Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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nientia, eaſdemq; </
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axium, vel diametrorum, ſumpto pro regula. </
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<
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drata deſcripti parallelogrammi ad omnia quadrata figurę
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duobus oppoſitis lateribus parallelogrammi regulæ æqui-
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diſtantibus, & </
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ctiones coniugatas, & </
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coniugatis ſectionibus, comprehenſæ, demptis ab ijſdem
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omnibus quadratis oppoſitarum hyperbolarum, quarum
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latus tranſuerſum non fuit ſumptum pro regula, erunt vt
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cubus dimidij lateris parallelogrammi regulæ non æqui-
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diſtantis, ad duo parallelepipeda, quorum vnum contine-
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tur ſub dimidio exceſſus dicti lateris ſuper baſim hyperbo-
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læ, quam idem latus abſcindit, & </
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<
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eiuſdem lateris, aliud verò ſub dimidio baſis dictæ hyper-
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bolæ, & </
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lateristranſuerſi, quod non eſt regula, ab his tamen dem-
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pto paralleledipedo ſub dimidio lateris tranſuerſi, quod
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non eſt regu a, & </
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<
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trius hyperbolarum, quarum eſt latus tranſuerſum, vna cũ
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{1/3}. </
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BFH, quarum communes aſymptoti indefinitè cum ſectionibus
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fint producti, qui ſint, TSV, RSX, ſint autem earum axes, vel dia-
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metri coniugatæ, EO, FI, quarum alterutra ſit ſumpta pro regu-
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la, vt, FI, ſit vlterius deſcriptum parallelogrammum, TV, latera
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habens æquidiſtantia ipſis, EO, FI, & </
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uenientia in punctis, T, R, V, X, ipſaſq; </
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vt, quæ inter ſectiones manent, fiuntq; </
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PQ, NM, HB, AC, quorum æquidiſtantia erunt æqualia. </
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ergo omnia quadrata parallelogrammi, TV, ad omnia quadrata
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figuræ inte, TX, RV, TB, HR, VQ, PX, & </
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cõcluſæ, demptis ab ijſdë omnibus quadratis oppoſitarum hyper-
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bolarum, AEC, MON, eſſe vt cubus dimidij, XV, ad parallelepi-
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pedum ſub, QV, & </
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lelepipedo ſub dimidio, PQ, & </
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dem dimidij, PQ, & </
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lepipedo ſub, SO, & </
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