Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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48
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est declarante, quemadmodum rectum ineſt lineæ, & circulare: & impar, & par
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numero, & primum, & compoſitum, & æquilaterum, & altera parte longius. &
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abbr
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oĩbus
">omnibus</
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bis inſunt in oratione, quid eſt
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abbr
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declarãte
">declarante</
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, ibi quidem linea, hic vero numerus)
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quia locus hic benè exponitur à Toleto, & melius etiam à Conymbr. </
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<
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id
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s.000898
">addam
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tantummodo quædam, quæ ad perfectam eius intelligentiam deſiderantur.
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</
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<
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id
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s.000899
">Sciendum igitur primò, nuſquam ab Euclide definiri rectum, circulare,
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impar, par, primum, compoſitum, æquilaterum, nec altera parte longius:
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<
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abbr
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verũ
">verum</
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ab ipſo in definitionibus primi definiri lineam rectam, non tamen cir
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cularem expreſsè. </
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<
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id
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s.000900
">in definitionibus deinde ſeptimi definiri
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abbr
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numerũ
">numerum</
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parem,
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& imparem, item numerum primum, & compoſitum, & æquilaterum, & al
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tera parte longiorem. </
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<
s
id
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s.000901
">ex quibus definitionibus poſſunt erui definitiones re
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cti, circularis, imparis, & cæterorum, quorum hic Ariſtoteles meminit.
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</
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<
s
id
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s.000902
">Cæterum Euclides definitione 11. ſeptimi, ſic definit numerum primum:
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primus numerus eſt, quem vnitas ſola metitur. </
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<
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id
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s.000903
">numerus autem, vel vnitas
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metiri dicitur alium numerum, quando ſæpius repetita ipſum omnino ad
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æquat, vt ternarius metitur nouenarium, quia ter repetitus ipſum ad vn
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guem explet. </
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>
<
s
id
="
s.000904
">illi igitur numeri dicuntur ab Arithmeticis primi, qui à nullo
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alio, præterquam ab vnitate menſurantur, quales ſunt, 2. 3. 5. 7. &c. </
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<
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id
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s.000905
">Defi
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nitione verò 13. definit numerum compoſitum ſic; compoſitus numerus eſt,
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quem numerus quiſpiam metitur, vt ſenarius erit compoſitus, quia ipſum
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binarius metitur, nam ter repetitus, ipſi perfectè adæquatur.</
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<
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id
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s.000906
">Per æquilaterum, intelligit quadratum, quadratus autem numerus defi
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nitione 18. ſeptimi ſic explicatur: Quadratus numerus eſt, qui ſub duobus
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æqualibus numeris continetur, ideſt, qui fit ex ductu vnius numeri in ſe ip
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ſum, vt ſi ducantur 3. in 3. fient 9. qui continetur ſub duobus
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ternarijs; omnes autem ternarij ſunt æquales. </
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>
<
s
id
="
s.000907
">is autem nu
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merus dicetur quadratus, quia, vt apparet in figura, nouem
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ipſius vnitates poſſunt in plano ita ad inuicem collocari, vt
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referant quadratum; & ſicuti quadratum geometricum ha
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bet latera æqualia, ita etiam quadratum arithmeticum: ſi
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ue numerus quadratus, habet ſua latera æqualia, quot enim vnitates ſunt
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in vno, tot etiam ſunt in reliquis, vt in præſenti ſunt tres vnitates in ſingulis
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lateribus. </
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>
<
s
id
="
s.000908
">pręterea quemadmodum quadratum geometricum reſolui poteſt
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in plura quadrata, ita etiam arithmeticum, vt præſens, qui reſoluitur in
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quatuor quadrata arithmetica. </
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<
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<
expan
abbr
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Neq;
">Neque</
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enim poteſt quilibet numerus, vt opi
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nantur ageometreti, in hunc modum diſponi, ſed ſolum ij, qui producuntur
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ex multiplicatione numeri alicuius in ſe ipſum.</
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<
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id
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s.000910
">Per altera parte longius, intelligit numerum, qui producitur à duobus
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numeris inæqualibus inuicem multiplicatis, qualis eſt
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duodenarius, qui ex ductu trium in quatuor produci
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tur, & refert figuram altera parte longiorem, ſiue, vt
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ait Boetius longilateram, cuius vnum latus eſt maius
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altero, vt in appoſita figura videre licet. </
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<
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id
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ſunt, quæ ex Mathematicis petenda erant, ad huius
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loci intelligentiam.</
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<
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(Per ſe autem, & ſecundum quod ipſum, idem, vt per ſe lineæ inest
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