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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199
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rhead
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IN QVINT. LIB. EVCLI.
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n
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211
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file
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0211
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0211
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<
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xml:space
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">QVARTVM.</
head
>
<
head
xml:id
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style
="
it
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xml:space
="
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">εuclidis uerò nona propoſitio.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2417
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xml:space
="
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">
<
emph
style
="
sc
">Qvotiescvnqve</
emph
>
proportio vnius plurium terminorum collatorum cum ali
<
lb
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quo tertio eiuſdem generis, eadem fuerit cum ea quæ eſt cuiuſuis alterius dictorum
<
lb
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terminorum cum eodem tertio, aut proportio dicti tertij, cum aliquo dictorum, ea-
<
lb
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dem fuerit cum ea quæ ipſius eſt ad aliquem alium eorundem
<
reg
norm
="
terminorum
"
type
="
context
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reg
>
, tunc eiuſ-
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modi termini, æquales erunt inter ſe.</
s
>
</
p
>
</
div
>
<
div
xml:id
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type
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4
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n
="
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<
head
xml:id
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xml:space
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">QVINTVM.</
head
>
<
head
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="
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style
="
it
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xml:space
="
preserve
">Euclidis uerò octaua propoſitio.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2418
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xml:space
="
preserve
">
<
emph
style
="
sc
">Qvoties</
emph
>
plures erunt termini, quorum vnus fuerit maior altero, ſi compa-
<
lb
/>
rentur alicui tertio eiuſdem generis, proportio maioris adtertium illum, maior erit
<
lb
/>
ea, quæ eſt minoris ad prædictum tertium, & proportio illius tertij ad maiorem, mi-
<
lb
/>
nor erit ea quæ eiuſdem tertij ad minorem terminum comparati.</
s
>
</
p
>
</
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>
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<
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xml:space
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">SEXTVM.</
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>
<
head
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style
="
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xml:space
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">εuclidis uerò decima propoſitio.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2419
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xml:space
="
preserve
">
<
emph
style
="
sc
">Qvoties</
emph
>
proportio vnius, ex pluribus terminis comparatis ad aliquem ter-
<
lb
/>
tium, maior fuerit proportione alicuius alterius dictorum cum eodem tertio, primus
<
lb
/>
ille terminus, altero maior erit. </
s
>
<
s
xml:id
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xml:space
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preserve
">Et quoties proportio tertij termini ad vnum
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quam
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type
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">quã</
reg
>
<
lb
/>
ad alterum terminum maior fuerit, eiuſmodi terminus altero minor erit.</
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>
</
p
>
</
div
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<
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xml:space
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">SEPTIMVM.</
head
>
<
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style
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xml:space
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">Euclidis uerò undecima propoſitio.</
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>
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p
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<
s
xml:id
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xml:space
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<
emph
style
="
sc
">Proportiones</
emph
>
, quarum vnaquęque cum aliqua tertia æqualis eſt, ipſæ quo-
<
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que inter ſe ſunt æquales. </
s
>
<
s
xml:id
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xml:space
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preserve
">Vtillud, Quæ vni & eidem ſunt æqualia, ſibi inuicem
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ſunt æqualia.</
s
>
</
p
>
</
div
>
<
div
xml:id
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type
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level
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n
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<
head
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xml:space
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preserve
">OCTAVVM.</
head
>
<
head
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="
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style
="
it
"
xml:space
="
preserve
">εuclidis uerò duodecima propoſitio.</
head
>
<
p
>
<
s
xml:id
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xml:space
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<
emph
style
="
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">Qvotiescvnqve</
emph
>
proportio vnius ex pluribus antecedentibus cum ſuo ex
<
lb
/>
pluribus conſequentibus, æqualis fuerit ei cuiuſuis alterius dictorum
<
reg
norm
="
antecedentium
"
type
="
context
">antecedentiũ</
reg
>
,
<
lb
/>
cum ſuo plurium
<
reg
norm
="
conſequentium
"
type
="
context
">cõſequentium</
reg
>
, proportio totius aggregati antecedentium cum to-
<
lb
/>
to aggregato conſequentium, dictæ primę proportioni ęqualis erit, nempe illius an
<
lb
/>
tecedentis ad ſuum conſequens.</
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>
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