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

Table of contents

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[191.] COROLLARIVM.
Page: 144 (124)
[192.] THEOREMA XII. PROPOS. XII.
Page: 144 (124)
[193.] COROLLARIVM.
Page: 145 (125)
[194.] THEOREMA XIII. PROPOS. XIII.
Page: 145 (125)
[195.] COROLLARIVM.
Page: 146 (126)
[196.] THEOREMA XIV. PROPOS. XIV.
Page: 146 (126)
[197.] COROLLARIVM.
Page: 147 (127)
[198.] THEOREMA XV. PROPOS. XV.
Page: 147 (127)
[199.] A. DEMONSTRATIONIS SECTIO I.
Page: 148 (128)
[200.] B. SECTIO SECVNDA.
Page: 149 (129)
[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)
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              <pb o="343" file="0363" n="363" rhead="LIBER IV."/>
            rallelepipedum ſub, AQ, & </s>
            <s xml:id="echoid-s8563" xml:space="preserve">his ſpatijs .</s>
            <s xml:id="echoid-s8564" xml:space="preserve">f. </s>
            <s xml:id="echoid-s8565" xml:space="preserve">quadrato, PQ {1/2}.
              <lb/>
            </s>
            <s xml:id="echoid-s8566" xml:space="preserve">quadrati, QZ, & </s>
            <s xml:id="echoid-s8567" xml:space="preserve">rectangulo ſub ſexquitertia, ZQ, & </s>
            <s xml:id="echoid-s8568" xml:space="preserve">ſub, Q
              <lb/>
            P, ab eodem dempta {1/6}. </s>
            <s xml:id="echoid-s8569" xml:space="preserve">para llelepipedi ſub, CD, & </s>
            <s xml:id="echoid-s8570" xml:space="preserve">quadra-
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            to, QP,</s>
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            <s xml:id="echoid-s8571" xml:space="preserve">Completo parallelogrammo, KP, omnia igitur quadrata trili-
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              <figure xlink:label="fig-0363-01" xlink:href="fig-0363-01a" number="245">
                <image file="0363-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0363-01"/>
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            nei, DPG, ad omnia qua-
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            drata figurę, CAZP, demp tis
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            omnibus quadratis trilinei, A
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            CD, habent rationem com-
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            poſitam ex ea, quam habent
              <lb/>
            omnia quadrata, DPG, ad
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            omnia quadrata, DG, .</s>
            <s xml:id="echoid-s8572" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8573" xml:space="preserve">ex
              <lb/>
            ratione compoſitæ ex {1/3}. </s>
            <s xml:id="echoid-s8574" xml:space="preserve">ZP,
              <lb/>
            & </s>
            <s xml:id="echoid-s8575" xml:space="preserve">{1/6}. </s>
            <s xml:id="echoid-s8576" xml:space="preserve">PG, ad, ZP, & </s>
            <s xml:id="echoid-s8577" xml:space="preserve">ex ratio-
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              <note position="right" xlink:label="note-0363-01" xlink:href="note-0363-01a" xml:space="preserve">47. huius.</note>
            ne omnium quadratorum, D
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            G, ad omnia quadrata, KP, .</s>
            <s xml:id="echoid-s8578" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8579" xml:space="preserve">ex ratione parallelepipedi ſub, D
              <lb/>
            P, & </s>
            <s xml:id="echoid-s8580" xml:space="preserve">quadrato, PG, ad parallel epipedum ſub, AQ, & </s>
            <s xml:id="echoid-s8581" xml:space="preserve">quadrato, Z
              <lb/>
            P, & </s>
            <s xml:id="echoid-s8582" xml:space="preserve">tandem ex ratione omnium quadratorum, KP, ad omnia qua-
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            drata figuræ, CAZP, demptis omnibus quadratis trilinei, ACD,
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            .</s>
            <s xml:id="echoid-s8583" xml:space="preserve">f. </s>
            <s xml:id="echoid-s8584" xml:space="preserve">ex ratione parallelepipedi ſub, AQ, & </s>
            <s xml:id="echoid-s8585" xml:space="preserve">quadrato, ZP, ad paralle-
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            pipedum ſub, AQ, & </s>
            <s xml:id="echoid-s8586" xml:space="preserve">his ſpatijs .</s>
            <s xml:id="echoid-s8587" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8588" xml:space="preserve">quadrato, PQ, {1/2}. </s>
            <s xml:id="echoid-s8589" xml:space="preserve">quadrati,
              <lb/>
              <note position="right" xlink:label="note-0363-02" xlink:href="note-0363-02a" xml:space="preserve">34. huius.</note>
            QZ, & </s>
            <s xml:id="echoid-s8590" xml:space="preserve">rectangulo ſub, PQ, & </s>
            <s xml:id="echoid-s8591" xml:space="preserve">ſexquitertia, QZ, ab eodem dem-
              <lb/>
            pta {1/6}. </s>
            <s xml:id="echoid-s8592" xml:space="preserve">parallelepipedi ſub, CD, & </s>
            <s xml:id="echoid-s8593" xml:space="preserve">quadrato, PQ; </s>
            <s xml:id="echoid-s8594" xml:space="preserve">duæ autem ra-
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            tiones parallelepipedi ſub, DP, & </s>
            <s xml:id="echoid-s8595" xml:space="preserve">quadrato PG, ad parallelepipe-
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            dum ſub, AQ, & </s>
            <s xml:id="echoid-s8596" xml:space="preserve">quadrato, ZP, & </s>
            <s xml:id="echoid-s8597" xml:space="preserve">huius parallelepipedi ad paral-
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            lelepipedum ſub, AQ, & </s>
            <s xml:id="echoid-s8598" xml:space="preserve">ſpatijs iam dictis, ab eodem dempta {1/6}. </s>
            <s xml:id="echoid-s8599" xml:space="preserve">pa-
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            rallelepipedi ſub, CD, & </s>
            <s xml:id="echoid-s8600" xml:space="preserve">quadrato, PQ, componunt rationem pa-
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            rallelepipedi ſub, DP, & </s>
            <s xml:id="echoid-s8601" xml:space="preserve">quadrato, PG, ad parallelepipedum ſub,
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              <note position="right" xlink:label="note-0363-03" xlink:href="note-0363-03a" xml:space="preserve">Defin. 12.
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              l. 1.</note>
            AQ, & </s>
            <s xml:id="echoid-s8602" xml:space="preserve">dictis ſpatijs ab eodem dempta {1/6}. </s>
            <s xml:id="echoid-s8603" xml:space="preserve">parallelepipedi ſub, CD,
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            & </s>
            <s xml:id="echoid-s8604" xml:space="preserve">quadrato, PQ, ergo omnia quadrata trilinei, DGP, ad omnia,
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            quadrata figuræ, CAZP, demptis omnibus quadratis trilinei, AC
              <lb/>
            D, erunt in ratione compoſita ex ea, quam habet {1/3}. </s>
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            G, ad, ZP, & </s>
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            drato, PG, ad parallelepipedum ſub, AQ, & </s>
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            <s xml:id="echoid-s8610" xml:space="preserve">f. </s>
            <s xml:id="echoid-s8611" xml:space="preserve">quadra-
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            to, PQ, {1/2}. </s>
            <s xml:id="echoid-s8612" xml:space="preserve">quadrati, QZ, cum rectangulo ſub, PQ, & </s>
            <s xml:id="echoid-s8613" xml:space="preserve">ſexquitertia,
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            QZ, ab eodem parallelepipedo dempta {1/6}. </s>
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            & </s>
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