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

Table of contents

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[201.] C. SECTIO III.
Page: 149 (129)
[202.] D. SECTIO IV.
Page: 150 (130)
[203.] E. SECTIO V. ET VLTIMA.
Page: 150 (130)
[204.] COROLLARIVM I.
Page: 151 (131)
[205.] COROLLARIVM II.
Page: 151 (131)
[206.] THEOREMA XVI. PROPOS. XVI.
Page: 151 (131)
[207.] SCHOLIV M.
Page: 152 (132)
[208.] THEOREMA XVII. PROPOS. XVII.
Page: 153 (133)
[209.] A. DEMONSTRATIONIS SECTIO I.
Page: 153 (133)
[210.] B. SECTIO II.
Page: 157 (137)
[211.] D. SECTIO IV.
Page: 160 (140)
[212.] E. SECTIO V.
Page: 161 (141)
[213.] F. SECTIO VI.
Page: 163 (143)
[214.] G. SECTIO VII.
Page: 164 (144)
[215.] H. SECTIO VIII. ET VLTIMA.
Page: 164 (144)
[216.] COROLLARIVM I.
Page: 165 (145)
[217.] COROLLARIVM II.
Page: 165 (145)
[218.] THE OREMA XVIII. PROPOS. XVIII.
Page: 165 (145)
[219.] THE OREMA XIX. PROPOS. XIX.
Page: 166 (146)
[220.] COROLLARIVM I.
Page: 167 (147)
[221.] COROLLARIVM II.
Page: 167 (147)
[222.] LEMMA.
Page: 168 (148)
[223.] THE OREMA XX. PROPOS. XX.
Page: 168 (148)
[224.] COROLLARIVM.
Page: 169 (149)
[225.] THE OREMA XXI. PROPOS. XXI.
Page: 169 (149)
[226.] COROLLARIVM.
Page: 170 (150)
[227.] THE OREMA XXII. PROPOS. XXII.
Page: 170 (150)
[228.] A. COROLLARII SECTIO I.
Page: 174 (154)
[229.] B. SECTIO II.
Page: 174 (154)
[230.] C. SECTIO III.
Page: 174 (154)
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          <head xml:id="echoid-head290" xml:space="preserve">D. SECTIO IV.</head>
          <p style="it">
            <s xml:id="echoid-s4506" xml:space="preserve">_I_N Propoſ. </s>
            <s xml:id="echoid-s4507" xml:space="preserve">II. </s>
            <s xml:id="echoid-s4508" xml:space="preserve">deducemus cylindricos ſimilibus baſibus inſiſtentes
              <lb/>
            habere inter ſe rationem compoſitam ex ratione baſium, & </s>
            <s xml:id="echoid-s4509" xml:space="preserve">altitu-
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            dinum, vel laterum æqualiter dictis baſibus inclinatorum.</s>
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        <div xml:id="echoid-div456" type="section" level="1" n="275">
          <head xml:id="echoid-head291" xml:space="preserve">E. SECTIO V.</head>
          <p style="it">
            <s xml:id="echoid-s4511" xml:space="preserve">_I_N Propoſ. </s>
            <s xml:id="echoid-s4512" xml:space="preserve">12. </s>
            <s xml:id="echoid-s4513" xml:space="preserve">colligemus cylindricos, quorum ſimiles baſes altitù-
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            dinibus, vel lateribus æqualiter baſibus inclinatis reciprocè re-
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            ſpondent, eſſe æquales; </s>
            <s xml:id="echoid-s4514" xml:space="preserve">& </s>
            <s xml:id="echoid-s4515" xml:space="preserve">cylindricos æquales, ſimilibus baſibus inſi-
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            ſtentes, baſes habere altitudinibus, vel lateribus æqualiter baſibus in-
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            clinatis, reciprocas.</s>
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          </p>
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        <div xml:id="echoid-div457" type="section" level="1" n="276">
          <head xml:id="echoid-head292" xml:space="preserve">F. SECTIO VI.</head>
          <p style="it">
            <s xml:id="echoid-s4517" xml:space="preserve">_I_N Prop. </s>
            <s xml:id="echoid-s4518" xml:space="preserve">13. </s>
            <s xml:id="echoid-s4519" xml:space="preserve">habebimus ſimiles cylindricos eſſe in tripla ratione la-
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            terum homologorum.</s>
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          <head xml:id="echoid-head293" xml:space="preserve">G. SECTIO VII.</head>
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            <s xml:id="echoid-s4521" xml:space="preserve">_E_X Prop. </s>
            <s xml:id="echoid-s4522" xml:space="preserve">14. </s>
            <s xml:id="echoid-s4523" xml:space="preserve">colligimus ſi prædicti cylindrici inſiſtant baſibus diſ-
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            ſimilibus, adh uc prædictas paſſiones de ipſis ver@ficari; </s>
            <s xml:id="echoid-s4524" xml:space="preserve">in quibus
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            tamen non numerant ur ſimiles cylindrici, cum oporteat eoſdem ſimiles
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            baſes habere.</s>
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          <head xml:id="echoid-head294" xml:space="preserve">H. SECTIO VIII.</head>
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            <s xml:id="echoid-s4526" xml:space="preserve">_I_N Prop. </s>
            <s xml:id="echoid-s4527" xml:space="preserve">22. </s>
            <s xml:id="echoid-s4528" xml:space="preserve">habemus in eius figura, ſolida ſimilaria genita ex pa-
              <lb/>
            rallelogrammis, AS, Τβ, iuxta regulas, ES, Ζβ, ea@dem ratio-
              <lb/>
            nem babere ad ſolidi ſimilaria genita ex triangulis, OES, & </s>
            <s xml:id="echoid-s4529" xml:space="preserve">Ζβ, ideſt
              <lb/>
              <note position="left" xlink:label="note-0204-01" xlink:href="note-0204-01a" xml:space="preserve">_Ex hae_
                <lb/>
              _Propoſ._</note>
            cyliadricos @enitos ex, AS, Τβ ad conicos genitos ex triangulis,
              <lb/>
            OES, & </s>
            <s xml:id="echoid-s4530" xml:space="preserve">Ζβ, eaadem rationem babere, vnde, cum conica
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            ſint partes
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            proportionales cylindricorum in eadem altitudine cum ipſis exiſten-
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            tium, quæeunq; </s>
            <s xml:id="echoid-s4531" xml:space="preserve">de cylindricis in huius Coroll. </s>
            <s xml:id="echoid-s4532" xml:space="preserve">Sectionibus 2. </s>
            <s xml:id="echoid-s4533" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4534" xml:space="preserve">4. </s>
            <s xml:id="echoid-s4535" xml:space="preserve">5. </s>
            <s xml:id="echoid-s4536" xml:space="preserve">6.
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            <s xml:id="echoid-s4537" xml:space="preserve">& </s>
            <s xml:id="echoid-s4538" xml:space="preserve">7. </s>
            <s xml:id="echoid-s4539" xml:space="preserve">collecta ſunt, eadem & </s>
            <s xml:id="echoid-s4540" xml:space="preserve">pro conicis tamquam collecta recipiemus.</s>
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