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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xlink:href
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g. æqualis erit
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tum productum
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in
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>.g.d.</
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ſit
<
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et
<
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æqualis
<
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et
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pariter
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lb
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ſecetur æqualis
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quæ omnia ex diametro
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cogitari poſſunt: </
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xml:space
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æ-
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qualis
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>.i.d.</
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<
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ſupereritque
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type
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quadratum
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differentiæ
<
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cognitum, hoc verò cogi-
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temus diuiſum eſſe in .4. partes æquales medijs diametris
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et
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</
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<
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partium cognoſcetur, &
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erit ipſius
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aut ipſius
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dimidij
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. </
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ſi aliquod iſtorum quadratorum detrahere voluerimus, nempe
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ex dimidio ſum
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mæ
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duorum quadratorum
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et
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cognitæ, hac via procedemus, primum con
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ſiderabimus
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coniunctam
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quæ quantitates erunt ſumma dimidij
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type
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qua-
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dratorum
<
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et
<
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quando quidem
<
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>.t.r.</
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>
<
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<
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type
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eſt quadrati
<
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et
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gnomonis
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var
>
coniunctum dimidio
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quadrati
<
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>.i.d.</
var
>
ex quo
<
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>.i.t.r.</
var
>
dimidium erit
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>.
<
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/>
b.</
var
>
ex qua quantitate
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>.i.t.r.</
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>
cogitare debe
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/>
mus detrahi quadratum ipſius
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>.K.h.</
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nem
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pe
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>
: </
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xml:space
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erit nempe
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cum
<
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>.n.i.</
var
>
ſed
<
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>.y.m.</
var
>
æqualis
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/>
eſt
<
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>.n.i.</
var
>
et
<
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>.y.m.</
var
>
cum
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>.y.s.</
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>
conſtituunt qua-
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dratum
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. </
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quadratum &
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conſequenter
<
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>.p.s.</
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>
eius radix cognoſce-
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lb
/>
tur, ita etiam & productum huius
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>.p.s.</
var
>
in
<
var
>.
<
lb
/>
s.x.</
var
>
æqualis
<
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>.c.</
var
>
nempe
<
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>.p.x</
var
>
:
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produ-
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ctum huiuſmodi ſemper minus quantita
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te
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>.r.t.i</
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>
: per
<
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>.u.i.</
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>
æquale quadrato minori
<
var
>.
<
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/>
i.d</
var
>
. </
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<
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var
>
cognoſcetur, conſequen-
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lb
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ter
<
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>.i.</
var
>
@q. tanquam reſiduum ex
<
var
>.b.</
var
>
& eo-
<
lb
/>
rum radices quadratæ cognoſcentur
<
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>.a.
<
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g.</
var
>
et
<
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>.g.d</
var
>
.</
s
>
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xml:space
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<
num
value
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63
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num
>
.</
head
>
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<
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xml:space
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">IDEM præſtari hac alia via, meo iudicio poteſt. </
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xml:space
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dimi
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<
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type
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multiplicetur,
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autem ex dimidio primi detrahatur, ex quo re-
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manens erit productum vnius quadratæ radicis in alteram partium primi numeri
<
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quæſitarum, deinde productum hoc duplicetur, & primo numero dato coniunga-
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tur,
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huius ſummæ quadrata radix erit ſumma radicum quadratarum dictarum
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partium, cui iuncto producto ex quadrageſimoquinto theoremate ſingulæ radices
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proferentur.</
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<
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<
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xml:space
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">Exempli gratia, primus numerus diuiſibilis erat .50. alter verò .6. </
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plicemus .6. per .3. nempe dimidium proferetur numerus .18. quo ex dimidio pri-
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/>
mi, nempe .25. detracto, ſupererit .7. productum vnius radicis in alteram, quod du
<
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plicatum dabit .14. quo coniuncto cum primo numero .50. dabitur numerus .64.
<
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/>
cuius quadrata radix ſcilicet .8. erit ſumma radicum duarum partium quæſitarum,
<
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qua & producto .7. ex quadrag eſimoquinto theoremate dictæ radices diſtinguen,
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tur, quarum vna erit .7. & altera
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.</
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>
</
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<
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<
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xml:space
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">Vtautem hocſpeculemur, præcedenti figura vti poterimus, in qua patet
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>
pro
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/>
ductum eſſe ſecundi numeri
<
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>.c.</
var
>
nempe
<
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>.a.h.</
var
>
hoc eſt
<
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>.t.u.</
var
>
in dimidio
<
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>.a.e.</
var
>
ſcilicet
<
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>.p.t.</
var
>
re-
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/>
ſiduum autem dimidij primi
<
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>
eſſe
<
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>.t.i.</
var
>
nempe
<
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>.a.i.</
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>
productum radicum, quod ſupple </
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