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

Table of contents

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[211.] Pag. 131. poſt Prop. 84.
[212.] Pag. 144. ad calcem Prop. 93.
[213.] SCHOLIVM.
[214.] Pag. 147. ad finem Prop. 97.
[215.] FINIS.
[216.] DE MAXIMIS, ET MINIMIS GEOMETRICA DIVINATIO In Qvintvm Conicorvm APOLLONII PERGÆI _IAMDIV DESIDERATVM._ AD SER ENISSIMVM PRINCIPEM LEOPOLDVM AB ETRVRIA. LIBER SECVNDVS. _AVCTORE_ VINCENTIO VIVIANI.
[217.] FLORENTIÆ MDCLIX. Apud Ioſeph Cocchini, Typis Nouis, ſub Signo STELLÆ. _SVPERIORVM PERMISSV._
[218.] SERENISSIMO PRINCIPI LEOPOLODO AB ETRVRIA.
[219.] VINCENTII VIVIANI DE MAXIMIS, ET MINIMIS Geometrica diuinatio in V. conic. Apoll. Pergæi. LIBER SECVNDVS. LEMMA I. PROP. I.
[220.] LEMMA II. PROP. II.
[221.] THEOR. I. PROP. III.
[222.] LEMMA III. PROP. IV.
[223.] THEOR. II. PROP. V.
[224.] THEOR. III. PROP. VI.
[225.] LEMMA IV. PROP. VII.
[226.] THEOR. IV. PROP. VIII.
[227.] THEOR. V. PROP. IX.
[228.] SCHOLIVM.
[229.] THEOR. VI. PROP. X.
[230.] THEOR. VII. PROP. XI.
[231.] THEOR. VIII. PROP. XII.
[232.] THEOR. IX. PROP. XIII.
[233.] THEOR. X. PROP. XIV.
[234.] THEOR. XI. PROP. XV.
[235.] LEMMA V. PROP. XVI.
[236.] COROLL.
[237.] THEOR. XII. PROP. XVII.
[238.] THEOR. XIII. PROP. XVIII.
[239.] THEOR. XIV. PROP. XIX.
[240.] PROBL. I. PROP. XX.
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            eiuſdem ſimilis concentrici ſolidi ſuperſiciem contingentium) ergo, & </s>
            <s xml:id="echoid-s8394" xml:space="preserve">por-
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            tio A B F à prædicto plano recto abſciſſa, erit minor eadem portione, quæ
              <lb/>
            dempta fuit à plano per A F, & </s>
            <s xml:id="echoid-s8395" xml:space="preserve">G L ducto, ſiue à plano, quod in conſtru-
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            ctione per A F obliquè ductum fuit ſuper planum per axem A B C: </s>
            <s xml:id="echoid-s8396" xml:space="preserve">& </s>
            <s xml:id="echoid-s8397" xml:space="preserve">hoc
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            ſemper verum eſſe demonſtrabitur, quodcunque ſit planum inclinatum
              <lb/>
            tranſiens per A F; </s>
            <s xml:id="echoid-s8398" xml:space="preserve">ergo portio ſolida A B F, quæ ex dato ſolido à plano
              <lb/>
            per A F ducto, & </s>
            <s xml:id="echoid-s8399" xml:space="preserve">ad planum per axem A B C erecto abſcinditur, _M I N I-_
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            _M A_ eſt omnium portionum à quibuslibet alijs planis per eandem A F du-
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            ctis abſciſſarum. </s>
            <s xml:id="echoid-s8400" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s8401" xml:space="preserve"/>
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        <div xml:id="echoid-div871" type="section" level="1" n="348">
          <head xml:id="echoid-head357" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s8402" xml:space="preserve">EX eo, quod prope finem huius demonſtratum eſt, elicitur, omnem por-
              <lb/>
            tionem cuiuſcunque prædictorum ſolidorum, cuius baſis ſecet ſimile
              <lb/>
            inſcriptum ſolidum concentricum, maiorem eſſe qualibet alia portione de
              <lb/>
            eodem exteriori ſolido, cuius baſis contingat idem inſeriptum ſolidum.</s>
            <s xml:id="echoid-s8403" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8404" xml:space="preserve">Ibienim oſtendimus prædictam exterioris ſolidi portionem, cuius baſis
              <lb/>
            ſecet inſcriptum ſolidum, maiorem eſſe ea, cuius baſis contingens idem in-
              <lb/>
            ſcriptum, ſimul ſit parallela ſecanti baſi; </s>
            <s xml:id="echoid-s8405" xml:space="preserve">ſed omnes portiones de eodem ſo-
              <lb/>
            lido, quarum baſes contingant idem ſimile inſcriptum concentricum, inter
              <lb/>
            ſe ſunt æquales: </s>
            <s xml:id="echoid-s8406" xml:space="preserve">ergo patet propoſitum, &</s>
            <s xml:id="echoid-s8407" xml:space="preserve">c.</s>
            <s xml:id="echoid-s8408" xml:space="preserve"/>
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          <note symbol="a" position="left" xml:space="preserve">Propoſ.
