum eſt productum numerorum
<
lb
/>
quæſitorum, quadratum adiungant; </
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>
<
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xml:space
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">tum radicem quadratam huius ſummæ co-
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lb
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pulet dimidio ſecundi numeri propoſiti, ei inquam, cui differentia quadratorum
<
lb
/>
æqualis eſſe debet, ex quo quadratum maius conſurgit, à quo, detracto ſecundo
<
lb
/>
numero, ſupereſt quadratum minus.</
s
>
</
p
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<
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>
<
s
xml:id
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xml:space
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">Exempli gratia, ſi proponeretur primo loco numerus .8. cui æquandum eſt
<
lb
/>
productum numerorum quæſitorum, tum proponeretur numerus .12. cui, detra-
<
lb
/>
cto minore à maiore, differentia quadratorum vtriuſque quæſiti numeri æqualis
<
lb
/>
eſſe debet, oportet huius vltimi numeri .12. dimidium in ſeipſum multiplicare,
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q́ue</
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.36. quadratum dimidij, vnde in ſummam colligeremus quadratum primi
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numeri .8. quod eſſet .64. quæ cum .36. efficerent .100. cuius centenarij radice, nem
<
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pe .10. collecta in ſummam cum dimidio ſecundi numeri, nempe .6. daretur qua-
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dratum maius, nempe .16. ex quo, detracto ſecundo numero, nempe .12. rema-
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neret quadratum minus .4.</
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<
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xml:space
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">Cuius ſpeculationis cauſa, maius quadratum
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fig-0036-02
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fig-0036-02a
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number
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51
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file
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0036-02
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xlink:href
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incognitum ſignificetur linea
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var
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var
>
minus verò
<
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/>
pariter incognitum linea
<
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>.g.i.</
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>
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xml:space
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">quare
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>
eorum
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differentia, tanquam data remanebit cognita,
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/>
vnà etiam
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var
>.b.i.</
var
>
et
<
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>.q.b.</
var
>
ſua dimidia; </
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>
<
s
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xml:space
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preserve
">tunc cogite-
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tur quadratum
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>
ſuper
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var
>
et
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type
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mum</
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rectangu
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lum
<
var
>.g.r.</
var
>
deſignatum, & ita etiam
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/>
gnomon
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>.u.g.t.</
var
>
prout ſexta ſecundi Euclidis pro
<
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/>
ponitur, ex quo quadratum
<
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>.b.i.</
var
>
nempe
<
var
>.u.t.</
var
>
co-
<
lb
/>
gnitum erit, ſed gnomon æqualis eſt rectangulo
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var
>.g.r.</
var
>
ex prædicta, aut ex .8. poſt .16. </
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