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

Table of contents

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[461.] B. SECTIO II.
Page: 344 (324)
[462.] C. SECTIO III.
Page: 344 (324)
[463.] D. SECTIO IV.
Page: 344 (324)
[464.] E. SECTIO V.
Page: 345 (325)
[465.] THEOREMA XXIX. PROPOS. XXXI.
Page: 345 (325)
[466.] THEOREMA XXX. PROPOS. XXXII.
Page: 346 (326)
[467.] COROLLARIVM.
Page: 347 (327)
[468.] THEOREMA XXXI. PROPOS. XXXIII.
Page: 347 (327)
[469.] THEOREMA XXXII. PROPOS. XXXIV.
Page: 348 (328)
[470.] COROLLARIVM.
Page: 349 (329)
[471.] THEOREMA XXXIII. PROPOS. XXXV.
Page: 349 (329)
[472.] COROLLARIVM.
Page: 350 (330)
[473.] THEOREMA XXXIV. PROPOS. XXXVI.
Page: 351 (331)
[474.] THEOREMA XXXV. PROPOS. XXXVII.
Page: 352 (332)
[475.] THEOREMA XXXVI. PROP. XXXVIII.
Page: 353 (333)
[476.] THEOREMA XXXVII. PROP. XXXIX.
Page: 354 (334)
[477.] THEOREMA XXXVIII. PROP. XL.
Page: 354 (334)
[478.] COROLLARIVM.
Page: 354 (334)
[479.] THEOREMA XXXIX. PROPOS. XLI
Page: 355 (335)
[480.] THEOREMA XL. PROPOS. XLII.
Page: 356 (336)
[481.] THEOREMA XLI. PROPOS. XLIII.
Page: 357 (337)
[482.] THEOREMA XLII. PROPOS. XLIV.
Page: 358 (338)
[483.] THEOREMA XLIII. PROP. XLV.
Page: 358 (338)
[484.] THEOREMA XLIV. PROP. XLVI.
Page: 359 (339)
[485.] THEOREMA XLV. PROP. XLVII.
Page: 360 (340)
[486.] THEOREMA XLVI. PROPOS. XLVIII.
Page: 361 (341)
[487.] THEOREMA XLVII. PROPOS. XLIX.
Page: 362 (342)
[488.] THEOREMA XLVIII. PROPOS. L.
Page: 364 (344)
[489.] THEOREMA XLIX. PROPOS. LI.
Page: 365 (345)
[490.] SCHOLIVM.
Page: 365 (345)
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          <head xml:id="echoid-head480" xml:space="preserve">A. COROLL. SECT IO I.</head>
          <note position="left" xml:space="preserve">A</note>
          <p style="it">
            <s xml:id="echoid-s7795" xml:space="preserve">_H_Inc habetur omnia quadrata trilineorum ſub tangentibus, & </s>
            <s xml:id="echoid-s7796" xml:space="preserve">ſe-
              <lb/>
            cantibus, veluti ſunt, AD, DC, regulis tangentibus, eſſe
              <lb/>
            inter ſe, vt omnia quadrata parallelogrammorum ſub eiſdem tangen-
              <lb/>
            tibus, & </s>
            <s xml:id="echoid-s7797" xml:space="preserve">ſecantibus, regulis ijſdem tangentibus, quoniam dictorum
              <lb/>
            trilineorum omnia quadrata ſunt ſextæ partes omnium quadratorum di-
              <lb/>
            ctorum parallelogram norum; </s>
            <s xml:id="echoid-s7798" xml:space="preserve">Etideò proipſis etiam has concluſiones
              <lb/>
            colligemus, ſcilicet.</s>
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          <head xml:id="echoid-head481" xml:space="preserve">B. SECTIO II.</head>
          <note position="left" xml:space="preserve">B</note>
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            <s xml:id="echoid-s7800" xml:space="preserve">_S_I dicti triliaei fuerint in eadem altitudine, quòd omnia quadrata
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            earundem erunt inter ſe, vt baſium quadrata @ſ. </s>
            <s xml:id="echoid-s7801" xml:space="preserve">tangentium; </s>
            <s xml:id="echoid-s7802" xml:space="preserve">Et
              <lb/>
            ſi fuerint dictitrilinei in eadem baſi ſcilicet tangente, dicta omnia qua-
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            drata erunt inter ſe, vt altitudines, vel, vt ſecantes æqualiter baſibus
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            ſcilicettangentibus, inclinata.</s>
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          <head xml:id="echoid-head482" xml:space="preserve">C. SECTIO III.</head>
          <note position="left" xml:space="preserve">C</note>
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            <s xml:id="echoid-s7804" xml:space="preserve">_I_Tem quod omnia quadrata dictorum trilineorum habebunt inter ſe
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            rationem compoſitam ex ratione quadratorum baſium, & </s>
            <s xml:id="echoid-s7805" xml:space="preserve">ex r atio-
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            ne altitudinum, vel ſecantium æqualiter baſibus, ſcilicet tangenti-
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            bus, inclinatarum.</s>
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          <head xml:id="echoid-head483" xml:space="preserve">D. SECTIO IV.</head>
          <note position="left" xml:space="preserve">D</note>
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            <s xml:id="echoid-s7807" xml:space="preserve">_P_Ariter quod omnia quadrata dictorum trilineorum, quorum tan-
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            gentium quadrata altitudinibus, vel ſecantibus æqualiter tangen-
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            t
              <unsure/>
            ibus inclinatis reciprocantur, eſſe æqualia; </s>
            <s xml:id="echoid-s7808" xml:space="preserve">& </s>
            <s xml:id="echoid-s7809" xml:space="preserve">quæ ſunt æqualia, eſſe
              <lb/>
            trilineorum, quorum baſium, vel tangentium quadrata altitudinibus,
              <lb/>
            vel ſecantibus equaliter tangentibus inclinatis, reciprocantur.</s>
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