Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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archimedes
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type
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main
">
<
s
id
="
s.000778
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<
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pagenum
="
40
"
xlink:href
="
009/01/040.jpg
"/>
<
expan
abbr
="
linearũ
">linearum</
expan
>
, ſed penes inclinationem, & mucronem, quem faciunt: vnde etiamſi
<
lb
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duæ lineæ prædictæ A B, A C, productæ, ſiue etiam decurtatæ fuerint, dum
<
lb
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modo ſitus, ſiue poſitio ipſarum, quam ad inuicem habent, non varietur,
<
lb
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erit ſemper eadem quantitas anguli A. </
s
>
<
s
id
="
s.000779
">Aduertendum præterea rationem
<
lb
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anguli non poſſe ſaluari in ſolo puncto A, in quo lineæ concurrunt, ſed ne
<
lb
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ceſſariam eſſe aliquam quantitatem, quamuis exiguam, linearum A B, A C.
<
lb
/>
</
s
>
<
s
id
="
s.000780
">Notandum etiam, quod in nominatione angulorum, quæ fit per tres lite
<
lb
/>
ras, ſemper literam illam eſſe medio loco proferendam, quæ ad acumen ip
<
lb
/>
ſum poſita eſt, vt in ſuperiori, litera A, debet ſemper media proferri, dicen
<
lb
/>
do angulum B A C, ſiue C A B,
<
expan
abbr
="
nũquam
">nunquam</
expan
>
tamen licet dicere angulum A C B,
<
lb
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vel C B A. </
s
>
<
s
id
="
s.000781
">Porrò quemadmodum vnus angulus vni angulo æqualis eſt, ita
<
lb
/>
<
expan
abbr
="
aliquãdo
">aliquando</
expan
>
duo anguli ſunt vni angulo æquales, vt patet, ſi vnus angulus, v.g.
<
lb
/>
angulus B A C, diuidatur in duos angulos à linea A D. tunc enim duo angu
<
lb
/>
<
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id
="
id.009.01.040.1.jpg
"
place
="
text
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xlink:href
="
009/01/040/1.jpg
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number
="
8
"/>
<
lb
/>
li partiales B A D, D A C, erunt æquales totali angulo
<
lb
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B A C, cum partes omnes ſimul ſumptæ ſint ſuo toti æqua
<
lb
/>
les. </
s
>
<
s
id
="
s.000782
">pariter tres anguli poſſunt æquari & vni, & duobus
<
lb
/>
alijs angulis, quando nimirum a cumina, ſiue mucrones il
<
lb
/>
li ſimul ad vnum punctum conſtituti
<
expan
abbr
="
adæquarẽtur
">adæquarentur</
expan
>
mucro
<
lb
/>
ni illi, quem conſtituerent alij duo anguli, quibus illi tres
<
lb
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ſunt pares, v.g. ſint tres anguli trianguli A B C,
<
expan
abbr
="
ſintq́
">ſintque</
expan
>
; alij duo anguli recti,
<
lb
/>
<
figure
id
="
id.009.01.040.2.jpg
"
place
="
text
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xlink:href
="
009/01/040/2.jpg
"
number
="
9
"/>
<
lb
/>
quos linea perpendicularis D E, facit cum li
<
lb
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nea F G; ſit
<
expan
abbr
="
inquã
">inquam</
expan
>
anguli recti D E F, D E G,
<
lb
/>
tunc tres anguli illius
<
expan
abbr
="
triãguli
">trianguli</
expan
>
<
expan
abbr
="
dicẽtur
">dicentur</
expan
>
æqua
<
lb
/>
les duobus hiſce rectis, ſi tres illi mucrones
<
lb
/>
trianguli ſimul ſumpti, & vniti ad punctum
<
lb
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E, ad quod duo
<
expan
abbr
="
quoq;
">quoque</
expan
>
mucrones angulorum
<
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<
figure
id
="
id.009.01.040.3.jpg
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place
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text
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xlink:href
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number
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10
"/>
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rectorum coeunt, congruent omnino duobus
<
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prædictis angulis rectis, ſiue duobus illis mu
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cronibus angulorum rectorum, ſiue conſti
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tuent lineam rectam F E G, ſicuti faciunt
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etiam duo illi anguli recti; ſiue etiam dica
<
lb
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mus, occupabunt idem ſpatium omninò, &
<
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præcisè, quod occupant duo recti: v.g. ſi mucro B, ibi poneretur, faceret
<
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angulum F E H, & ſi ibi iuxta ipſum apponeretur mucro A, faceret angulum
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lb
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H E I. quem ſi deinceps ſubſequetur reliquus angulus C, conſtitueret
<
expan
abbr
="
reli-quũ
">reli
<
lb
/>
quum</
expan
>
angulum I E G. iam, vt vides, illi tres anguli ad E, tranſlati, ſunt æqua
<
lb
/>
les duobus rectis ad E, pariter conſtitutis, cum illi tres fiant partes duorum
<
lb
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rectorúm, vel quia occupant idem ſpatium, vel eandem lineam rectam F E G,
<
lb
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conſtituant. </
s
>
<
s
id
="
s.000783
">habet igitur omne triangulum ſiue ęquilaterum, ſiue ſcalenum,
<
lb
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ſiue Iſoſceles mirabilem hanc proprietatem, vt tres anguli, cuiuſuis trian
<
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guli ſint æquales duobus rectis angulis. </
s
>
<
s
id
="
s.000784
">Quam demonſtrationem primi om
<
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nium Pythagorici perfecerunt, vt refert Proclus ad 32. primi Elem. Eucli
<
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des deinde ibidem aliter, quam Pythagorici idem demonſtrauit. </
s
>
<
s
id
="
s.000785
">Quod ſi
<
lb
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quis huius rei
<
expan
abbr
="
experiẽtiam
">experientiam</
expan
>
aliquam velit; etiamſi non exactam (cum æqua
<
lb
/>
litas mathematica non cadat ſub ſenſum, ſed ſola intelligentia percipiatur,
<
lb
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quippe quæ in materia intelligibili, non autem ſenſibili verſatur, & cuius </
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>
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archimedes
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