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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<div xml:id="echoid-div333" type="section" level="3" n="14">
<p>
<s xml:id="echoid-s1686" xml:space="preserve">Ponamus nunc quadratum lateris
<var>.a.u.</var>
eſſe .12. clarum erit quodlibet quadratum
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aliorum duorum laterum
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et
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futurum nouem, ex ijs quæ poſteriore loco dixi
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eſt tantò minus aliorum duorum quadratorum
<lb/>
ſumma, quantum eſt duplum producti ipſius
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in
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ex .13. ſecundi, ſed alia duo
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<var>.a.
<lb/>
q.</var>
ideſt nouem, remanebit numerus .12. pro duplo producti ipſius
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in
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cuius
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dupli me-
<lb/>
dia pars, id-
<lb/>
eſt ſimplex
<lb/>
productum
<lb/>
ipſius
<var>.q.a.</var>
<lb/>
<reg norm="in" type="wordlist">ĩ</reg>
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erit 6.
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Sed
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qua
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dratum ip-
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ſius
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eſt
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nouem,
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<var>.
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q.a.</var>
crit .3.
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per
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di-
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uidendo .6.
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productum
<lb/>
ipſius
<var>.q.a.</var>
<lb/>
in
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pro
<lb/>
latere
<var>.a.o.</var>
<lb/>
conſurgent
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duo, cum er
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go
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ſint
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duo tertia
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ipſius
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<lb/>
certi
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eſſe latus dicti exagoni.</s>
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</figure>
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</div>
<div xml:id="echoid-div337" type="section" level="3" n="15">
<p>
<s xml:id="echoid-s1687" xml:space="preserve">
<reg norm="DEſiderantes" type="context">DEſiderãtes</reg>
ſcire deinde
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in figura
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quar
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ti cap. tertiæ partis perſpectiuę Danielis
<lb/>
Barbari, ſeu Zamberti, eſſe veram
<reg norm="altitudinem" type="context">altitudinẽ</reg>
cor-
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poris octoaedri,
<reg norm="primum" type="context">primũ</reg>
ſcire debemus
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<reg norm="exiſtente" type="context">exiſtẽte</reg>
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h.</var>
vt
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vt ex ijs, quę ſuperius
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diximus, facile percipi poteſt; </s>
<s xml:id="echoid-s1688" xml:space="preserve">ex penultima primi
<var>.
<lb/>
b.l.</var>
<var>.k.l.</var>
ipſa et
<var>.k.
<lb/>
l.</var>
dupla
<reg norm="inpotentia" type="context">inpotẽtia</reg>
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& ob id ducta
<reg norm="cum" type="context">cũ</reg>
eſſet
<var>.h.
<lb/>
l.</var>
<var>.h.k.</var>
& ſeſquialtera
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<var>.l.k.</var>
<var>.l.b.</var>
<var>.h.b.</var>
vnde
<var>.l.h.</var>
<lb/>
æqualis eſſet vni ex lateribus
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ęquilateri di-
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cti corporis. </s>
<s xml:id="echoid-s1689" xml:space="preserve">Ex rationibus igitur ſuperius hîc poſi-
<lb/>
tis
<var>.l.k.</var>
erit altitudo dicta, id eſt diſtantia inter duas
<lb/>
facies inuicem oppoſitas, octoaedri.</s>
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<p>
<s xml:id="echoid-s1690" xml:space="preserve">
<reg norm="Neque" type="simple">Neq;</reg>
volo te ignorare
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<reg norm="non" type="context">nõ</reg>
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fuiſſe
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illius Zamberti: </s>
<s xml:id="echoid-s1691" xml:space="preserve">cum
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capite affirmet angulos
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octoacdri rectos eſſe
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ſint acuti,
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<reg norm="vnuſquiſque" type="simple">vnuſquiſq;</reg>
minor eſt angulo cubi ſolido.</s>
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