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

Table of contents

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[251.] COROLLARIVM II.
Page: 186 (166)
[252.] COROLLARIVM III.
Page: 186 (166)
[253.] THEOREMA XXVII. PROPOS. XXVII.
Page: 187 (167)
[254.] THEOREMA XXVIII. PROPOS. XXVIII:
Page: 188 (168)
[255.] COROLLARIVM.
Page: 189 (169)
[256.] THEOREMA XXIX. PROPOS. XXIX.
Page: 190 (170)
[257.] COROLLARIVM.
Page: 190 (170)
[258.] THEOREMA XXX. PROPOS. XXX.
Page: 191 (171)
[259.] COROLLARIVM.
Page: 192 (172)
[260.] THEOREMA XXXI. PROPOS. XXXI.
Page: 193 (173)
[261.] COROLLARIVM.
Page: 194 (174)
[262.] THEOREMA XXXII. PROPOS. XXXII.
Page: 195 (175)
[263.] COROLLARIVM.
Page: 196 (176)
[264.] THEOREMA XXXIII. PROPOS. XXXIII.
Page: 197 (177)
[265.] COROLLARIVM I.
Page: 198 (178)
[266.] COROLLARIVM II.
Page: 199 (179)
[267.] THEOREMA XXXIV. PROPOS. XXXIV.
Page: 199 (179)
[268.] COROLLARIVM I.
Page: 201 (181)
[269.] COROLLARIVM II.
Page: 201 (181)
[270.] COROLLARIVM III.
Page: 201 (181)
[271.] A. COROLLARII IV. GENERALIS. SECTIO I.
Page: 203 (183)
[272.] B. SECTIO II.
Page: 203 (183)
[273.] C. SECTIO III.
Page: 203 (183)
[274.] D. SECTIO IV.
Page: 204 (184)
[275.] E. SECTIO V.
Page: 204 (184)
[276.] F. SECTIO VI.
Page: 204 (184)
[277.] G. SECTIO VII.
Page: 204 (184)
[278.] H. SECTIO VIII.
Page: 204 (184)
[279.] I. SECTIO IX.
Page: 205 (185)
[280.] K. SECTIO X.
Page: 205 (185)
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            neo, TGEOX, eſſe ve, RF, adportion
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            em, SET, ergo ex æquali
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            o nnia quadrata portionis, SMT, cum rectangulis bis ſub eadem,
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            & </s>
            <s xml:id="echoid-s5763" xml:space="preserve">ſub quadrilineo, MTXC, ad omnia quadrata portionis, SET,
              <lb/>
            cum rectangulis bis ſub eadem, & </s>
            <s xml:id="echoid-s5764" xml:space="preserve">ſub quadrilineo, TGEOX,
              <lb/>
            erunt vt portio, SMT, ad portionem, SET, quod oſtendere o-
              <lb/>
            portebat.</s>
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          </p>
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        <div xml:id="echoid-div573" type="section" level="1" n="339">
          <head xml:id="echoid-head356" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s5766" xml:space="preserve">_H_INC patet omnia quadrata parallelogrammorum in eadem al-
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            titudine cum portionibus, vel portionum fruſtibus exiſtentium,
              <lb/>
            vna cum rectangulis bis ſub ijſdem parallelogrammis, & </s>
            <s xml:id="echoid-s5767" xml:space="preserve">reliquis pa-
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            rallelogram nis illis in directum exiſtentibus, ad omnia quadrata por.
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            </s>
            <s xml:id="echoid-s5768" xml:space="preserve">tionum, vel fruſtorum eorundem, ſimul cumrectangulis bis ſub ijſdem,
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            & </s>
            <s xml:id="echoid-s5769" xml:space="preserve">ſub quadrilineis illis in directum iacentibus, veluti fuerunt quadri-
              <lb/>
            lineun, MTXC, TGEOX, eſſe, vt dicta parallelogramma ad di-
              <lb/>
            ctas portiones, vel portionum fruſta; </s>
            <s xml:id="echoid-s5770" xml:space="preserve">quodex prædictis clarè patet; </s>
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            Vnde ex. </s>
            <s xml:id="echoid-s5772" xml:space="preserve">g. </s>
            <s xml:id="echoid-s5773" xml:space="preserve">omnia quadrata, RG, ſimul cum rectangulis bis ſub paral-
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            lelogrammis, RG, GX, ad omnia quadrata fruſti, SBGT, cum re-
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            ctangulis bis ſub, SGBT, & </s>
            <s xml:id="echoid-s5774" xml:space="preserve">quadrilineo, TG, PX, erunt vt paral-
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            lelogrammum, RG, ad fruſtum, SBGT, hoc .</s>
            <s xml:id="echoid-s5775" xml:space="preserve">n. </s>
            <s xml:id="echoid-s5776" xml:space="preserve">pariter oſtendetur,
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            veluti probatum eſt omnia quadrata, HV, ſimul cum rectangulis bis
              <lb/>
            ſub, HV, VC, ad omnia quadrata portionis, SMT, ſimul cum re-
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            ctingulis bis ſub eadem, & </s>
            <s xml:id="echoid-s5777" xml:space="preserve">ſub quadrilineo, MTXC, eſſe vt, HV,
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            ad portionem, SMT, vnde manifeſtum eſt, quod in hoc Corollaris
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            colligitur.</s>
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          <head xml:id="echoid-head357" xml:space="preserve">THEOREMA XX. PROPOS. XXI.</head>
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            <s xml:id="echoid-s5779" xml:space="preserve">SIin circulo, vel ellipſi apteturrecta linea, per cuius ex-
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            trema puncta ducantur duæ rectæ lineæ, quæ ſint (exi-
              <lb/>
            ſtente apta parallela vniaxium, vel diametrorum) paralle-
              <lb/>
            læ ſecundo axi, vel diametro, quæ ſumatur pro regula: </s>
            <s xml:id="echoid-s5780" xml:space="preserve">Re-
              <lb/>
            ctangula ſub portione minori abſciſſa per aptatam, & </s>
            <s xml:id="echoid-s5781" xml:space="preserve">ſub
              <lb/>
            quadrilineo, quodaptata, & </s>
            <s xml:id="echoid-s5782" xml:space="preserve">duabus dictis parallelis vſque
              <lb/>
            ad curuam circuli, vel ellipſis productis, & </s>
            <s xml:id="echoid-s5783" xml:space="preserve">ab ijſdem inclu-
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            ſa curua comprehenditur, in circulo, erunt æqualia rectan-
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            gulis ſub duobus triangulis per diametrum quadrati, vel
              <lb/>
            rhombi (& </s>
            <s xml:id="echoid-s5784" xml:space="preserve">hoc in ellipſicum diametri coniugatę ſe obliquę
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            ſecabunt, quibus latera dictirhombi ſint æquidiſtantia) </s>
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