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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<div xml:id="echoid-div7" type="body" level="1" n="1">
<div xml:id="echoid-div7" type="chapter" level="2" n="1">
<div xml:id="echoid-div230" type="math:theorem" level="3" n="120">
<p>
<s xml:id="echoid-s1083" xml:space="preserve">Pro cuius ratione conſideremus triangulum hic ſubnotatum
<var>.a.b.c.</var>
cuius
<lb/>
unumquodque latus ſignificet ſummam duorum ſociorum, vtputa latus
<var>.a.b.</var>
ſignifi-
<lb/>
cet ſummam primi cum ſecundo, latus verò
<var>.b.c.</var>
ſummam ſecundi cum tertio, la-
<lb/>
rus autem
<var>.a.c.</var>
ſummam primi cum tertio, et
<var>.a.e.</var>
ſeu
<var>.a.o.</var>
ſit numerus primi ſocij, et
<var>.
<lb/>
e.b.</var>
vel
<var>.b.u.</var>
ſit ſecundi ſocij, et
<var>.c.u.</var>
ſeu
<var>.c.o.</var>
ſit tertij, cum autem
<var>.a.e.</var>
æqualis ſit
<var>.a.o.</var>
<lb/>
</figure>
et
<var>.b.e</var>
:æ qualis
<var>.b.u.</var>
et
<var>.c.u.</var>
æqualis
<var>.c.o.</var>
<lb/>
ex ſuppoſito ſi
<reg norm="dempta" type="context">dẽpta</reg>
fuerit ſumma ſeu
<lb/>
latus
<var>.a.c.</var>
datum ex aggregato laterum
<var>.
<lb/>
a.b.</var>
cum
<var>.b.c.</var>
reliquarum ſummarum, re
<lb/>
linquet nobis cognitum aggregatum
<lb/>
ex
<var>.b.e.</var>
cum
<var>.b.u</var>
. </s>
<s xml:id="echoid-s1084" xml:space="preserve">Quare & eius medic-
<lb/>
tas
<var>.b.e.</var>
ſiue
<var>.b.u.</var>
nobis cognita erit, qua
<lb/>
detracta exſumma
<var>.b.a.</var>
relinquetur no
<lb/>
bis cognitus numerus
<var>.a.e.</var>
detracto ve-
<lb/>
ro numero
<var>.a.e.</var>
hoc eſt
<var>.a.o.</var>
ex
<var>.a.c.</var>
ſum-
<lb/>
ma, ſeu latus, aut
<var>.b.u.</var>
ex
<var>.b.c.</var>
remanebit
<lb/>
<var>o.c.</var>
ſeu
<var>.c.u.</var>
cognitus.</s>
</p>
</div>
<div xml:id="echoid-div232" type="math:theorem" level="3" n="121">
<num value="121">CXXI</num>
<p>
<s xml:id="echoid-s1085" xml:space="preserve">HAC etiam methodo hoc facere poſſumus non
<reg norm="ſolum" type="context">ſolũ</reg>
de tribus ſocijs, ſed
<reg norm="etiam" type="context">etiã</reg>
<lb/>
de omnibus quotquot volueris, vt exempli gratia,
<lb/>
</figure>
ſint ſex ſocij
<var>.a.b.c.d.e.f.</var>
quorum ſumma per binos co-
<lb/>
gnita, vtputà ſumma numeri
<var>.a.</var>
cum
<var>.b.</var>
cognita nobis ſit,
<lb/>
& ſumma numeri
<var>.b.</var>
cum
<var>.c.</var>
& ſumma
<var>.c.</var>
cum
<var>.d.</var>
& ſum-
<lb/>
ma
<var>.d.</var>
cum
<var>.e.</var>
& ſumma
<var>.e.</var>
cum
<var>.f.</var>
neceſle eft etiam ſcire
<lb/>
ſummam duorum vno relicto, vtputa ſummam
<var>.a.</var>
cum
<lb/>
c. vt poſſimus triangulum
<var>.a.b.c.</var>
conſtituere. </s>
<s xml:id="echoid-s1086" xml:space="preserve">Vnde ex
<lb/>
præmiffa, cognitus numerus nobis erit vniuſcuiuſque
<var>.a.
<lb/>
b.c</var>
. </s>
<s xml:id="echoid-s1087" xml:space="preserve">Quapropter dempto numero
<var>.c.</var>
ex ſumma
<var>.c.</var>
cum
<lb/>
d. & numero
<var>.d.</var>
ex ſumma
<var>.d.</var>
cum
<var>.e.</var>
& numero
<var>.e.</var>
ex ſum
<lb/>
ma
<var>.e.</var>
cum
<var>.f.</var>
habebimus intentum.</s>
</p>
</div>
<div xml:id="echoid-div234" type="math:theorem" level="3" n="122">
<num value="122">CXXII</num>
<p>
<s xml:id="echoid-s1088" xml:space="preserve">CVM aliquando, illud quod Archimedes inuenit, vt furtum Regiab aurifa-
<lb/>
bro in regia corona factum, quemadmodum ſcribit Vitruuius, proderet, con-
<lb/>
templarer, mihi etiam viſum eſt, vt aliquem modum ſcientiſicum inueſtigarem, quo
<lb/>
proportio auri ad argentum, quod in aliquo propoſito corpore exipſis miſto cogni
<lb/>
ti ponderis cognoſci poſſet. </s>
<s xml:id="echoid-s1089" xml:space="preserve">Et cum multos diuerſis temporibus excogitarim offi-
<lb/>
cio meo deeſſe nolui in ijſdem literarum monumentis mandandis, quorum hic
<lb/>
vnus erit: </s>
<s xml:id="echoid-s1090" xml:space="preserve">propoſita nobis ſint tria corpora
<var>.A.M.V.</var>
æqualia inter ſe, ſed diuer-
<lb/>
ſarum ſpecierum materiei, vtputa quod
<var>.A.</var>
ſit argenteum, & omogeneum
<var>.V.</var>
ve-
<lb/>
rò aureum omogeneum, & M. mixtum exauro, & argento, ideſt heterogeneum,
<lb/>
cupimusergo ſcire
<reg norm="iuſtam" type="context">iuſtã</reg>
quantitatem auri & argenti, quæ eſt in ipſo corpore
<var>.M.</var>
<lb/>
miſto. </s>
<s xml:id="echoid-s1091" xml:space="preserve">Ita igitur faciamus. </s>
<s xml:id="echoid-s1092" xml:space="preserve">Videamus primum quantum ſit pondus vniuſcuiuſque
<lb/>
ipſorum corporum, ponamus autem pondus corporis
<var>.V.</var>
auri eſſe vt .234. pondus </s>
</p>
</div>
</div>
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