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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94
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file
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0094
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0094
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<
s
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xml:space
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">Pro cuius ratione conſideremus triangulum hic ſubnotatum
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cuius
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unumquodque latus ſignificet ſummam duorum ſociorum, vtputa latus
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ſignifi-
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cet ſummam primi cum ſecundo, latus verò
<
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>.b.c.</
var
>
ſummam ſecundi cum tertio, la-
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rus autem
<
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>.a.c.</
var
>
ſummam primi cum tertio, et
<
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>.a.e.</
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ſeu
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>.a.o.</
var
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ſit numerus primi ſocij, et
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>.
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e.b.</
var
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vel
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var
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ſit ſecundi ſocij, et
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ſeu
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>.c.o.</
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ſit tertij, cum autem
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æqualis ſit
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var
>
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<
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fig-0094-01
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xlink:href
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number
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128
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file
="
0094-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0094-01
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</
figure
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et
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:æ qualis
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et
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æqualis
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var
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ex ſuppoſito ſi
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type
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fuerit ſumma ſeu
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latus
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datum ex aggregato laterum
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a.b.</
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cum
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>.b.c.</
var
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reliquarum ſummarum, re
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linquet nobis cognitum aggregatum
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ex
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var
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cum
<
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>.b.u</
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. </
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<
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xml:space
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">Quare & eius medic-
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tas
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ſiue
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nobis cognita erit, qua
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detracta exſumma
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>.b.a.</
var
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relinquetur no
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bis cognitus numerus
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>.a.e.</
var
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detracto ve-
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ro numero
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>.a.e.</
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hoc eſt
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>.a.o.</
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>
ex
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var
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ſum-
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ma, ſeu latus, aut
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ex
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remanebit
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<
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>o.c.</
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ſeu
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cognitus.</
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<
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<
head
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xml:space
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">THEOREMA
<
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">CXXI</
num
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.</
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<
s
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xml:space
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">HAC etiam methodo hoc facere poſſumus non
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type
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">ſolũ</
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de tribus ſocijs, ſed
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norm
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type
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">etiã</
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de omnibus quotquot volueris, vt exempli gratia,
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<
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xlink:label
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fig-0094-02
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xlink:href
="
fig-0094-02a
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number
="
129
">
<
image
file
="
0094-02
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0094-02
"/>
</
figure
>
ſint ſex ſocij
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var
>
quorum ſumma per binos co-
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gnita, vtputà ſumma numeri
<
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>.a.</
var
>
cum
<
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>.b.</
var
>
cognita nobis ſit,
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& ſumma numeri
<
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>.b.</
var
>
cum
<
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>.c.</
var
>
& ſumma
<
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>.c.</
var
>
cum
<
var
>.d.</
var
>
& ſum-
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ma
<
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>.d.</
var
>
cum
<
var
>.e.</
var
>
& ſumma
<
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>.e.</
var
>
cum
<
var
>.f.</
var
>
neceſle eft etiam ſcire
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ſummam duorum vno relicto, vtputa ſummam
<
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>.a.</
var
>
cum
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c. vt poſſimus triangulum
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var
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conſtituere. </
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>
<
s
xml:id
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echoid-s1086
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xml:space
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">Vnde ex
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præmiffa, cognitus numerus nobis erit vniuſcuiuſque
<
var
>.a.
<
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b.c</
var
>
. </
s
>
<
s
xml:id
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xml:space
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">Quapropter dempto numero
<
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>.c.</
var
>
ex ſumma
<
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>.c.</
var
>
cum
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d. & numero
<
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>.d.</
var
>
ex ſumma
<
var
>.d.</
var
>
cum
<
var
>.e.</
var
>
& numero
<
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>.e.</
var
>
ex ſum
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/>
ma
<
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>.e.</
var
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cum
<
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>.f.</
var
>
habebimus intentum.</
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</
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<
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type
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<
head
xml:id
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xml:space
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">THEOREMA
<
num
value
="
122
">CXXII</
num
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,</
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<
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<
s
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xml:space
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">CVM aliquando, illud quod Archimedes inuenit, vt furtum Regiab aurifa-
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bro in regia corona factum, quemadmodum ſcribit Vitruuius, proderet, con-
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templarer, mihi etiam viſum eſt, vt aliquem modum ſcientiſicum inueſtigarem, quo
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proportio auri ad argentum, quod in aliquo propoſito corpore exipſis miſto cogni
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ti ponderis cognoſci poſſet. </
s
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<
s
xml:id
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xml:space
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">Et cum multos diuerſis temporibus excogitarim offi-
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cio meo deeſſe nolui in ijſdem literarum monumentis mandandis, quorum hic
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vnus erit: </
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<
s
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xml:space
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">propoſita nobis ſint tria corpora
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æqualia inter ſe, ſed diuer-
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ſarum ſpecierum materiei, vtputa quod
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>.A.</
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ſit argenteum, & omogeneum
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>
ve-
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rò aureum omogeneum, & M. mixtum exauro, & argento, ideſt heterogeneum,
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cupimusergo ſcire
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quantitatem auri & argenti, quæ eſt in ipſo corpore
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>
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miſto. </
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<
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">Ita igitur faciamus. </
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<
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xml:space
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">Videamus primum quantum ſit pondus vniuſcuiuſque
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ipſorum corporum, ponamus autem pondus corporis
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auri eſſe vt .234. pondus </
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