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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23
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THEOR. ARITH.
"
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35
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file
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0035
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0035
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ipſius
<
var
>.a.x.</
var
>
tam ſit multiplex ad vnitatem, quam cupimus numerum
<
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>.a.e.</
var
>
numero
<
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>.
<
lb
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e.o.</
var
>
multiplicem eſſe.</
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<
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xml:space
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<
num
value
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37
">XXXVII</
num
>
.</
head
>
<
p
>
<
s
xml:id
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echoid-s325
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xml:space
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">CVR inuenire cupientes duos numeros, quorum quadrata in ſummam colle-
<
lb
/>
cta, æqualia ſint numero propoſito, & ijſdem numeris multiplicatis ad-
<
lb
/>
inuicem, productum alteri numero propoſito ſit æquale, rectè ſumant dimidium
<
lb
/>
primi numeri propoſiti, cui ſumma quadratorum æquari debet,
<
reg
norm
="
hocque
"
type
="
simple
">hocq́;</
reg
>
dimidium
<
lb
/>
in ſeipſum multiplicent, vnà etiam alterum numerum propoſitum in ſeipſum
<
lb
/>
multiplicent, quod quadratum detrahunt de primo, & reſidui quadratam radicem,
<
lb
/>
dimidio primi numeri propoſiti coniungunt, ex qua ſumma, quadratam radicem
<
lb
/>
<
reg
norm
="
eruunt
"
type
="
context
">eruũt</
reg
>
, quæ duobus quæſitis numeris maior erit, cuius quadrato de primo numero
<
lb
/>
detracto, & exreliquo erutaradice quadrata, detur minor numerus, duorum
<
reg
norm
="
quae- ſitorum
"
type
="
simple
">quę-
<
lb
/>
ſitorum</
reg
>
.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s326
"
xml:space
="
preserve
">Exempli gratia, ſi proponerentur .34. pro primo numero cui æquari de-
<
lb
/>
beret ſumma duorum quadratorum, quorum radicum productum æquale eſſe de-
<
lb
/>
beret alteri numero, verbi gratia .15. iubet antiquorum regula, dimidium primi
<
lb
/>
numeri in ſeipſum multiplicari, cuius dimidij quadratum erit .289. è quo ſi detra-
<
lb
/>
has quadratum ſecundi numeri, nempe .225. remanebit .64.
<
reg
norm
="
atque
"
type
="
simple
">atq;</
reg
>
huius ſi quadra-
<
lb
/>
tam radicem ſumas nempe .8. quam dimidio primi numeri, nempe .17. coniun-
<
lb
/>
gas, dabitur duorum quadratorum numerorum quęſitorum maior numerus .25. hac
<
lb
/>
deinde radice è dimidio detracta, minus quadratum dabitur .9. ſcilicet, quorum
<
lb
/>
radices .5. et .3. eſſent ij numeri, qui quæruntur.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s327
"
xml:space
="
preserve
">Cuius ſpeculationis gratia, cogitemus primum numerum, cui quadratorum fum
<
lb
/>
ma æquari debet, ſignificari linea
<
var
>.a.n.</
var
>
tum concipiamus quæſita quadrata ſignifi-
<
lb
/>
cari,
<
reg
norm
="
coniungique
"
type
="
simple
">coniungiq́</
reg
>
modo ſubſcripto
<
var
>.t.b.k.</
var
>
ſecundum porrò numerum propoſitum,
<
lb
/>
ſignificari producto
<
var
>.d.b</
var
>
. </
s
>
<
s
xml:id
="
echoid-s328
"
xml:space
="
preserve
">Iam nil ſupereſt aliud quam vt quantitates
<
var
>.d.p.</
var
>
et
<
var
>.b.p.</
var
>
<
lb
/>
quæramus.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s329
"
xml:space
="
preserve
">Itaque cum in linea
<
var
>.a.n.</
var
>
ſummæ quadratorum numerus detur, quadratum di-
<
lb
/>
midij
<
var
>.o.a.</
var
>
ſit
<
var
>.s.a.</
var
>
quod nobis erit cognitum; </
s
>
<
s
xml:id
="
echoid-s330
"
xml:space
="
preserve
">ſit etiam
<
var
>.a.u.</
var
>
numerus quadrati ma
<
lb
/>
ioris, et
<
var
>.u.n.</
var
>
minoris, et
<
var
>.a.z.</
var
>
productum vnius in alterum; </
s
>
<
s
xml:id
="
echoid-s331
"
xml:space
="
preserve
">qui quidem numerus
<
var
>.a.
<
lb
/>
z.</
var
>
æqualis erit
<
lb
/>
quadrato nume
<
lb
/>
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xlink:label
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fig-0035-01
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xlink:href
="
fig-0035-01a
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number
="
49
">
<
image
file
="
0035-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0035-01
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</
figure
>
ri
<
var
>.d.b.</
var
>
ex .19.
<
lb
/>
theoremate hu-
<
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ius libri. </
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>
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<
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norm
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Itaque
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type
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">Itaq;</
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>
<
lb
/>
<
var
>a.z.</
var
>
cognitum
<
lb
/>
erit, cum eius
<
lb
/>
radix
<
var
>.d.b.</
var
>
ſit
<
reg
norm
="
ſe- cundus
"
type
="
context
">ſe-
<
lb
/>
cũdus</
reg
>
numerus
<
lb
/>
propoſitus, quæ
<
lb
/>
minor erit
<
var
>.a.s.</
var
>
ex quinta ſecundi, aut ſeptima conſequentia poſt .16. noni Eucli-
<
lb
/>
dis. </
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>
<
s
xml:id
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xml:space
="
preserve
">Iam ſubtracta quantitate
<
var
>.z.a.</
var
>
è quadrato
<
var
>.a.s.</
var
>
cognoſcetur quadratum
<
var
>.t.x.</
var
>
<
lb
/>
cuius radix æqualis erit
<
var
>.o.u.</
var
>
ex poſtremo adductis, Itaque cognoſcemus
<
var
>.o.u.</
var
>
qui
<
lb
/>
numerus coniunctus dimidio
<
var
>.o.a.</
var
>
cognito, dabit quadratum
<
var
>.a.u.</
var
>
cognitum, at-
<
lb
/>
queita
<
var
>.u.n.</
var
>
pariter cognoſcetur, & eorum radices conſequenter.</
s
>
</
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