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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THEOR. ARITH.
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file
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0095
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xlink:href
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autem corporis
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miſti
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.216. argentei verò
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vt .156. detrahatur nunc pon-
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dus
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ex pondere
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. </
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<
s
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xml:space
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">Reliquum erit .78. quod vocetur prima differentia ſeruan-
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da, dematur etiam pondus
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ex pondere
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reliquum erit .18. pro ſecunda diffe-
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rentia, etiam ſeruanda, multiplicetur poſteà pondus
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>.A.</
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per ſecundam differen-
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tiam, productum verò diuidatur per primam differentiam. </
s
>
<
s
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xml:space
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preserve
">Vnde in præſenti exem
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plo proueniet nobis .36. quiquidem prouentus erit quantitas argenti ipſius corpo-
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ris miſti
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quo etiam detracto ex pondere totali ipſius
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reliquum erit quanti-
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tas auri eius corporis, hoc eſt .180.</
s
>
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<
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<
s
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xml:space
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preserve
">In cuius operationis ſpeculatione, aliquid natura ſua prius cognitum præcedere
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oportet hoc eſt, quod omnia corpora omogenea eandem proportionem obtinent
<
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inter quantitates, quam inter pondera. </
s
>
<
s
xml:id
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echoid-s1096
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xml:space
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preserve
">Quo ſuppoſito denotetur corpus
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>.A.</
var
>
li-
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nea
<
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>.o.a.</
var
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corpus autem
<
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>.V.</
var
>
linea
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>.o.c.</
var
>
& corpus
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var
>.M.</
var
>
linea
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>.e.u</
var
>
: ſed
<
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>.e.o.</
var
>
ſignificet par-
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tem argenti, et
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>.o.u.</
var
>
partem auri in corpore miſto
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>.M.</
var
>
vnde ex communi conceptu
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habebimus
<
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>.o.e.</
var
>
æqualem
<
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>.u.c.</
var
>
cum ex hypotheſi
<
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>.e.u.</
var
>
æqualis ſit
<
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>.o.c.</
var
>
et
<
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>.a.o.</
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>
ſimiliter.
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</
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<
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xml:space
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">Significetur poſteà pondus
<
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>.a.o.</
var
>
ab
<
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>.f.</
var
>
& pondus
<
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>.e.u.</
var
>
ab
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>.b.x.</
var
>
& pondus
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>.o.c.</
var
>
ab
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>.f.g.</
var
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pon
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dus verò
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>.o.e.</
var
>
ab
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var
>
pondus autem
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var
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ab
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>
pondus enim
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var
>
ab
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>.b.d.</
var
>
et
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>.g.</
var
>
ſit diffe-
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rentia, qua
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>.f.g.</
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>
maior eſt .f: et
<
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>.d.</
var
>
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<
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number
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130
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xlink:href
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</
figure
>
differentia qua
<
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>.b.d.</
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maior eſt
<
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>.b</
var
>
.
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</
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<
s
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xml:space
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">Vnde ex ratione omogeneitatis ea
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dem proportio erit
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>.a.o.</
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ad
<
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>.e.o.</
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>
vt
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>.
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f.</
var
>
ad
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>.b.</
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>
et
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>.o.c.</
var
>
ad
<
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>.u.c.</
var
>
quæ
<
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>.x.b.d.</
var
>
ſeu
<
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/>
<
var
>f.g.</
var
>
(quodidem eſt) ad
<
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>.b.d</
var
>
. </
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>
<
s
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xml:space
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">Quare
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ex
<
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">.11. quinti
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erit proportio
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f.</
var
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ad
<
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>.b.</
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vt
<
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>.f.g.</
var
>
ad
<
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>.b.d.</
var
>
& permutan-
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do ita erit
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>.f.</
var
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ad
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>.f.g.</
var
>
vt
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>.b.</
var
>
ad
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>.b.d.</
var
>
&
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ſeparando ita
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>.f.</
var
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ad
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>.g.</
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vt
<
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>.b.</
var
>
ad
<
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>.d</
var
>
. </
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<
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">Sed
<
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cognita nobis eſt, vt differentia in
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ter
<
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g, et
<
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>.f</
var
>
: cognita nobis eſt etiam
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>.f</
var
>
: cognoſcimus itidem
<
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>.d.</
var
>
vt differentiam inter
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>.
<
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x.b.d.</
var
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et
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quapropter cognoſcemus
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ex .20. ſeptimi Eucli. & ſic
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reſiduum.
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</
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<
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.</
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<
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">THEOREMA
<
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">CXXIII</
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<
s
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xml:space
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">NVNC ex methodo præcedentis propoſiti deuenire poſſumus in cognitio-
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nem veræ quantitatis auri, & argenti confuſi in corona Hieronis conſtituen-
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do primum duo corpora ſimplicia æqualia inter ſe, & coronæ hoc modo videlicet,
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immergendo coronam, ſeu corpus miſtum in aliquod vas aqua plenum, & diligen-
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ter colligere aquam, quæ ex eo effundetur, poſteà verò oportet, aliud vas inuenire
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præciſæ capax illius a quæ collectæ, in quod demum infundatur tantum auri, & po-
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ſteà tantum argenti, quantum ſieri poteſt, vnde vnumquodque horum duorum cor
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porum ſimplicium æquale erit mixto, ſeu coronæ, & ſic quod dictum eſt in præce-
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cedenti theoremate exequemur.</
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<
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<
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xml:space
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">THEOREMA
<
num
value
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124
">CXXIIII</
num
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.</
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<
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<
s
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xml:space
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">SED vt breuiori methodo idem præſtemus, quod in antecedenti propoſito di-
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ctum eſt, quædam theoremata præmittenda ſunt, videlicet quòd quotíeſcunque
<
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fuerint tria corpora, quorum duo inuicem æqualia ſint in quantitate, ſed diuerſa- </
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