Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER I.
"/>
uX, oſtenderemus figuras his ductis comprehenſas, quales fuerunt,
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LPIK, YdXu, eſſe ſimiles, ex quo propoſitum quoque noſtrum
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haberemus. </
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<
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xml:space
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">Similiter ſi anguli ſolidi, Q, f, pluribus, quam tribus
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angulis planis contineantur, currit tamen demonſtratio, cum trian-
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<
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xml:space
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">Ex Lem.
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4. & 1.</
note
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gula, GOo, 8fs, licet non ſint in ambitu ſolidorum ſint tamen ſi-
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milia, & </
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<
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">ęquè ad eandem partem inclinata figuris, cum quibus con-
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currunt, etenim ex. </
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<
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">gr. </
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<
s
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xml:space
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">pyramides, SGOo, p8fs, ſi eorum latera
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iungerentur, ſimiles eſſent, quapropter ipſius demonſtrationis vis
<
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non eneruatur. </
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<
s
xml:id
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echoid-s1721
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xml:space
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">Similiter ſi, oOS, sfp, non eſſent triangula, ſed
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aliæ quæcumque figuræ ſimiles, pro, oS, sp, acceptis lateribus ip-
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ſis, Oo, fs, adiuncta, os, conterminantibus, & </
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<
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xml:space
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">planis ad hæc la-
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tera pariter terminantibus, eodem modo demonſtratio abſoluere-
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tur: </
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<
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xml:space
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">hæc omnia autem ſingillatim proſequi nimis longum, ac ſche-
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matibus rem aperire, res tricis plena eſſet, quapropter Lectoris in-
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duſtriæ hoc relinquo, ſi enim ea rectè percepcrit, quę ſuperius expli-
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cata ſunt, circa huius veritatem minimè hæſitabit, infinita autem ſi-
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milium ſolidorum planis contentorum varietas efficit, vt ægrè ip-
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ſius demonſtrationis vniuerſalitatem oculis ſubijcere poſſim, quod
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Lector æqui, bonique faciat, hæc verò oſtendenda proponebantur.</
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<
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xml:space
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<
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">ſimilium ſolidarum figura-
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rum, ſequitur, & </
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lidorum.</
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">figuris, ſint adhuc ſimilia ſolida
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iuxta Euclidem ipſa, AGS, T8p. </
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<
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xml:space
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">Dico eadem eſſe etiam ſimilia
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iuxta definit. </
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<
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<
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xml:space
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">huius, quam de ſimilibus ſolidis generaliter attuli.
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</
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<
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xml:space
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">Sint autem ducta eadem oppoſita tangentia plana, vt ibi, ita vt duę
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ſimiles figurę, GFSO, f8 & </
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<
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xml:space
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">p, ſint plana contactuum ex vna par-
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te, ex alia verò ſint plana tangentia, AC, TR, captis autem alijs
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duabus ſimilibus figuris cum baſibus concurrentibus, ipſis nempè, O
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So, fps, illarum plana extendantur, ita vt ſecent oppoſita tangen-
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tia plana, in rectis nempè, BC, OD; </
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<
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<
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xml:space
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">extenſis autem vl-
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terius planis, GOo, 8fs, quęnunc ſint in ambitibus ſolidorum ipſa
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ſecent oppoſita tangentia plana in rectis, AB, TQ; </
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plana figurarum, OSO, fps, producta in rectis, BO, Qf, ſecen-
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tur verò hęc ſolida duobus planis oppoſitis tangentibus parallelis vt-
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cumque, & </
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<
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MP, YVZd, iſtæ ergo ſimiles erunt, & </
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