Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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41
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æqualitas nullum diſcrimen, quantumuis minimum admittat, quod ſenſui
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vitare ob ſui imperfectionem non licet: vnde inter eæ, quæ mathematicè
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ſunt æqualia, nullus intellectus aliquam valeat reperire differentiam) ſumat
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inquam triangulum quodpiam materiale, vt ex charta, quantum fieri po
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teſt perfectum, deinde ducat lineam vnam perpendicularem ſuper aliam,
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quæ ſcilicet faciat, cum illa duos angulos rectos. </
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<
s
id
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s.000786
">poſtea abſcindat tres an
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gulos trianguli materialis,
<
expan
abbr
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eosq́
">eosque</
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; ita ſimul componat, vt mucrones illorum
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ſint vniti, & contigui ad punctum lineæ perpendicularis cum altera, vti eſt
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in ſuperiori figura punctum E; & illicò apparebit tres illos angulos mate
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riales obtegere adæquatè totum illud ſpatium duorum rectorum, quos per
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pendicularis conſtituit. </
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<
s
id
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s.000787
">Hoc autem experiri poteris in diuerſis admodum
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triangulis Scalenis, Rectangulis, Iſoſcelibus, Aequilateris, &c. </
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<
s
id
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s.000788
">non ſine de
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lectatione, atque hic eſt ſenſus illorum verborum, omnis triangulus habet
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tres ęquales duobus rectis. </
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<
s
id
="
s.000789
">Abſtineo à demonſtrationibus geometricis, quo
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niam ij, qui Mathematicis ſunt imbuti, noſtra hac opera parum indigent.
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</
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<
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id
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s.000790
">ſi quis tamen volet, conſulat 32. primi Elem. </
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<
s
id
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s.000791
">Ex hac igitur declaratione
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licet cognoſcere nonnullos ageometretos locum hunc, & ſimiles ſubſequen
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tes non ſatis intelligere, dicentes, nihil aliud verba illa Ariſt. velle ſignifi
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care, quàm omnem triangulum habere tres angulos, quod inquiunt, notiſ
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ſimum eſt. </
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<
s
id
="
s.000792
">Sed ſi incidant in ſequentia; æquales duobus rectis, tunc, cum
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hæc non intelligant, abſtinent etiam à priorum declaratione, quibus præ
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miſſis facile eſt Ariſt. textum percipere. </
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<
s
id
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s.000793
">ſit A, duo recti, ideſt, duo anguli
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recti ſint paſſio demonſtranda, in quo B, triangulus, in quo C, æquicrus. </
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<
s
id
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s.000794
">ipſi
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itaque C, ideſt triangulo æquicruſi, ineſt A, ſcilicet duo recti, hoc eſt, ineſt
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æquicruſi hæc, paſſio habere tres angulos æquales duobus rectis per B, ideſt
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per
<
expan
abbr
="
triangulũ
">triangulum</
expan
>
vniuerſale, quia hæc proprietas eſt trianguli propria, &
<
expan
abbr
="
cõpe-tit
">compe
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tit</
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>
æquicruſi, non vt æquicrus eſt, ſed, vt triangulum eſt; quare B, non erit
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medium ipſius A, quia prædicta paſſio. </
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>
<
s
id
="
s.000795
">A, non competit triangulo B, per
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aliud, ſed per ſe, de eo enim primo, & per ſe demonſtratur in 32. primi Elem.
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optimè Aegydius, & Niphus in hunc locum.</
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11</
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<
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">Ex eodem cap.
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(Non oportet autem exiſtimare penes id, quod exponimus, ali
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quid accidere abſurdum, nihil enim vtimur eo, quod eſt hoc aliquid eſſe. </
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<
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id
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s.000799
">ſed ſicut
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Geometra pedalem, & rectam hanc, & ſine latitudine dicit, quæ non ſunt. </
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<
s
id
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s.000800
">verum
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non ſic vtitur, tanquam ex his ratiocinans)
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italics
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Quoniam Ariſt. in exemplis affert
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pro rebus characteres, A, B, C, poſſet quiſpiam ſuſpicari aliquod propterea
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abſurdum accidere: cui ſuſpicioni Ariſt. reſpondet, dicens, nihil inde abſur
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di accidere poſſe, quoniam ipſe vtitur hiſce literis,
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expan
abbr
="
nõ
">non</
expan
>
quatenus literæ ſunt,
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ſed quatenus rerum vicem, pro quibus exponuntur, gerunt: quemadmodum
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etiam Geometræ faciunt, qui lineam, quæ pedalis non eſt, pedalem, & quæ
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non eſt recta, rectam; & quæ lata eſt, non latam, ſupponunt, & tamen nihil
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inde abſurdi contingit. </
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<
s
id
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s.000801
">Ex quibus intelligimus per lineas illas ſenſibiles, &
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phyſicas, quas Geometræ in ſuis figuris ducunt, intelligendas eſſe lineas ve
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rè Mathematicas omni latitudine carentes; vtitur enim inquit Ariſt. Geo
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metra lineis phyſicis, non tanquam phyſicis, nec de eis tanquam de phyſicis
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lineis ratiocinatur, ſed ijs vtitur tanquam verè mathematicis. </
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<
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id
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">idem dicen
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dum eſt de ſuperficiebus, necnon de corporibus, quæ ijdem Geometræ de
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ſcribunt, vt per ea, de verè mathematicis diſcurrant.</
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