Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER V.
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nientia, eaſdemq; </
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<
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xml:id
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echoid-s10587
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xml:space
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">oppoſitas ſectiones diuidentia’ alterutro
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axium, vel diametrorum, ſumpto pro regula. </
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<
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xml:space
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">Omnia qua-
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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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<
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echoid-s10589
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xml:space
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">reliquorum laterum portionibus inter ſe-
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ctiones coniugatas, & </
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<
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">prædicta latera concluſis, & </
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<
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xml:id
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xml:space
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">ipſis
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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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xml:id
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xml:space
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">ſub quadrato dimidij
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eiuſdem lateris, aliud verò ſub dimidio baſis dictæ hyper-
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bolæ, & </
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<
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xml:space
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">ſub @. </
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<
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xml:space
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">quadrati eiuſdem, cum quadrato dimidij
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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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<
s
xml:id
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echoid-s10595
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xml:space
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">ſub quadrato axis, vel diametri alteru-
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trius hyperbolarum, quarum eſt latus tranſuerſum, vna cũ
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{1/3}. </
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<
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xml:id
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xml:space
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">cubi eiuſdem axis, vel diametri.</
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<
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">Sintigitur expoſitæ ſectiones coniugatæ, AEC, MON, PIQ,
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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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<
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xml:space
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">in aſymptotis, TV, XR, cõ-
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uenientia in punctis, T, R, V, X, ipſaſq; </
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<
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xml:space
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">ſectiones diuidentia, ita
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vt, quæ inter ſectiones manent, fiuntq; </
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<
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xml:space
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">hyperbolarum baſes ſint,
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PQ, NM, HB, AC, quorum æquidiſtantia erunt æqualia. </
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<
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">Dico
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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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<
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xml:space
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preserve
">ſectiones, BFH, PIQ,
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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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<
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xml:space
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">quadrato dimidij lateris, XV, vna cum paral-
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lelepipedo ſub dimidio, PQ, & </
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<
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">ſub compoſito ex {1/3}. </
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<
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xml:space
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">quadrati eiuſ-
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dem dimidij, PQ, & </
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<
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">quadrato, SO, ab his tamen dempto paralle-
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lepipedo ſub, SO, & </
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<
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