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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130 - 139
140 - 149
150 - 159
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170 - 179
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IO. BAPT. BENED.
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0030
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<
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xml:space
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">Proponunt hi numerum in binas eiuſmodi partes diuidendum, vt ſumma qua-
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dratorum dictarum partium, alteri numero poſsibili propoſito æqualis ſit, poſſi-
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bili inquam, etenim ſi eiuſmodi numerus propoſitus, minor eſſet producto totius
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primi in ſuum dimidium, eſſet huiuſmodi factum impoſſibile. </
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<
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xml:space
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cupientes, ſumamus primum
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propoſitum, quem in ſe ipſum multiplice-
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mus. </
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<
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xml:space
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">ab hoc quadrato deducamus ſecundum numerum propoſitum, tum quod re-
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manſerit duplicemus, quod duplum denuo iubeo ex eodem primo quadrato detra-
<
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hi, accepta poſtea radice quadrata reſidui & dempta ex priori numero propoſito,
<
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</
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<
s
xml:id
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xml:space
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">tunc dimidium reſidui vna pars erit ex duabus primi numeri quæſita.</
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<
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<
s
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xml:space
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">Exempli gratia proponantur .20. diuidenda in duas eiuſmodi partes, vt ſumma
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quadratorum ipſarum partium æqualis ſit .272. qui numerus maior eſt .200. maior
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inquam dimidio quadrati .400. ipſorum .20. hic autem numerus .272. è quadra-
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to .400. deducatur,
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enim .128. quod duplicari iubeo,
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<
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256.</
num
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quæ pariter deducta è quadrato totali, remanebunt .144. cuius radicem ſumi
<
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volo, quæ erit .12. & dempta ex .20. priori numero dato remanebit .8. cuius di-
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midium erit .4: pars vna ex quæſitis, quæ ex primo numero propoſito .20. detra-
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hetur,
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.16. pro altera parte.</
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<
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<
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xml:space
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cognitum nu-
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meri
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>
primò propoſiti, qui cogitetur diuiſus in duo quadrata
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et
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q́</
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ſupplementa
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et
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numerus autem ſummæ duorum quadratorum
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>.d.e.
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b.</
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>
pro ſecundo propoſito datur; </
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xml:space
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">ex quo, ſumma duorum ſupplementorum
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>
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conſequenter erit cognita, quę cum duplicata fuerit, & quatuor hæc ſupplementa
<
unsure
/>
<
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cogitatione accommodata, prout in
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quadrato
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apparet (
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idipſum
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proueniret ſi modo Eucl. octaua
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aptaretur) æquali quadrato
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>
ita vt
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cogitatis quatuor ſupplementis numeri
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cogniti in quadrato
<
var
>.f.g.</
var
>
ex conſequen-
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/>
ti cognoſcetur numerus quadrati partia
<
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lis
<
var
>.h.i.</
var
>
& vna etiam eius radix qua de-
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tracta ex numero
<
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>.a.b.</
var
>
aut
<
var
>.f.n.</
var
>
(quod
<
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idem eſt) primo propoſiti, relinquetur numerus cognitus duplum
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var
>
aut
<
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>.t.b.</
var
>
<
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pars vna totius
<
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>.a.b.</
var
>
ex quo uerum erit hoc meum problema.</
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.</
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huius rei quærat, hoc præſtet inuen-
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to numero huius ſupplementi, cum in
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præcedenti theoremate dictum fuerit,
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qua ratione manifeſtetur duplum ſupple-
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menti ipſius.</
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<
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<
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xml:space
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">Cogitemus in ſubſcripta figura lineam
<
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a.b.</
var
>
tanquam primum numerum propoſi-
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tum, & productum
<
var
>.a.e.</
var
>
ſupplemento
<
var
>.a.e.</
var
>
primæ præcedentis figuræ æquale ſit,
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ac deinde ordine ab antiquis tradito procedatur, ad quadratum reducto dimidio
<
var
>.
<
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a.b.</
var
>
videlicet
<
var
>.b.c.</
var
>
quod erit
<
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var
>
ex quo detrahatur deinde
<
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>.a.e</
var
>
. </
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