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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            vtcunque eleuatum, concipiaturque Acu-
              <lb/>
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                <image file="0280-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0280-01"/>
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            minatum A B C moueri motu ſibi ipſi pa-
              <lb/>
            rallelo, ſed ita vt recta B D æquidiſtanter
              <lb/>
            incedat ſuper parallelogrammum B E, do-
              <lb/>
            nec congruat cum oppoſito latere E F.
              <lb/>
            </s>
            <s xml:id="echoid-s7819" xml:space="preserve">Huiuſmodi ſolidum occluſum à parallelis,
              <lb/>
            & </s>
            <s xml:id="echoid-s7820" xml:space="preserve">congruentibus Acuminatis A B C, G F
              <lb/>
            H, atque à ſuperficie, quæ à perimetro A
              <lb/>
            B C A in ſua latione deſcribitur, vocetur
              <lb/>
            CYLINDRICVS, Acuminatum verò A B C eius BASIS, & </s>
            <s xml:id="echoid-s7821" xml:space="preserve">parallelo-
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            grammum B E CANON DIAMETRALIS prædicti Cylindrici, cuius
              <lb/>
            altitudo metietur per rectam ad vtrunque oppoſitorum planorum perpen-
              <lb/>
            dicularem.</s>
            <s xml:id="echoid-s7822" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7823" xml:space="preserve">Itaque CYLINDRICVS dicetur omne ſolidum circa parallelogrãmum
              <lb/>
            quodcunque deſcriptum, & </s>
            <s xml:id="echoid-s7824" xml:space="preserve">cuius omnia plana baſi ſolidi æquidiſtantia, ac
              <lb/>
            per applicatas in parallelogrammo ducta, ſint plana Acuminata, eidem
              <lb/>
            baſi, ac inter ſe æqualia, & </s>
            <s xml:id="echoid-s7825" xml:space="preserve">ſimilia, & </s>
            <s xml:id="echoid-s7826" xml:space="preserve">ſimiliter poſita, & </s>
            <s xml:id="echoid-s7827" xml:space="preserve">quorum homologę
              <lb/>
            diametri ſint ipſæ applicatæ in prædicto parallelogrammo; </s>
            <s xml:id="echoid-s7828" xml:space="preserve">quod CANON
              <lb/>
            DIAMETRALIS Cylindrici vocabitur.</s>
            <s xml:id="echoid-s7829" xml:space="preserve"/>
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            <s xml:id="echoid-s7830" xml:space="preserve">Omittimus vniuerſaliores Solidorum Acuminatorũ, ac Cylindricorum
              <lb/>
            definitiones, cum hoc loco de ijs ſermo minimè habendus ſit.</s>
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          <head xml:id="echoid-head328" xml:space="preserve">PROBL. XIV. PROP. LXIX.</head>
          <p>
            <s xml:id="echoid-s7832" xml:space="preserve">Si Conoides quodcunque, vel Sphæra, aut Sphæroides ob-
              <lb/>
            longum, vel prolatum plano ſecetur ex dato ſolido portionem
              <lb/>
            abſcindent: </s>
            <s xml:id="echoid-s7833" xml:space="preserve">poſſibile eſt per axem ſolidi, planum ducere, quod
              <lb/>
            ad baſim abſciſſæ portionis ſit erectum. </s>
            <s xml:id="echoid-s7834" xml:space="preserve">Item.</s>
            <s xml:id="echoid-s7835" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7836" xml:space="preserve">Poſſibile eſt baſi portionis aliud planum æquidiſtans ducere,
              <lb/>
            quod conuexam ſolidæ portionis ſnperficiem contingat.</s>
            <s xml:id="echoid-s7837" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7838" xml:space="preserve">ESto quodcunque ex prædictis ſolidis A B C, cuius axis reuolutionis ſit
              <lb/>
            B D, atque ex eo per planum E H G I ſit abſciſſa portio ſolida E F G,
              <lb/>
            cuius baſis E H G I (quæ, vel erit Ellipſis, vel circulus.) </s>
            <s xml:id="echoid-s7839" xml:space="preserve">Dico
              <note symbol="a" position="left" xlink:label="note-0280-01" xlink:href="note-0280-01a" xml:space="preserve">ex 13. 14
                <lb/>
              15. Arch.
                <lb/>
              de Conoi.
                <lb/>
              &c.</note>
            eſſe baſi E H G I planum ducere per ſolidi axem B D, quod ad baſim E H
              <lb/>
            G I rectum ſit. </s>
            <s xml:id="echoid-s7840" xml:space="preserve">Præterea poſſibile eſſe eidem baſi aliud planum æquidiſtans
              <lb/>
            ducere, quod ſolidæ portionis ſuperficiem contingat.</s>
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            <s xml:id="echoid-s7842" xml:space="preserve">Si enim planum ſecans E I G fuerit ad axem B D erectum, hunc ſecans
              <lb/>
            in K, ſectio circulus erit, cuius centrum K; </s>
            <s xml:id="echoid-s7843" xml:space="preserve">& </s>
            <s xml:id="echoid-s7844" xml:space="preserve">ſi per axim B K
              <note symbol="b" position="left" xlink:label="note-0280-02" xlink:href="note-0280-02a" xml:space="preserve">12. Ar-
                <lb/>
              chim. ib.
                <lb/>
              à Comãd.
                <lb/>
              reſtit.</note>
            quodcunque planum E B G baſim portionis E H G I ſecans per rectam E
              <lb/>
            G, ſectionis portio plana E B G erit ea, quæ ſolidum genuit, cuius
              <note symbol="c" position="left" xlink:label="note-0280-03" xlink:href="note-0280-03a" xml:space="preserve">ibidem.</note>
            eadem E G, axis verò ipſe B K, & </s>
            <s xml:id="echoid-s7845" xml:space="preserve">ad baſim E H G I recta erit. </s>
            <s xml:id="echoid-s7846" xml:space="preserve">
              <note symbol="d" position="left" xlink:label="note-0280-04" xlink:href="note-0280-04a" xml:space="preserve">18. vnd.
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              Elem.</note>
            primò, &</s>
            <s xml:id="echoid-s7847" xml:space="preserve">c.</s>
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