Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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133
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ſed figuræ rectilineæ illius, quæ dicitur Altera parte longior, qualis eſt præ
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ſens figura A B C D, cuius quadrandæ ratio eſt huiuſmodi. </
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<
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">per 13. 6. inue
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niatur recta linea media proportionalis inter
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duo latera figuræ A B, B C,
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eaq́
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; ſit B D, in ſe
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quenti figura. </
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<
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id
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">eſſe autem mediam proportio
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nalem nihil aliud eſt quam ita eſſe A B, ad B D,
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ſicut B D, ad B C.
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diciturq́
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; media proportio
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nalis, quia in hac habitudine medium locum obtinet. </
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<
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id
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">quadratum autem li
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neæ B D, æquale eſt rectangulo dato A B C D, per 17.6. Inuentio porrò hu
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ius mediæ proportionalis, quia facilis eſt, & ſcitu iucunda, eam ſic habeto.
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accipe duo latera A B, & B C,
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quadrãdi
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rectan
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guli,
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eaq́
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; in directum conſtitue, vt vnicam re
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ctam conſtituant A C, vt apparet in figura; de
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inde diuiſa tota A C, bifariam in E, facto cen
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tro in E, deſcribe ſemicirculum ſuper lineam
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A C, demum à puncto B, in quo duo latera con
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iunguntur, erigatur linea perpendicularis
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vſq;
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ad periphæriam, quæ ſit B D. hæc enim B D, eſt media proportionalis inter
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latera A B, B D, quam nimirum habitudinem habet A B, ad B D, eam quo
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que obtinet B D, ad B C. </
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<
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">Quadratum igitur huius B D, hoc eſt quadratum,
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cuius quatuor latera ſint æqualia lineæ B D, quale eſt præſens, æquale erit
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dato ſuperiori rectangulo A B C D,
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atq;
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hoc modo per
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acta erit quadratio, ſeu tetragoniſmus dati quadrilateri
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A B C D. </
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<
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">Vides igitur, qua ratione quadratum conſti
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tuatur æquale dato quadrilatero; & qua rationem inuen
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tio illius mediæ proportionalis ſit cauſa quadraturæ re
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ctanguli, & proinde ſi quis dicat quadrationem hanc eſſe
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effectionem rectanguli æquilateri, ideſt quadrati, æqualis dato quadrilate
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ro, hic definitionem formalem ſolum afferet: quæ definitio, vt dixit in Lo
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gicis, eſt inſtar concluſionis. </
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<
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">ſi quis verò dicat tetragoniſmum hunc quadri
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lateri dati eſſe mediæ prædictæ inuentionem cauſalem afferet definitionem,
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cum rei cauſam dicat. </
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<
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id
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">Aduerte 10. Grammaticum immeritò accuſare Ale
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xandrum, quod dicat quadrationem hanc per inuentionem mediæ propor
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tionalis tradi in 2. Elem. nam verè in 14. 2. traditur talis inuentio, quam
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uis enim ibi nulla fiat expreſſa mentio huiuſmodi mediæ, in ipſa tamen ea
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reperitur, ac per eam figuræ rectilineæ quadrantur: quod patet ex figura
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14. prædictæ, quæ eadem eſt cum figura 13. 6. qua docemur prædictam in
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uentionem.</
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186</
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<
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">Tex. 86.
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(Acutum mouet ſenſum in tempore pauco multùm: graue autem in
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multo parùm; non igitur velox eſt acutum, graue autem tardum, ed ſit illius qui
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dem propter velocitatem motus huiuſmodi, huius autem propter tarditatem)
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vide
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quæ de hac re primo topic. </
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<
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id
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">cap. 13. dicta ſunt, illa enim omnia in hunc lo
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cum quadrant. </
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<
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">Verum occurrit illa dubitatio; quod cum Ariſt. ibi dicat
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(Vox acuta quidem velox)
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hic autem
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(Non igitur velox eſt acutum
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) repugnan
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tia dicere videtur. </
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<
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">cui dubitationi ſic occurrendum; vt dicamus ibi Philo
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ſophum dicere vocem acutam eſſe velocem, quatenus acumen vocis oritur </
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