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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37
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rhead
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THEOREM. ARITH.
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49
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file
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0049
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0049
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g. in
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. </
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<
s
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xml:space
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">Nunc ex ſpeculatione præcedentis theorematis, eadem erit proportio
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t.</
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ad
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quæ eſt
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</
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<
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xml:space
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">quare pro-
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ductum
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ex definitione ſimile erit
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producto
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>.m.</
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>
cum vtraque ſint rectan-
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gula, vnde proportio
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ad
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ad pro-
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portionem
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ad
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ex .18. ſexti du-
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pla erit. </
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<
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xml:space
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">Igitur proportio
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ad
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>.m.</
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æ-
<
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qualis erit proportioni
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var
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ad
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var
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et
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ad
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>.q.</
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et
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ad
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& permutando ſic ſe ha-
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bebit
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ad
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>.i.</
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ſicut
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ſed
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ad
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ſicſe habere probatum eſt vt
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var
>
ad
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>.l</
var
>
.
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</
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<
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xml:id
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xml:space
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preserve
">Quare ex eadem .24. quinti ſic ſe habe
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bit
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ad
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ſicut
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ſed
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m.</
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æqualis eſt
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. </
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xml:space
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pariter
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>.i.</
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æqualis erit.</
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</
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<
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<
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xml:space
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<
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value
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58
">LVIII</
num
>
.</
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<
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xml:space
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">ALIVD quoque problema, nec tamen definitum, veteres propoſuerunt,
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nempe an aliquis numerus in .4. eiuſmodi partes diuidi poſſit, vt ſumma qua-
<
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dratorum duarum partium dupla ſit ſummæ quadratorum reliquarum duarum.</
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<
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<
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xml:space
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">Verum huius effectio & ſpeculatio non erit difficilis,
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cum
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type
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>
ſit eadem quæ præmiſsis
<
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/>
proximè duobus theorematibus allata fuit, ſumpta nempe ſumma radicum quarun
<
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/>
cunque ſic ſe habentium, prout dictum fuit. </
s
>
<
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xml:id
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xml:space
="
preserve
">Verbigratia .44. cuius partes erunt.
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16. 12. 14. 2.
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type
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progrediemur regula de tribus dicentes. </
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<
s
xml:id
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xml:space
="
preserve
">Si .44 numerum propoſi-
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tum valet, quid .16. pars maior? </
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>
<
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xml:space
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">nempe valebit partem maiorem numeri propoſi-
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ti reſpondentem .16. idem de cæteris dico.</
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</
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<
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<
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xml:space
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<
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xml:space
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">THEOREMA
<
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value
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59
">LIX</
num
>
.</
head
>
<
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<
s
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xml:space
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">CVR diuidens propoſitum numerum in duas eiuſmodi partes, vt productum
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radicum quadratarum ipſarum partium æquale ſit alteri numero propoſito,
<
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/>
cuius
<
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norm
="
tamen
"
type
="
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">tamẽ</
reg
>
quadratum maius
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norm
="
non
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type
="
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">nõ</
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ſit quadrato dimidij primi numeri propoſiti. </
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>
<
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xml:space
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">Rectè
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ſecundum numerum propoſitum in ſeipſum multiplicat, &
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eundem
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type
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">eundẽ</
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>
ex quadrato di-
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midij primi detrahit,
<
reg
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reſiduique
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type
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">reſiduiq́;</
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quadratam radicem ſubtrahit ex dimidio ipſius pri-
<
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mi, ex quo datur minor pars quæſita, quaipſi dimidio coniuncta, maior pars ha-
<
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/>
betur.</
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>
</
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<
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<
s
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xml:space
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">Exempli gratia, ſi proponatur numerus, 20. propoſito modo, in duas partes
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eiuſmodi diuidendus, vt productum radicum æquale ſit (verbigratia) 8. </
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>
<
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xml:space
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dium priminumeri in ſeipſum multiplicabimus, cuius quadratum erit .100. ex
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quo quadratum ſecundi numeri, nempe .64. detrahemus,
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.36. cuius radi
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ce quadrata coniuncta .10. dimidio inquam primi numeri propoſiti, dabitur nume
<
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rus .16. pars maior, & ſubtracta à dimidio, dabitur minor pars, nempe .4.</
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