Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

Table of contents

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[281.] THEOR. XXVI. PROP. XLV.
Page: 242 (58)
[282.] COROLL.
Page: 243 (59)
[283.] THEOR. XXVII. PROP. XLVI.
Page: 243 (59)
[284.] COROLL. I.
Page: 245 (61)
[285.] COROLL. II.
Page: 245 (61)
[286.] THEOR. XXVIII. PROP. XLVII.
Page: 245 (61)
[287.] THEOR. XXIX. PROP. XLVIII.
Page: 247 (63)
[288.] THEOR. XXX. PROP. XLIX.
Page: 248 (64)
[289.] THEOR. XXXI. PROP. L.
Page: 249 (65)
[290.] COROLL.
Page: 250 (66)
[291.] THEOR. XXXII. PROP. LI.
Page: 251 (67)
[292.] SCHOLIVM.
Page: 252 (68)
[293.] THEOR. XXXIII. PROP. LII.
Page: 253 (69)
[294.] THEOR. XXXIV. PROP. LIII.
Page: 253 (69)
[295.] ALITER.
Page: 254 (70)
[296.] THEOR. XXXV. PROP. LIV.
Page: 255 (71)
[297.] THEOR. XXXIV. PROP. LV.
Page: 256 (72)
[298.] THEOR. XXXVII. PROP. LVI.
Page: 257 (73)
[299.] PROBL. VIII. PROP. LVII.
Page: 259 (75)
[300.] PROBL. IX. PROP. LVIII.
Page: 260 (76)
[301.] PROBL. X. PROP. LIX.
Page: 261 (77)
[302.] PROBL. XI. PROP. LX.
Page: 262 (78)
[303.] PROBL. XII. PROP. LXI.
Page: 262 (78)
[304.] PROBL. XIII. PROP. LXII.
Page: 265 (79)
[305.] MONITVM.
Page: 268 (82)
[306.] THEOR. XXXVIII. PROP. LXIII.
Page: 268 (82)
[307.] THEOR. XXXIX. PROP. LXIV.
Page: 270 (84)
[308.] THEOR. XL. PROP. LXV.
Page: 271 (85)
[309.] THEOR. XLI. PROP. LXVI.
Page: 273 (87)
[310.] LEMMA XIII. PROP. LXVII.
Page: 274 (88)
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          <head xml:id="echoid-head339" xml:space="preserve">THEOR. XLV. PROP. LXXII.</head>
          <p>
            <s xml:id="echoid-s8041" xml:space="preserve">Si Cylindricus plano ſecetur baſi æquidiſtante, erit Cylin-
              <lb/>
            dricus ad Cylindricum, vt altitudo ad altitudinem.</s>
            <s xml:id="echoid-s8042" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8043" xml:space="preserve">HOc eadem penitus conſtructione, ijſdemque argumentis demonſtrabi-
              <lb/>
            tur, ac 13. </s>
            <s xml:id="echoid-s8044" xml:space="preserve">duodecimi Elem. </s>
            <s xml:id="echoid-s8045" xml:space="preserve">opetamen præcedentis Corollarij; </s>
            <s xml:id="echoid-s8046" xml:space="preserve">ani-
              <lb/>
            maduertendo ſimul, quod dum Cylindricus plano ſecatur baſi æquidiſtante,
              <lb/>
            in ipſa ſectione oritur figura ſimilis, & </s>
            <s xml:id="echoid-s8047" xml:space="preserve">æqualis, ſiue in totum congruens baſi
              <lb/>
            Cylindrici: </s>
            <s xml:id="echoid-s8048" xml:space="preserve">nam ipſæ Cylindricus, ex motu parallelo ſuæ baſis procreari
              <lb/>
            concipitur, ex definitione, &</s>
            <s xml:id="echoid-s8049" xml:space="preserve">c.</s>
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        <div xml:id="echoid-div836" type="section" level="1" n="331">
          <head xml:id="echoid-head340" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s8051" xml:space="preserve">EX hac pendet huius concluſionis demonſtratio, quod eſt conuerſum
              <lb/>
            prop. </s>
            <s xml:id="echoid-s8052" xml:space="preserve">71. </s>
            <s xml:id="echoid-s8053" xml:space="preserve">huius; </s>
            <s xml:id="echoid-s8054" xml:space="preserve">nempe.</s>
            <s xml:id="echoid-s8055" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s8056" xml:space="preserve">Cylindrici æqualium baſium ſunt inter ſe, vt altitudines; </s>
            <s xml:id="echoid-s8057" xml:space="preserve">quod oſtenditur
              <lb/>
            vt in 14. </s>
            <s xml:id="echoid-s8058" xml:space="preserve">duodecimi Elementorum.</s>
            <s xml:id="echoid-s8059" xml:space="preserve"/>
          </p>
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          <head xml:id="echoid-head341" xml:space="preserve">THEOR. XLVI. PROP. LXXIII.</head>
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            <s xml:id="echoid-s8060" xml:space="preserve">Cylindrici, quorum baſes altitudinibus reciprocantur, inter ſe
              <lb/>
            ſunt æquales: </s>
            <s xml:id="echoid-s8061" xml:space="preserve">& </s>
            <s xml:id="echoid-s8062" xml:space="preserve">è conuerſo.</s>
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          <p>
            <s xml:id="echoid-s8064" xml:space="preserve">HVius Theorematis demonſtratio elicitur ex præcèdenti, eſtque omni-
              <lb/>
            nò ſimilis 15. </s>
            <s xml:id="echoid-s8065" xml:space="preserve">duodec. </s>
            <s xml:id="echoid-s8066" xml:space="preserve">Element. </s>
            <s xml:id="echoid-s8067" xml:space="preserve">itaque breuitatis gratia, hanc ipſam
              <lb/>
            o mittimus, ſimulque nonnullas alias Cylindricorum affectiones, cum hìc
              <lb/>
            de ijs diſſerere non ſit opus.</s>
            <s xml:id="echoid-s8068" xml:space="preserve"/>
          </p>
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          <head xml:id="echoid-head342" xml:space="preserve">THEOR. XLVII. PROP. LXXIV.</head>
          <p>
            <s xml:id="echoid-s8069" xml:space="preserve">Solida Acuminata proportionalia, quorum baſes altitudinibus
              <lb/>
            ſint reciprocè proportionales inter ſe ſunt æqualia.</s>
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            <s xml:id="echoid-s8071" xml:space="preserve">SInt duo Acuminata ſolida proportionalia, quorum Canones A B C, D
              <lb/>
            E F ſint ſuper baſes A C, D F, & </s>
            <s xml:id="echoid-s8072" xml:space="preserve">circa diametros B G, E H; </s>
            <s xml:id="echoid-s8073" xml:space="preserve">baſes
              <lb/>
            verò horum ſolidorum ſint Acuminata plana A L C, N F O circa diametros
              <lb/>
            A C, D F, ſitque vnius ſolidi altitudo B I, ad alterius altitudinem E Q re-
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            ciprocè, vt baſis N F O ad baſim A L C. </s>
            <s xml:id="echoid-s8074" xml:space="preserve">Dico huiuſmodi ſolida inter ſe
              <lb/>
            æqualia eſſe.</s>
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