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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0018
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cato
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per
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dabitur productum
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partium. </
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conſtabit ex duode-
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cim partibus eiuſdem rationis cum reliquis duobus
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productis, quod quadratum
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vnitas eſt ſuperficia-
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lis, & communis denominans duorum productorum.
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">quod ſi in præſentiarum cogitabimus lineam
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tri-
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gintatrium partium æqualium, et
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duodecim ſimi-
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lium, et
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viginti
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duodecim, multiplicato
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d.</
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cum
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dabitur ſuperficies
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660. fractorum
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ſuperficialium, quorum vnitas integra ſuperficialis
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erit quadratum
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144. partium cuiuſmodi
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partes habet .660. diuiſo itaque
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per
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pro-
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poſitum conſequetur. </
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producti
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ad
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>
quæ producti eius quòd fit ex
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a.e.</
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in
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nam proportio
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ea-
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dem eſt quæ
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ad
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&
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vt
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ex prima ſexti vel 18. ſeptimi, ſed vt
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ad id
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type
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fit ex
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in
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eſt vt
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ad
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>
& vt eius
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type
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fit ex
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>
in
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ad
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>
eſt vt
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>
ad
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>
ex dictis pro-
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poſitionibus </
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xml:space
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">quare ex æqua proportionalitate, eodem
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modo diſcurrendo in figura
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>
ita ſe habebit
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>
<
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ad
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>
vt
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ad
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>
. </
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<
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xml:space
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">Porrò ex ijs, quæ hactenus de
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fractorum multiplicatione conſiderata fuerunt, apertè
<
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ratio deprehenditur, cur productum, ſingulis producen
<
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tibus ſemper minus ſit, cum producta ſint ſuperficialia
<
lb
/>
producentia verò ſemper linearia, omiſſis productis
<
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corporeis, quæ omnia ad ſuperficialia reducuntur.</
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<
num
value
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9
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num
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.</
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<
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fractorum diuiſione, animaduertendum eſt, denominantes numeros
<
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ſemper æquales inuicem eſſe debere, vnius ſcilicet ſpeciei, quòd ſi æquales non
<
lb
/>
fuerint, neceſſe eſt via multiplicationis ipſorum denominantium adinuicem effice-
<
lb
/>
re æquales vt ſint, ex quo productum oritur eiuſmodi, vt aptum ſit habere partes
<
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/>
fractorum, quæ deſiderabantur.</
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<
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<
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xml:space
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">Exempli gratia, ſi proponerentur diuidenda ſeptem octaua per tria quarta præ-
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cipit antiquorum regula, vt ad vnam tantum denominationem reducantur. </
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<
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">quare
<
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multiplicant denominantes inuicem. </
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>
<
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xml:space
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preserve
">ex quo productum in materia propoſita ori-
<
lb
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tur triginta duarum partium commune denominans, cuius duo numerantes ſunt vi-
<
lb
/>
gintiquatuor & vigintiocto, producti ex multiplicatione vnius numerantis in deno
<
lb
/>
minantem alterius, ex quo dantur vigintiquatuor tamquam tria quarta trigintaduo
<
lb
/>
rum, & vigintiocto tanquam ſeptem octaua particularum vniformium, prout ope
<
lb
/>
primæ ſexti aut decimæoctauæ ſeptimi in ſubſcripta figura cognoſci poteſt.</
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