Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
page
|<
<
of 355
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
p
type
="
main
">
<
s
id
="
s.000744
">
<
pb
pagenum
="
38
"
xlink:href
="
009/01/038.jpg
"/>
propoſitionis, quæ falſa eſt, nimirum ſuppoſito prædictas lineas eſſe comm.
<
lb
/>
deducit ad impoſſibile, ſiue, vt ait hic Ariſt. falſum ratiocinatur, quod ſci
<
lb
/>
licet idem numerus eſſet par, & impar, quod Ariſt. ſignificat, quando ait,
<
lb
/>
imparia æqualia paribus fiunt. </
s
>
<
s
id
="
s.000745
">ex quo abſurdo deducitur falſam eſſe prædi
<
lb
/>
ctam ſuppoſitionem, quæ aſtruebat eſſe comm. & proinde altera pars con
<
lb
/>
tradictionis, quæ eſt, eſſe incomm. vera aſtruitur. </
s
>
<
s
id
="
s.000746
">ex quibus ſatis videtur ex
<
lb
/>
plicari hic locus. </
s
>
<
s
id
="
s.000747
">videas igitur, quàm leuiter nonnulli noſtræ tempeſtatis
<
lb
/>
ageometreti iſtud exponant, dicentes diametrum eſſe incomm. coſtæ, nihil
<
lb
/>
aliud ſignificare, quam diametrum eſſe longiorem coſta, qua expoſitione
<
lb
/>
nihil ineptius. </
s
>
<
s
id
="
s.000748
">Aduerte tandem figuram vulgatæ editionis eſſe ineptam,
<
lb
/>
cum habeat duo quadrata alterum ſuper diametro alterius, quorum maius
<
lb
/>
ſuperuacaneum eſt.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.000749
">
<
arrow.to.target
n
="
marg6
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.000750
">
<
margin.target
id
="
marg6
"/>
6</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.000751
">Et cap. 24. ſecti primi libri primi
<
emph
type
="
italics
"/>
(Sed magis efficitur manifeſtum in deſcri
<
lb
/>
ptionibus, vt quod æquicruris, qui ad baſim æquales ſint, ad centrum ductæ A B,
<
lb
/>
A C, ſi igitur æqualem accipiat A G, angulum ipſi A B D, non omnino exiſtimans
<
lb
/>
æquales, qui ſemicirculorum, & rurſus G, ipſi D, non omnem aſſumens eum, qui ſe
<
lb
/>
cti. </
s
>
<
s
id
="
s.000752
">amplius ab æqualibus existentibus totis angulis, & ablatorum æquales eſſe re
<
lb
/>
liquos E, F, quod ex principio petet, niſi acceperit ab æqualibus demptis æqualia
<
lb
/>
derelinqui.)
<
emph.end
type
="
italics
"/>
Primum ſcias characteres vulgatæ editionis, vna cum figura ip
<
lb
/>
ſis reſpondente, eſſe mendoſos; propterea ex textu græco vtrunque corri
<
lb
/>
gendum putaui in hunc, quem vidiſti modum. </
s
>
<
s
id
="
s.000753
">Secundo, per deſcriptiones
<
lb
/>
Ariſt. intelligere
<
expan
abbr
="
demõſtrationes
">demonſtrationes</
expan
>
Geometricas ſupra diximus, quod ex hoc
<
lb
/>
loco euidenter confirmatur, vbi manifeſtè loco deſcriptionis ſupponit li
<
lb
/>
nearem demonſtrationem. </
s
>
<
s
id
="
s.000754
">In hoc
<
expan
abbr
="
itaq;
">itaque</
expan
>
exemplo vult Ariſt. illud demon
<
lb
/>
ſtrare, quod Euclides in 5. primi oſtendit, alio tamen modo, ſcilicet Iſoſce
<
lb
/>
lium triangulorum, qui ad baſim ſunt anguli, inter ſe ſunt æquales. </
s
>
<
s
id
="
s.000755
">eſt au
<
lb
/>
tem figura in omnibus textibus deprauata, quam ſic puto
<
expan
abbr
="
rèſtītuendam
">rèſtituendam</
expan
>
eſſe
<
lb
/>
ex quodam græco codice, qui characteres hoc modo appoſuerat. </
s
>
<
s
id
="
s.000756
">ſit Iſoſce
<
lb
/>
<
figure
id
="
id.009.01.038.1.jpg
"
place
="
text
"
xlink:href
="
009/01/038/1.jpg
"
number
="
6
"/>
<
lb
/>
les C A B, cuius baſis C B, Dico angulos ſupra baſim,
<
lb
/>
in quibus literæ E F, eſſe inuicem æquales. </
s
>
<
s
id
="
s.000757
">facto centro
<
lb
/>
in A, deſcribatur circulus A B C, tranſiens per puncta
<
lb
/>
C B, iam ſic. </
s
>
<
s
id
="
s.000758
">omnes anguli ſemicirculi ſunt æquales in
<
lb
/>
ter ſe, ergo anguli A C G, A B D, ſunt æquales. </
s
>
<
s
id
="
s.000759
">Præte
<
lb
/>
rea cùm anguli eiuſdem ſectionis ſint æquales ad inui
<
lb
/>
cem, erunt anguli ſectionis C B D G, nimirum anguli,
<
lb
/>
in quibus ſunt G, & D, inter ſe æquales:
<
expan
abbr
="
cumq́
">cumque</
expan
>
; hi duo
<
lb
/>
anguli ſectionis ſint partes
<
expan
abbr
="
angulorũ
">angulorum</
expan
>
ſemicirculi A C G,
<
lb
/>
A B D, ſi illi ab his auferantur, auferuntur æquales anguli ab æqualibus an
<
lb
/>
gulis, ergo anguli, qui remanent, ſcilicet E, & F, erunt æquales, quod erat
<
lb
/>
demonſtrandum. </
s
>
<
s
id
="
s.000760
">hinc Ariſt. infert manifeſtum eſſe oportere in omni ſyllo
<
lb
/>
giſmo, reperiri vniuerſales, & affirmatiuas propoſitiones, vt Factum eſt in
<
lb
/>
præcedenti aliter eſſet petitio principij. </
s
>
<
s
id
="
s.000761
">Quænam vero ſit æqualitas, quam
<
lb
/>
Geometræ conſiderant, infra cap. 1. ſecti 3. explicabitur.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.000762
">
<
arrow.to.target
n
="
marg7
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.000763
">
<
margin.target
id
="
marg7
"/>
7</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.000764
">Ex cap. 2. ſecti 2. lib. 1.
<
emph
type
="
italics
"/>
(Secundum veritatem quidem ex ijs, quæ ſecundum
<
lb
/>
veritatem deſcribuntur ineſſe, ad dialecticos autem ſyllogiſmos ex propoſitionibus
<
lb
/>
ſecundum opinionem)
<
emph.end
type
="
italics
"/>
verba illa; ex ijs, quæ
<
expan
abbr
="
ſecundũ
">ſecundum</
expan
>
veritatem deſcribuntur </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>