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

Table of contents

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[311.] THEOR. XLII. PROP. LXVIII.
Page: 274 (88)
[312.] COROLL. I.
Page: 276 (90)
[313.] COROLL. II.
Page: 276 (90)
[314.] MONITVM.
Page: 276 (90)
[315.] DEFINITIONES. I.
Page: 278 (92)
[316.] II.
Page: 278 (92)
[317.] III.
Page: 279 (93)
[318.] IIII.
Page: 279 (93)
[319.] PROBL. XIV. PROP. LXIX.
Page: 280 (94)
[320.] SCHOLIVM I.
Page: 282 (96)
[321.] COROLL. I.
Page: 282 (96)
[322.] SCHOLIVM II.
Page: 282 (96)
[323.] COROLL. II.
Page: 282 (96)
[324.] SCHOLIVM III.
Page: 283 (97)
[325.] COROLL. III.
Page: 283 (97)
[326.] THEOR. XLIII. PROP. LXX.
Page: 284 (98)
[327.] COROLL.
Page: 286 (100)
[328.] THEOR. XLIV. PROP. LXXI.
Page: 286 (100)
[329.] COROLL.
Page: 287 (101)
[330.] THEOR. XLV. PROP. LXXII.
Page: 288 (102)
[331.] SCHOLIVM.
Page: 288 (102)
[332.] THEOR. XLVI. PROP. LXXIII.
Page: 288 (102)
[333.] THEOR. XLVII. PROP. LXXIV.
Page: 288 (102)
[334.] MONITVM.
Page: 290 (104)
[335.] LEMMA XIV. PROP. LXXV.
Page: 290 (104)
[336.] SCHOLIVM.
Page: 291 (105)
[337.] LEMMA XV. PROP. LXXVI.
Page: 292 (106)
[338.] THEOR. XLVIII. PROP. LXXVII.
Page: 292 (106)
[339.] MONITVM.
Page: 293 (107)
[340.] THEOR. IL. PROP. LXXVIII.
Page: 294 (108)
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            ma P Q, R S, &</s>
            <s xml:id="echoid-s8013" xml:space="preserve">c, concipiantur deſcripta ſolida parallelepipeda æqualium
              <lb/>
            altitudinum cum Cylindrico A, vel L; </s>
            <s xml:id="echoid-s8014" xml:space="preserve">& </s>
            <s xml:id="echoid-s8015" xml:space="preserve">quorum inſiſtentes lineæ ſint
              <lb/>
            æquidiſtantes inſiſtentibus Cylindrici A, &</s>
            <s xml:id="echoid-s8016" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8017" xml:space="preserve">erit ergo vnumquodque pa-
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            rallelepipedorum inſcriptorum, ad parallelepipedum L, vt propria baſis
              <note symbol="a" position="right" xlink:label="note-0287-01" xlink:href="note-0287-01a" xml:space="preserve">32. vnd.
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            baſim, ac ideò omnia ſimul inſcripta ſuper P Q, R S, &</s>
            <s xml:id="echoid-s8018" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8019" xml:space="preserve">ad vnicum paralle-
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            lepipedum, vel Cylindricum L, erunt vt omnes baſes P Q, R S, &</s>
            <s xml:id="echoid-s8020" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8021" xml:space="preserve">hoc eſt
              <lb/>
            vt figura inſcripta ad baſim R T; </s>
            <s xml:id="echoid-s8022" xml:space="preserve">ſed inſcripta ad K T maiorem habet ratio-
              <lb/>
            nem quàm Cylindricus A ad L, ergo, & </s>
            <s xml:id="echoid-s8023" xml:space="preserve">omnia ſimul parallelepipeda in-
              <lb/>
            ſcripta, ad Cylindricum L maiorem habebunt rationem, quàm Cylindri-
              <lb/>
            cus A circumſcriptus ad eundem Cylindricum L, ergo inſcripta ſimul pa-
              <lb/>
            rallelepipeda maiora erunt Cylindrico A, pars ſuo toto, quod eſt abſurdũ:
              <lb/>
            </s>
            <s xml:id="echoid-s8024" xml:space="preserve">non eſt ergo baſis C D E maior quàm opus eſt ad hoc vt ad baſim K T ſit vt
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            Cylindricus A ad L.</s>
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            <s xml:id="echoid-s8026" xml:space="preserve">Si verò ponatur baſim
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                <image file="0287-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0287-01"/>
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            C D E ad K T hab ere mi-
              <lb/>
            norem rationem quàm
              <lb/>
            Cylindricus A ad L, erit
              <lb/>
            baſis C D E minor quàm
              <lb/>
            opus eſt ad hoc vt huiuſ-
              <lb/>
            modi magnitudines ſint
              <lb/>
            proportionales, inuento
              <lb/>
            igitur defectu, &</s>
            <s xml:id="echoid-s8027" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8028" xml:space="preserve">& </s>
            <s xml:id="echoid-s8029" xml:space="preserve">facta
              <lb/>
            baſi C D E circumſcri-
              <lb/>
            ptione figuræ ex paralle-
              <lb/>
            logrammis, &</s>
            <s xml:id="echoid-s8030" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8031" xml:space="preserve">quæ ad
              <lb/>
            baſim K T adhuc minorẽ
              <lb/>
            habeat rationem quàm
              <lb/>
            Cylindricus A ad L, & </s>
            <s xml:id="echoid-s8032" xml:space="preserve">
              <lb/>
            circumſcriptis parallele-
              <lb/>
            pipedis vt ſupra, oſtendetur aggregatum circumſcriptorum parallelepipe-
              <lb/>
            dorum ad Cylindricum L eſſe vt figura circumſcripta ab baſim K T, hoc eſt
              <lb/>
            habere minorem rationem quàm Cylindricus A ad eundem Cylindricum
              <lb/>
            L, ideoque prædictum aggregatum parallelepipedorum minùs eſſe Cylin-
              <lb/>
            drico A, totum ſua parte, quod eſt abſurdum. </s>
            <s xml:id="echoid-s8033" xml:space="preserve">Non ergo baſis C ad K T
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            habet maiorem, nec minorem rationem quàm Cylindricus A ad L, ergo
              <lb/>
            erit baſis C D E ad baſim K T, vt Cylindricus A ad L. </s>
            <s xml:id="echoid-s8034" xml:space="preserve">Eadem ratione
              <lb/>
            demonſtrabitur, baſim K T ad Acuminatum F G H, ſiue ad baſim Cylin-
              <lb/>
            drici B, eſſe vt Cylindricus L ad Cylindricum B; </s>
            <s xml:id="echoid-s8035" xml:space="preserve">quare, ex æquo, erit vt
              <lb/>
            baſis C D E ad baſim F G H, ita Cylindricus A ad Cylindricum B. </s>
            <s xml:id="echoid-s8036" xml:space="preserve">Quod
              <lb/>
            erat, &</s>
            <s xml:id="echoid-s8037" xml:space="preserve">c.</s>
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          <head xml:id="echoid-head338" xml:space="preserve">COROLL.</head>
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            <s xml:id="echoid-s8039" xml:space="preserve">PErſpicuum hinc eſt, quod ſi huiuſmodi Cylindrici æqualiũ altitudinum
              <lb/>
            æquales baſes habuerint inter ſe æquales erunt.</s>
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