Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER III.
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ibi oſtenſum eſt, ſumpta regula, DP, omnia quadrata portionis, D
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EP, ad omnia quadrata parallelogrammi, FP, eſſe vt compoſita ex
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ſexta parte, EB, & </
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<
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">dimidia, BR, ad ipſam, BR, oſtenſum etiam
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eſt ſolidum ſimilare genitum ex portione, DEP, ad ſolidum ſibi ſi-
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milare genitum ex parallelogrammo, FP, eſſe vt compoſita ex ſex-
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ta parte, EB, & </
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<
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<
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xml:space
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">Cum verò oſten-
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ſum eſt omnia quadrata portionis, EDP, ad omnia quadrata trian-
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guli, DEP, eſſe vt compoſita ex dimidia totius, ER, & </
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<
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">ipſa, BR,
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ad eandem, BR; </
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<
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">pariter oſtenſum eſt ſolidum ſimilare genitum ex
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portione, EDP, ad ſibi ſimilare genitum ex triangulo, DEP, iux-
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ta eaſdem regulas eſſe, vt compoſita ex dimidia totius, ER, & </
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<
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BR, ad eandem, BR.</
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<
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">Cum verò in Corollario eiuſdem Theorem. </
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<
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">collectum eſt, omnia
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quadrata parallelogrammi, FP, eſſe ſexquialtera omnium quadra-
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torum portionis, DEP, (ſi, DP, per centrum, A, tranſeat) hæc
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verò eſſe dupla omnium quadratorum trianguli, DEP; </
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<
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etiam ſolidum ſimilare genitum ex parallelogrammo, FP, ſexquial-
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terum erit ſolidi ſibi ſimilaris geniti ex portione, DEP, iuxta ean-
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dem regulam, DP, hoc verò erit duplum ſolidi ſibi ſimilaris geniti
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ex triangulo, DEP, iuxta eandem regulam, DP.</
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_lib. 1._</
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planis, iuxta datas regulas, totuplicia ſunt, quotuplices ſunt fi-
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guræ ſimiles, quæ dicuntur, omnes figuræ ſimiles duarum genitri-
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cium figurarum, cum eiſdem regulis aſſu
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mpta, iuxta quas dicta ſolida
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ſimilaria genita dicuntur, figurarum autem variationes nullo dato nu-
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mero clauduntur, ideò nec horum ſimilarium ſolidorum variationes vl-
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lo dato coarctantur numero, vnde euidentiſſimè apparet banc demon.
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">ſtrandi methodum, ipſamque demonſtrationem, infinitè (vt ita dicam)
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locupletem eſſe; </
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expendendæ ſunt ipſæ figuræ, quæ dicuntur (omnes figuræ ſimiles, &</
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patet igitur ex alibi à me o
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ſtenſis, ſi figuræ aſſumptæ ſint omnes figuræ ſi-
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miles parall@logrammi, quod tunc i
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ſtæ erunt omnia plana cylindrici; </
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verò illæ ſint omnes figuræ ſimiles trianguli (intellige in parallelogram-
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mo, & </
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">triangulo vnum laterum pro regula) illæ erunt omnia plana Co-
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nici; </
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erit cylindricus rectus, ſcalenus autem niſi ſit rectangulum, vel figuræ
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non eidem erecta; </
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">ex quo babes, qualeſcunque figuras intellexeris eſſe
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eas, quæ dicuntur omnes figuræ ſimiles parallelogrammi, FP, regula,
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DP, veltrianguli, EDP, regula eadem, ſolidum genitum ex </
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