Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER III.
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ctangula triplicata, rectangulum autem ſub, DR, & </
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ta ex, {1/2}, RM, &</
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<
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<
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M, & </
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<
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<
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xml:space
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">, MA, triplicetur rectangulum ſub, DR, &</
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<
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{1/2}, RM, fit rectangulum ſub tripla, DR, & </
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datur rectangulum ſub, MR, &</
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<
s
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">, {1/2}, RM, fit rectangulum ſub com-
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poſita ex tripla, RD, & </
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<
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<
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dupla, RD, & </
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<
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<
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xml:space
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huc ſub, DR, MA, & </
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<
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<
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">, {1/2}, MA, triplicanda, quod
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ſic fiet; </
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<
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">rectangulum ſub, DR, MA, æquatur rectangulo ſub dupla,
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DR, &</
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<
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">, {1/2}, MA, cui ſi addatur rectangulum ſub, {1/2}, MA, & </
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<
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MR, fiet rectangulum ſub, {1/2}, MA, & </
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<
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dupla, RD, .</
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<
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rectangulum ſub compoſita ex, MD, DR, & </
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A, quod ſimul cum rectangulo ſub compoſita ex, MD, & </
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R, & </
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<
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">ſub, {1/2}, MR, ad rectangulum, DRA, conuertendo, habe-
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bit eandem rationem, quam omnia quadrata portionis, ICFS, ad
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omnia quadrata trianguli, CMF; </
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<
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">Ex 9. & @.
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Coroll.
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22. lib. 2@</
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ctum parallelogrammum, & </
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<
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">triangulum, ſint quidem in eadem baſi
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cum portione, ſed non circa eundem axim, vel diametrum cum ea-
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dem portione, vt ſupra patere poteſt in antecedentibus, quod erat
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oſtendendum.</
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<
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<
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">IN eadem antecedentis figura ſi parallelogrammum ſit
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quidem in eadem altitudine cum portione, ſed in baſi æ-
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quali ſecundæ diametro; </
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<
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">omnia quadrata dicti parallelo-
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grammiad omnia quadrata dictę portionis erunt, vt quadra-
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tum dimidijaxis, vel diametri eorumdem ad eadem conſe-
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quentia rectangula, retenta eadem regula.</
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<
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0223-01
"/>
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& </
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<
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lis ſecundæ diametro, quæ ſit, EH, &</
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VR, æqualis, RX, & </
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<
s
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">in, VX, baſi ſit
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conſtructum parallelogrammum, GX,
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in altitudine eadem cum portione, ICF
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S, ſit etiam circa eandem axim, vel dia-
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metrum, MR, cum portione, IECFH
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S: </
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<
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">Omnia ergo quadrata parallelogram-
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mi, GR, ad omnia quadrata parallelogrammi, BR, (regula, CF,)
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