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

Table of contents

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[231.] D. SECTIO IV.
Page: 174 (154)
[232.] E. SECTIO V.
Page: 175 (155)
[233.] F. SECTIO VI.
Page: 175 (155)
[234.] THEOR EMA XXIII. PROPOS. XXIII.
Page: 175 (155)
[235.] A. COROLLARII SECTIO I.
Page: 176 (156)
[236.] B. SECTIO II.
Page: 177 (157)
[237.] C. SECTIO III.
Page: 177 (157)
[238.] D. SECTIO IV.
Page: 177 (157)
[239.] E. SECTIO V.
Page: 177 (157)
[240.] F. SECTIO VI.
Page: 177 (157)
[241.] G. SECTIO VII.
Page: 177 (157)
[242.] H. SECTIO VIII.
Page: 178 (158)
[243.] I. SECTIO IX.
Page: 178 (158)
[244.] K. SECTIO X.
Page: 178 (158)
[245.] L. SECTIO XI.
Page: 178 (158)
[246.] THEOREMA XXIV. PROPOS. XXIV.
Page: 179 (159)
[247.] COROLLARIVM.
Page: 180 (160)
[248.] THEOREMA XXV. PROPOS. XXV.
Page: 181 (161)
[249.] THE OREMA XXVI. PROPOS. XXVI.
Page: 183 (163)
[250.] COROLLARIVM I.
Page: 185 (165)
[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)
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              <pb o="215" file="0235" n="235" rhead="LIBER III."/>
            quorum latera ſint prædictis diametris parallela, quæ ideò ſunt æquian-
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            gula, vniuerſaliter igitur prædicta ſunt iter ſe, vt parallelogramna re-
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            ctangula, vel æquiangula illis circumſcripta; </s>
            <s xml:id="echoid-s5224" xml:space="preserve">Vnde etiam habetur pa-
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            rallelogramma rectangula illis circumſcripta eſſe, vt parallelogramma
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            æquiangula pariter illis circumſcripta.</s>
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        <div xml:id="echoid-div532" type="section" level="1" n="317">
          <head xml:id="echoid-head334" xml:space="preserve">COROLL II. A. SECTIO I.</head>
          <note position="right" xml:space="preserve">A.</note>
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            <s xml:id="echoid-s5226" xml:space="preserve">_H_INC vlterius colligitur, quod quæcunque de binis parallelo-
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            grammis oſtenſa ſunt in Theorem. </s>
            <s xml:id="echoid-s5227" xml:space="preserve">5. </s>
            <s xml:id="echoid-s5228" xml:space="preserve">6. </s>
            <s xml:id="echoid-s5229" xml:space="preserve">7. </s>
            <s xml:id="echoid-s5230" xml:space="preserve">8. </s>
            <s xml:id="echoid-s5231" xml:space="preserve">lib 2. </s>
            <s xml:id="echoid-s5232" xml:space="preserve">præſuppoſitis
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            conditionibus illic conſideratis circa eorum baſes, & </s>
            <s xml:id="echoid-s5233" xml:space="preserve">altitudines, vel
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            circa eorum latera, eadem & </s>
            <s xml:id="echoid-s5234" xml:space="preserve">de ellipſibus verificabuntur eaſdem con-
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            ditiones in proprijs axibus, vel diametris habentibus; </s>
            <s xml:id="echoid-s5235" xml:space="preserve">nam his poſitis
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            parallelogrammaillis circumſcripta, & </s>
            <s xml:id="echoid-s5236" xml:space="preserve">æquiangula habent in ſuis la-
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            teribus, vel in baſi, & </s>
            <s xml:id="echoid-s5237" xml:space="preserve">altitudine eaſdem conditiones, vnde ſicuti di-
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            ctæ concluſiones ſequuntur pro parallelogrammis circumſcriptis, ita
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            etiam verificantur pro inſcriptis ellipſibus, ad quas dicta parallelo-
              <lb/>
            gramma habent eaſdem rationes, vt probatum eſt, quæ igitur hic non
              <lb/>
              <note position="right" xlink:label="note-0235-02" xlink:href="note-0235-02a" xml:space="preserve">_11. Huius._</note>
            ſunt pro ellipſibus ad inuicem comparatis oſtenſa, per ſupracitata
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            Theoremata ſupplentur, pro circulis autem hoc tantum habemus, quod
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            ſint, vt eorum axium, vel (ſimanis dicere) diametrorum quadrata,
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            non aliaque circa eoſdem variatio contingit.</s>
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          <head xml:id="echoid-head335" xml:space="preserve">B. SECTIO II.</head>
          <note position="right" xml:space="preserve">B.</note>
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            <s xml:id="echoid-s5239" xml:space="preserve">_C_olliguntur ergo hæc de binis ellipſibus .</s>
            <s xml:id="echoid-s5240" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5241" xml:space="preserve">quod quæ ſunt circa ean.
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            </s>
            <s xml:id="echoid-s5242" xml:space="preserve">dem diametrum, ſunt vt reliquæ ſecundæ diametri.</s>
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        <div xml:id="echoid-div535" type="section" level="1" n="319">
          <head xml:id="echoid-head336" xml:space="preserve">C. SECTIO III.</head>
          <note position="right" xml:space="preserve">C.</note>
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            <s xml:id="echoid-s5244" xml:space="preserve">_Q_V æcunq; </s>
            <s xml:id="echoid-s5245" xml:space="preserve">ellipſes habent rationem ex axibus, vel diametris con-
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            iugatis, æqualiter ad inuicem inclinatis compoſitam.</s>
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          <head xml:id="echoid-head337" xml:space="preserve">D. SECTIO IV.</head>
          <note position="right" xml:space="preserve">D.</note>
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            <s xml:id="echoid-s5247" xml:space="preserve">_E_Llipſes habentes axes, vel diametros coniugatas, quæ æqualiter
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            ſunt inclinatæ, reciprocè reſpondentes, ſunt æquales; </s>
            <s xml:id="echoid-s5248" xml:space="preserve">& </s>
            <s xml:id="echoid-s5249" xml:space="preserve">quæ
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            ſunt æquales, & </s>
            <s xml:id="echoid-s5250" xml:space="preserve">habent axes, vel diametros ad inuicem æqualiter in-
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            clinatas, eaſdem habent reciprocè reſpondentes.</s>
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