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

Table of contents

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[271.] THEOR. XXIII. PROP. XXXX.
Page: 235 (51)
[272.] COROLL. I.
Page: 237 (53)
[273.] COROLL. II.
Page: 237 (53)
[274.] COROLL. III.
Page: 237 (53)
[275.] PROBL. VI. PROP. XXXXI.
Page: 238 (54)
[276.] PROBL. VII. PROP. XXXXII.
Page: 238 (54)
[277.] COROLL.
Page: 239 (55)
[278.] THEOR. XXIV. PROP. XXXXIII.
Page: 240 (56)
[279.] THEOR. XXV. PROP. XXXXIV.
Page: 240 (56)
[280.] SCHOLIVM.
Page: 242 (58)
[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)
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            diſpoſitum, ſintque omnia plana G M H, I N L, &</s>
            <s xml:id="echoid-s7783" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7784" xml:space="preserve">quæ baſi A E C F
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            æquidiſtanter ducuntur per Acuminati A B C applicatas G H, I L, &</s>
            <s xml:id="echoid-s7785" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s7786" xml:space="preserve">ipſi baſi, ac inter ſe, ſimilia Acuminata, & </s>
            <s xml:id="echoid-s7787" xml:space="preserve">ſimiliter poſita, atque ipſæ
              <lb/>
            applicatæ G H, I L ſint eorundem Acuminatorum homologæ diametri: </s>
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            huiuſmodi figura SOLIDVM REGVLARE ACVMINATVM vocetur,
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            vel tantùm ACVMINATVM SOLIDVM; </s>
            <s xml:id="echoid-s7789" xml:space="preserve">A E C F verò BASIS ſoli-
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            di Acuminati; </s>
            <s xml:id="echoid-s7790" xml:space="preserve">ſed portionem A B C Acuminati plani intra Acuminatum
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            ſolidum interceptam (eò quod ipſa ſit tanquam Regula, vel Modulus,
              <lb/>
            aut Canon homologarum diametrorum ſimilium planorum ęquidiſtantium,
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            ac ſolidum procreantium) nuncupare liceat CANONEM ſolidi Acumina-
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            ti, qui ſi ad planum ba
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            ſis A E C F rectus fuerit, dicatur CANON RECTVS
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            ſolidi Acuminati, & </s>
            <s xml:id="echoid-s7791" xml:space="preserve">B D diameter Canonis, nuncupetur quoque AXIS
              <lb/>
            ſolidi, & </s>
            <s xml:id="echoid-s7792" xml:space="preserve">eius VERTEX punctum B, in quod abit ſolidum, atque eiuſdem
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            ſolidi ALTITVDO dicatur recta B O, quæ à vertice B ſuper baſim A E C
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            F recta ducitur. </s>
            <s xml:id="echoid-s7793" xml:space="preserve">Plana verò A C, G H, I L, &</s>
            <s xml:id="echoid-s7794" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7795" xml:space="preserve">dicantur PLANA OR-
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            DINATIM DVCTA ad axim ſolidi Acuminati.</s>
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          <head xml:id="echoid-head326" xml:space="preserve">III.</head>
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            <s xml:id="echoid-s7797" xml:space="preserve">SOLIDA ACVMINATA PROPORTIONALIA dicantur illa, quo-
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            rum omnia plana ordinatim applicata per puncta, eorum axes proportio-
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            naliter diuidentia, ſint quoque inter ſe, & </s>
            <s xml:id="echoid-s7798" xml:space="preserve">baſibus proportionalia.</s>
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            <s xml:id="echoid-s7800" xml:space="preserve">Videlicet ſi duo ſolida Acumi-
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                <image file="0279-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0279-01"/>
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            nata A B C, D E F, quorum baſes
              <lb/>
            ſint A G C I, L F H D axes verò
              <lb/>
            ſint B K, E O proportionaliter ſe-
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            cti in M, P; </s>
            <s xml:id="echoid-s7801" xml:space="preserve">& </s>
            <s xml:id="echoid-s7802" xml:space="preserve">in N, Q; </s>
            <s xml:id="echoid-s7803" xml:space="preserve">ita vt K
              <lb/>
            M, ad M B ſit vt O P, ad P E; </s>
            <s xml:id="echoid-s7804" xml:space="preserve">& </s>
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            K N ad N B, vt O Q ad Q E, &</s>
            <s xml:id="echoid-s7806" xml:space="preserve">c.
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            </s>
            <s xml:id="echoid-s7807" xml:space="preserve">ſitque baſis A G C ad baſim L F H,
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            vt planum ordinatim applicatum
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            per M ad applicatum per P, & </s>
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            applicatum per N ad applicatum
              <lb/>
            per Q, &</s>
            <s xml:id="echoid-s7809" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7810" xml:space="preserve">talia ſolida, dicentur
              <lb/>
            SOLIDA ACVMINATA PROPORTIONALIA.</s>
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          <head xml:id="echoid-head327" xml:space="preserve">IIII.</head>
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            <s xml:id="echoid-s7812" xml:space="preserve">Si ſuper diametrum Acuminati plani deſcriptum ſit parallelogrammum
              <lb/>
            quodlibet ſuper ipſum planum quomodocunque eleuatum, idem que Acu-
              <lb/>
            minatum concipiatur ſibi ipſi æquidiſtanter moueri, ita vt eius diameter ſuo
              <lb/>
            motu parallelo prædictum parallelogrammum deſcribat: </s>
            <s xml:id="echoid-s7813" xml:space="preserve">ſolidum occluſum
              <lb/>
            à duobus oppoſitis Acuminatis congruentibus, ac parallelis, atque à ſuper-
              <lb/>
            ficie, quæ à perimetro figuræ motæ deſcribitur CYLINDRICVS vocetur.
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            <s xml:id="echoid-s7814" xml:space="preserve">Acuminatum verò ſolidum procreans, dicatur BASIS, & </s>
            <s xml:id="echoid-s7815" xml:space="preserve">parallelogram-
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            mum, per quod fit æquidiſtans latio Acuminati plani Cylindricum pro-
              <lb/>
            creantis, CANON DIAMETRALIS nuncupetur.</s>
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            <s xml:id="echoid-s7817" xml:space="preserve">Nimirum, ſit Acuminatum planum A B C, cuius diameter B D, cui in-
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            ſiſtat parallelogrammum quodcumq; </s>
            <s xml:id="echoid-s7818" xml:space="preserve">B D E F ſuper planum figuræ A B </s>
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