Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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xml:space
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">_Q_Via verò oppoſitæ tangentes, AH, DF, MN, RQ, ductæ ſunt
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vtcumque, angulos tamen æquales ad eandem partem cum homo-
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logis lateribus continentes, ideò quaſcumq; </
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<
s
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xml:space
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">duxerimus oppoſitas
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tangentes in figuris rectilineis ſimilibus iuxta Euclidem, dummodo fa-
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ciant angulos æquales ad eandem partem cum lateribus homologis, ea-
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ſdem eſſe regulas homologarum ſimilium figurarum poterit probari.</
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<
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xml:space
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<
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xml:space
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">POſita infraſcripta definitione ſimilium portionum ſectio-
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num coni, illi adiuncti, quod infra dicetur, ſequitur
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pro ipſis etiam mea definitio generalis ſimilium planarum fi-
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gurarum. </
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<
s
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xml:space
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">Hoc autem dico pro ſpatijs ſub ipſis ſectionibus,
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& </
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<
s
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xml:space
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">rectis lineis contentis, non autem pro ipſis tanquam lineis,
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licet crediderim Apolloniũ ipſarum ſimilium ſectionum tan-
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quam linearum, non autem figurarum, quę fiunt ab ipſis, ſi-
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militudinem attendiſſe, ego verò ipſam recipio tanquam ip-
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ſarum figurarum ſimilitudini congruam, dum illi adiungitur,
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quod in ipſa Propoſ. </
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<
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">SImiles portiones ſectionum coni ſunt, in quarum ſingulis ductis
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lineis baſi parallelis numero æqualibus, ſunt ipſæ parallelæ, & </
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baſes ad abſciſſas diametrorum partes ſumptas à verticibus, in ijſdem
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rationibus, tumabſciſſæ ipſæ ad abſciſſas: </
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corum, vt refert Eutocius.</
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<
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">Sint ſimiles portiones ſectionum coni, DAF, QRK, in baſibus,
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DF, QK, quarum diametri ſint ipſæ, AE, RG, ſecentur autem
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ſimiliter ipſæ diametri in punctis, N, O; </
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">& </
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A, vt, Q K, ad, G R, &</
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<
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<
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M, ad, N A, vt, S P, ad, V R; </
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<
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xml:space
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">has igitur Apollonius in ſupradicta
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definitione ſimiles vocat, mihi autem hoc opus eſt illi adiungere.</
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<
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</
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">diametris, ad eandem partem contenti ſint
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æquales, vt angulus, A E D, ipſi, R G Q, ſi.</
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poſſet contingere eſſe baſes, D F, Q K, æquales, & </
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G, in quo caſu tot figuras ſimiles, & </
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