Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

Table of contents

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[421.] THEOREMA X. PROPOS. XI.
Page: 318 (298)
[422.] COROLLARIV M.
Page: 320 (300)
[423.] THEOREMA XI. PROPOS. XII.
Page: 320 (300)
[424.] THEOREMA XII. PROPOS. XIII.
Page: 321 (301)
[425.] THEOREMA XIII. PROPOS. XIV.
Page: 323 (303)
[426.] THEOREMA XIV. PROPOS. XV.
Page: 324 (304)
[427.] THEOREMA XV. PROPOS. XVI.
Page: 325 (305)
[428.] THEOREMA XVI. PROPOS. XVII.
Page: 325 (305)
[429.] COROLLARIVM.
Page: 327 (307)
[430.] THEOREMA XVII. PROPOS. XVIII.
Page: 327 (307)
[431.] THEOREMA XVIII. PROPOS. XIX.
Page: 328 (308)
[432.] A. COROLL. SECTIO I.
Page: 328 (308)
[433.] B. SECTIO II.
Page: 329 (309)
[434.] C. SECTIO III.
Page: 329 (309)
[435.] D. SECTIO IV.
Page: 329 (309)
[436.] E. SECTIO V.
Page: 329 (309)
[437.] SCHOLIV M.
Page: 330 (310)
[438.] THEOREMA XIX. PROPOS. XX.
Page: 330 (310)
[439.] COROLLARIVM.
Page: 331 (311)
[440.] THEOREMA XX. PROPOS. XXI.
Page: 331 (311)
[441.] THEOREMA XXI. PROPOS. XXII.
Page: 332 (312)
[442.] THEOREMA XXII. PROPOS. XXIII.
Page: 333 (313)
[443.] COROLLARIVM.
Page: 334 (314)
[444.] THEOREMA XXIII. PROPOS. XXIV.
Page: 334 (314)
[445.] PROBLEMA II. PROPOS. XXV.
Page: 335 (315)
[446.] COROLLARIVM.
Page: 336 (316)
[447.] THEOREMA XXIV. PROPOS. XXVI.
Page: 337 (317)
[448.] THEOREMA XXV. PROPOS. XXVII.
Page: 337 (317)
[449.] COROLLARIVM I.
Page: 339 (319)
[450.] COROLLARIVM II.
Page: 339 (319)
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            nientia, eaſdemq; </s>
            <s xml:id="echoid-s10587" xml:space="preserve">oppoſitas ſectiones diuidentia’ alterutro
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            axium, vel diametrorum, ſumpto pro regula. </s>
            <s xml:id="echoid-s10588" xml:space="preserve">Omnia qua-
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            drata deſcripti parallelogrammi ad omnia quadrata figurę
              <lb/>
            duobus oppoſitis lateribus parallelogrammi regulæ æqui-
              <lb/>
            diſtantibus, & </s>
            <s xml:id="echoid-s10589" xml:space="preserve">reliquorum laterum portionibus inter ſe-
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            ctiones coniugatas, & </s>
            <s xml:id="echoid-s10590" xml:space="preserve">prædicta latera concluſis, & </s>
            <s xml:id="echoid-s10591" xml:space="preserve">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
              <lb/>
            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, & </s>
            <s xml:id="echoid-s10592" xml:space="preserve">ſub quadrato dimidij
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            eiuſdem lateris, aliud verò ſub dimidio baſis dictæ hyper-
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            bolæ, & </s>
            <s xml:id="echoid-s10593" xml:space="preserve">ſub @. </s>
            <s xml:id="echoid-s10594" xml:space="preserve">quadrati eiuſdem, cum quadrato dimidij
              <lb/>
            lateristranſuerſi, quod non eſt regula, ab his tamen dem-
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            pto paralleledipedo ſub dimidio lateris tranſuerſi, quod
              <lb/>
            non eſt regu a, & </s>
            <s xml:id="echoid-s10595" xml:space="preserve">ſub quadrato axis, vel diametri alteru-
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            trius hyperbolarum, quarum eſt latus tranſuerſum, vna cũ
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            {1/3}. </s>
            <s xml:id="echoid-s10596" xml:space="preserve">cubi eiuſdem axis, vel diametri.</s>
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            <s xml:id="echoid-s10598" xml:space="preserve">Sintigitur expoſitæ ſectiones coniugatæ, AEC, MON, PIQ,
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            BFH, quarum communes aſymptoti indefinitè cum ſectionibus
              <lb/>
            fint producti, qui ſint, TSV, RSX, ſint autem earum axes, vel dia-
              <lb/>
            metri coniugatæ, EO, FI, quarum alterutra ſit ſumpta pro regu-
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            la, vt, FI, ſit vlterius deſcriptum parallelogrammum, TV, latera
              <lb/>
            habens æquidiſtantia ipſis, EO, FI, & </s>
            <s xml:id="echoid-s10599" xml:space="preserve">in aſymptotis, TV, XR, cõ-
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            uenientia in punctis, T, R, V, X, ipſaſq; </s>
            <s xml:id="echoid-s10600" xml:space="preserve">ſectiones diuidentia, ita
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            vt, quæ inter ſectiones manent, fiuntq; </s>
            <s xml:id="echoid-s10601" xml:space="preserve">hyperbolarum baſes ſint,
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            PQ, NM, HB, AC, quorum æquidiſtantia erunt æqualia. </s>
            <s xml:id="echoid-s10602" xml:space="preserve">Dico
              <lb/>
            ergo omnia quadrata parallelogrammi, TV, ad omnia quadrata
              <lb/>
            figuræ inte, TX, RV, TB, HR, VQ, PX, & </s>
            <s xml:id="echoid-s10603" xml:space="preserve">ſectiones, BFH, PIQ,
              <lb/>
            cõcluſæ, demptis ab ijſdë omnibus quadratis oppoſitarum hyper-
              <lb/>
            bolarum, AEC, MON, eſſe vt cubus dimidij, XV, ad parallelepi-
              <lb/>
            pedum ſub, QV, & </s>
            <s xml:id="echoid-s10604" xml:space="preserve">quadrato dimidij lateris, XV, vna cum paral-
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            lelepipedo ſub dimidio, PQ, & </s>
            <s xml:id="echoid-s10605" xml:space="preserve">ſub compoſito ex {1/3}. </s>
            <s xml:id="echoid-s10606" xml:space="preserve">quadrati eiuſ-
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            dem dimidij, PQ, & </s>
            <s xml:id="echoid-s10607" xml:space="preserve">quadrato, SO, ab his tamen dempto paralle-
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            lepipedo ſub, SO, & </s>
            <s xml:id="echoid-s10608" xml:space="preserve">quadrato reliquæ ad medietatem, XV, </s>
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