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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THEOREM. ARIT.
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97
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0097
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xlink:href
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pori
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argentei, corpus autem
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æqualis ma-
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gnitudinis corpori
<
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aurei. </
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<
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xml:space
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nem ponderis
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ad pondus
<
var
>.e.</
var
>
eadem eſſe, quæ pon-
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deris
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>.b.</
var
>
ad pondus
<
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>.u.</
var
>
vt in præcedenti theoremate
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iam dictum eſt, vel quæ ponderis
<
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ad pondus
<
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>.a.</
var
>
ex
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11. quinti Euclidis. </
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<
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xml:space
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">Proptereà quòe ponderis
<
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>.
<
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/>
n.</
var
>
ad pondus
<
var
>.a.</
var
>
eft vt poderis
<
var
>.b.</
var
>
ad pondus
<
var
>.u.</
var
>
eo
<
lb
/>
quòd permutando ponderis
<
var
>.n.</
var
>
ad pondus
<
var
>.b.</
var
>
eſt vt
<
lb
/>
ponderis
<
var
>.a.</
var
>
ad pondus
<
var
>.u.</
var
>
ex corporum omogenei-
<
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/>
tate, & ex æqualitate magnitudinum corporum antecedentium & conſequentium.</
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.</
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<
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xml:space
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">SCire etiam nos oportet, quòd quotieſcumque fuerint duo corpora aquea, quo-
<
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/>
rum vnum æqualis magnitudinis ſit alicui miſto, quod quidem miſtum graue
<
lb
/>
ſit tam in aere, quàm in aqua, alterum verò corpus aquem æqualis ſit magnitudi-
<
lb
/>
nis alicui corpoli ſimplici, quod quidem corpus ſimplex æqualis ponderis ſit dicto
<
lb
/>
corpori miſto. </
s
>
<
s
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xml:space
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">Tunc proportio ponderis aquei, cuius magnitudo æquatur magni
<
lb
/>
tudini corporis miſti, ad pondus corporis aquei, cuius magnitudo æqualis eſt ma-
<
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/>
gnitudini corporis ſimplicis, eadem erit, quæ proportio ponderis alicuius corpo-
<
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/>
ris ſimplicis, cuius magnitudo æqualis ſit magnitudini corporis miſti ſuperius dicti,
<
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/>
ſed ſpeciei corporis ſimplicis iam dicti, ad pondus dicti miſti.</
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<
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<
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xml:space
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">Exempli gratia, ſit corpus aqueum
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var
>
magnitudinis æqualis corpori
<
var
>.m.</
var
>
mixto,
<
lb
/>
corpus verò aqueum
<
var
>.i.</
var
>
æqualis magnitudinis ſit corpori ſimplici
<
var
>.a.</
var
>
quod quidem
<
lb
/>
corpus
<
var
>.a.</
var
>
æqualis ponderis ſit cum corpore
<
var
>.m.</
var
>
& corpus
<
var
>.u.</
var
>
ſit æqualis magnitudinis
<
lb
/>
cum corpore
<
var
>.m.</
var
>
ſed ſpeciei corporis
<
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>.a</
var
>
. </
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>
<
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xml:id
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xml:space
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">Tunc dico proportionem ponderis
<
var
>.e.</
var
>
ad
<
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/>
pondus
<
var
>.i.</
var
>
<
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norm
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type
="
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">eãdem</
reg
>
eſſe, quæ ponderis
<
var
>.u.</
var
>
ad pondus
<
var
>.m.</
var
>
primum nulli dubium eſt, quin
<
lb
/>
eadem proportio ſit magnitudinis
<
var
>.e.</
var
>
ad magnitudinem
<
var
>.i.</
var
>
quæ magnitudinis
<
var
>.m.</
var
>
ad
<
lb
/>
a. ſed
<
var
>.m.</
var
>
ad
<
var
>.a.</
var
>
eſt vt
<
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>.u.</
var
>
ad
<
var
>.a.</
var
>
ex .7. quinti </
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>
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xml:space
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">quare
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/>
ex .11. eiuſdem proportio
<
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>.e.</
var
>
ad
<
var
>.i.</
var
>
erit vt
<
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>.u.</
var
>
ad
<
var
>.a.</
var
>
<
lb
/>
<
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fig-0097-02
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number
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xlink:href
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de ipſius magnitudinibus loquendo, ſed propor-
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tio ponderis
<
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>.u.</
var
>
ad pondus
<
var
>.a.</
var
>
eadem eſt, quæ ma
<
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/>
gnitudinis
<
var
>.u.</
var
>
ad magnitudinem
<
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>.a.</
var
>
ex omogenei-
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tate. </
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<
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xml:space
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>.e.</
var
>
ad pondus .1. </
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>
<
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xml:space
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">Qua-
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re proportio ponderis
<
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>.e.</
var
>
ad pondus
<
var
>.i.</
var
>
eadem erit
<
lb
/>
quæ ponderis
<
var
>.u.</
var
>
ad pondus
<
var
>.a</
var
>
. </
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>
<
s
xml:id
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xml:space
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">Sed ponderis
<
var
>.u.</
var
>
<
lb
/>
ad pondus
<
var
>.m.</
var
>
eadem eſt quæ ponderis
<
var
>.u.</
var
>
ad pondus
<
var
>.a.</
var
>
ex .7. quinti, ergò ex .11.
<
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eiuſdem proportio ponderis
<
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>.e.</
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>
ad pondus
<
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>.i.</
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>
eadem erit, quæ ponderis
<
var
>.u.</
var
>
ad pon-
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dus
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>
quod eſt propoſitum.</
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>
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</
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xml:space
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<
num
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">CXXVIII</
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.</
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<
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<
s
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xml:space
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">NVNC ad cognoſcendam proportionem duarum diuerſarum ſpecierum in
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corpore miſto propoſito, tribus corporibus aqueis mediantibus, quæ
<
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corpora æqualium magnitudinum ſint alijs tribus corporibus vnius & eiuſdem pon
<
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deris, quorum vnum ſit mixtum, reliqua verò duo ſimplicia, ſed ſpecierum mixti,
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hoc ordine procedemus.</
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