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          80. h.</note>
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          <head xml:id="echoid-head358" xml:space="preserve">PROBL. XV. PROP. LXXXII.</head>
          <p>
            <s xml:id="echoid-s8409" xml:space="preserve">Per datum punctum intra Conum rectum, vel Conoides Para-
              <lb/>
            bolicum, aut Hyperbolicum, ſiue Sphæram, aut Sphæroides ob-
              <lb/>
            longum, vel prolatum, planum ducere, quod de ſolido abſcindat
              <lb/>
            portionem MINIMAM; </s>
            <s xml:id="echoid-s8410" xml:space="preserve">atque in Sphæroide, vel Sphæra portio-
              <lb/>
            nem MAXIMAM.</s>
            <s xml:id="echoid-s8411" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8412" xml:space="preserve">ESto quodlibet prædictorum ſolidorum A B C, cuius axis reuolutionis
              <lb/>
            ſit B D, ac datum vbicunque intra ſolidum ſit punctum E: </s>
            <s xml:id="echoid-s8413" xml:space="preserve">oportet per
              <lb/>
            E planum ducere, quod ex dato ſolido abſcindat portionem _MINIMAM_,
              <lb/>
            atque ampliùs in Sphæroide, vel Sphæra, portionem _MAXIMAM_. </s>
            <s xml:id="echoid-s8414" xml:space="preserve">Opor-
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            tet autem ſi ſolidum fuerit Sphæroides, vel Sphæra, quod datum punctum
              <lb/>
            non ſit idem, ac centrum, tune enim neque _MAXIMA_, neque _MINIMA_
              <lb/>
            portio exhiberi poſſet, cum omnia plana per centra eorum ſolidorum ducta
              <lb/>
            in duas æquas portiones diuidant ipſa ſolida; </s>
            <s xml:id="echoid-s8415" xml:space="preserve">veluti in Ellipſi, vel circulo
              <lb/>
            dum quærebatur _MAXIMA_, & </s>
            <s xml:id="echoid-s8416" xml:space="preserve">_MINIMA_ portio, neceſſe fuit datum pun-
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            ctum non eſſe in centro, cum rectæ omnes per ipſum ductæ, huiuſmodi ſu-
              <lb/>
            perficies bifariam ſecent, vt iam ſatis conſtat.</s>
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          </p>
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            <s xml:id="echoid-s8418" xml:space="preserve">Secetur folidum plano per axem B D, ac per datum punctum E tran-
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            ſeunte, efficienteque in ſolido genitricem ſectionem A B C, quæ
              <note symbol="b" position="left" xlink:label="note-0302-02" xlink:href="note-0302-02a" xml:space="preserve">12. Ar-
                <lb/>
              chim. de
                <lb/>
              Conoid.
                <lb/>
              &c.</note>
            nitè producatur, ac de ipſa per idem punctum E, cum recta F E G </s>
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