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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140 - 149
150 - 159
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<
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41
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rhead
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THEOREM. ARITH.
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n
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53
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file
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0053
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0053
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mentum eſt quadrati
<
var
>.q.d.</
var
>
totalis. </
s
>
<
s
xml:id
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xml:space
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preserve
">Quare duplicato
<
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>.a.i.</
var
>
& coniuncto
<
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>.b.</
var
>
cognoſci-
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mustotum
<
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>.q.d.</
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>
& conſequenter
<
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>.a.d.</
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>
ſuam radicem, hoc eſt ſummam duarum radi
<
lb
/>
cum
<
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>.a.g.</
var
>
et
<
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>.g.d.</
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quæ medio
<
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>.a.i.</
var
>
cognito, & quadrageſimoquinto theoremate ſingu-
<
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/>
læ cognoſcuntur.</
s
>
</
p
>
</
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>
<
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type
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64
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<
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xml:space
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">THEOREMA
<
num
value
="
64
">LXIIII</
num
>
.</
head
>
<
p
>
<
s
xml:id
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xml:space
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preserve
">CVR propoſitum aliquem num erum in duas eiuſmodi partes diuiſuri, vt ſum-
<
lb
/>
ma radicum dictarum partium æqualis ſit alteri numero propoſito. </
s
>
<
s
xml:id
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echoid-s551
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xml:space
="
preserve
">Rectè ſe-
<
lb
/>
cundum numerum in ſeipſum multiplicant, ex quo quadrato, primum datum nu-
<
lb
/>
merum detrahunt,
<
reg
norm
="
rurſusque
"
type
="
simple
">rurſusq́;</
reg
>
reſiduum in ſeipſum multiplicant, & ex eo quadrato
<
lb
/>
quartam partem deſumunt,
<
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norm
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quam
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type
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context
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ex quadrato dimidij primi numeri detrahunt, radi-
<
lb
/>
cemq́ue qua dratam reſidui cum iunxerint, & ex dimidio primi numeri detraxerint,
<
lb
/>
partes quæſitæ proferuntur.</
s
>
</
p
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<
p
>
<
s
xml:id
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xml:space
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">Exempli gratia, ſi proponeretur primus numerus .20. diuidendus et .6. ſecundus
<
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pro ſumma radicum, hunc ſecundum .6. in ſeipſum multiplicabimus,
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type
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nu-
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merus .36. ex quo quadrato primus numerus detrahetur,
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ſupereritque
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type
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numerus .16.
<
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qui quadratus dabit .256. cuius numeri quarta pars ſumetur, nempe .64. quæ ex qua
<
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/>
drato dimidij primi numeri detrahetur, nempe .100.
<
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.36. cuius radix qua
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drata .6. coniuncta & detracta ex .10. dabit .16. partem maiorem et .4. minorem.</
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<
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<
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xml:id
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xml:space
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">Cuius rei hæc ſpeculatio, primus numerus diuiſibilis ſignificetur linea
<
var
>.a.b.</
var
>
diui-
<
lb
/>
ſa in puncto
<
var
>.e.</
var
>
in partes adhuc incognitas, et
<
var
>.a.c.</
var
>
ſit productum
<
var
>.a.e.</
var
>
in
<
var
>.e.b.</
var
>
item
<
var
>.q.
<
lb
/>
p.</
var
>
ſecundum numerum ſignificet, æqualem ſummæ radicum, quæ puncto
<
var
>.n.</
var
>
diſtin-
<
lb
/>
guantur. </
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<
s
xml:id
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xml:space
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">Poſtmodum totum quadratum
<
var
>.p.d.</
var
>
erigatur (quod nobis eſt cognitum),
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lb
/>
in duo quadrata diuiſum
<
var
>.o.p.</
var
>
et
<
var
>.o.d.</
var
>
quorum ſumma
<
var
>.a.b.</
var
>
cum detur, cognita rema-
<
lb
/>
net ſumma
<
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norm
="
duorum
"
type
="
context
">duorũ</
reg
>
<
reg
norm
="
ſupplementorum
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type
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context
">ſupplementorũ</
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>
<
var
>.o.u.</
var
>
et
<
var
>.o.q.</
var
>
qua quadrata
<
reg
norm
="
cum
"
type
="
context
">cũ</
reg
>
fuerit dabit quadru
<
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/>
<
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plum
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type
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context
">plũ</
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>
quadrati
<
reg
norm
="
ſupplementi
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type
="
context
">ſupplemẽti</
reg
>
<
var
>.o.q.</
var
>
<
reg
norm
="
nempe
"
type
="
context
">nẽpe</
reg
>
<
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norm
="
quadruplum
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type
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context
">quadruplũ</
reg
>
producti
<
var
>.a.c.</
var
>
etenim
<
var
>.a.c.</
var
>
ex .19. theo
<
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/>
remate huius libri quadratum eft ipſius
<
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>.q.o.</
var
>
<
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norm
="
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type
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poterant etiam veteres quadrare
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/>
dimidium differentiæ
<
var
>.a.b.</
var
>
ab
<
var
>.p.d.</
var
>
nempe quadrato tantummodo ſupplemento
<
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>.q.
<
lb
/>
o</
var
>
. </
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>
<
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xml:id
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xml:space
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">Tunc habito
<
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>.a.c.</
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>
eius ope tanquam producti
<
var
>.a.e.</
var
>
in
<
var
>.e.b.</
var
>
ex .45. theoremate ſingu
<
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/>
læ partes cognoſcentur.</
s
>
</
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<
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<
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xml:space
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preserve
">Quod alia etiam ratione præſtari poterat, nempe cognito ſupplemento
<
var
>.
<
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q.o.</
var
>
diſtinguendæ radices
<
var
>q.n.</
var
>
et
<
var
>.n.p.</
var
>
ex .45. theoremate, quibus cognitis, eorum
<
lb
/>
etiam quadrata cognoſcuntur.</
s
>
</
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