Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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hæc addenda ſunt. </
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<
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">Reſpondet Ariſt. quæ
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ſito pręcedenti, cur ſcilicet angulus in ſe
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micirculo ſit rectus, qualis eſt in figura
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angulus A C B,
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; cauſam eſſe, quia
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in figura tres lineæ ſunt æquales, duæ ni
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mirum, in quas baſis B A, diuiditur, quæ
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ſunt B D, D A, & tertia, quæ ex medio
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baſis erigitur,
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; D C, cum omnes ſint
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ſemidiametri eiuſdem circuli. </
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<
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">educta
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itaq;
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linea D C, de potentia in actum,
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ſi cuipiam trium harum linearum æqualitas innoteſcat, continuò ei etiam
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manifeſtum erit angulum A C B, in ſemicirculo, eſſe rectum. </
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<
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parent duo iſoſcelia B D C, A D C, quorum anguli ad baſes B C, A C, ſunt
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æquales inuicem; & anguli duo ad D, ſunt dupli duorum
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angulorũ
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A C D,
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D C B, ex quibus conflatur totus angulus A C B, ergo duo anguli ad D, ſunt
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dupli anguli B C A, ſed duo anguli ad D, ſunt æquales duobus rectis, ergo
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duo recti ſunt dupli anguli A C B, ergo angulus B C A, eſt dimidium duo
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rum rectorum. </
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<
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">cum autem omnes recti ſint æquales, conſectarium eſt dimi
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dium duorum rectorum eſſe angulum rectum. </
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<
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">patet igitur, qua ratione ex
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ductu linearum prædictarum actu, manifeſtum fiat angulum in ſemicirculo
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A C B, eſſe rectum. </
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<
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">ne mireris ſi vulgatam tranſlationem antiquam non
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ſum ſequutus, indigebat enim correctione, quam iuxta græcum exem
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plar adhibui.</
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223</
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<
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">Tex. 22. (
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Vt puta ſi triangulum non putet mutari, non opinabitur modo duos
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rectos habere, modo non, mutaretur enim
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) quia nimirum huius habemus ſcien
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tiam per demonſtrationem 32. primi Elementorum. </
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<
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">quomodo autem tri
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angulus habeat duos rectos, ideſt tres angulos æquales duobus rectis angu
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lis, explicatum eſt primo Priorum, ſecto 3. cap. 1.</
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224</
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<
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">Ibidem (
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Verum aliquid quidem, aliquid verò non, vt puta parem numerum
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primum nullum eſſe; aut quoſdam quidem, quoſdam verò non
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) definitione 11.
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7. Elem. ſic numerus ille, qui à Mathematicis dicitur primus, definitur, pri
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mus numerus eſt, quem vnitas ſola metitur, vnde patet inter numeros pa
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res ſolum binarium eſſe primum, cum ipſum ſola vnitas bis replicata men
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ſuraret. </
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<
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">quaternarium autem, ſenarium, &c. </
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<
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">pares, non eſſe primos, cum
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eos non ſola vnitas, ſed alius numerus metiatur: quaternarium enim bina
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rius bis replicatus menſurat: ſenarium menſurat & binarius, & ternarius:
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quare verum erit exiſtimare inter pares numeros aliquos eſſe primos, ideſt
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binarium, aliquos verò non, ideſt cæteros pares vltra binarium.</
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Ex Decimo Metaphyſicæ.
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225</
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<
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">Tex. 4. (
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Ac etiam motum ſimplici, & velociſſimo motu menſurant, mi
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nimum enim tempus hic habet. </
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<
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cipium, & menſura eſt. </
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<
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ponunt, ad quem cæteros iudicant
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) intelligit motum diurnum, quam
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primo cœlo, ſeu mobili aſcribunt, hic enim velociſſimus eſt omnium reli</
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