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

Table of contents

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[191.] THEOR. XLV. PROP. XCI.
Page: 163 (139)
[192.] COROLL. I.
Page: 164 (140)
[193.] COROLL. II.
Page: 164 (140)
[194.] THEOR. XLVI. PROP. XCII.
Page: 165 (141)
[195.] THEOR. XLVIII. PROP. XCIII.
Page: 166 (142)
[196.] PROBL. XXXIV. PROP. XCIV.
Page: 168 (144)
[197.] PROBL. XXXV. PROP. XCV.
Page: 169 (145)
[198.] PROBL. XXXVI. PROP. XCVI.
Page: 169 (145)
[199.] THEOR. XLVIII. PROP. XCVII.
Page: 170 (146)
[200.] COROLL.
Page: 171 (147)
[201.] THEOR. IL. PROP. IIC.
Page: 172 (148)
[202.] THEOR. L. PROP. IC.
Page: 172 (148)
[203.] THEOR. LI. PROP. C.
Page: 173 (149)
[204.] PRIMI LIBRI FINIS.
Page: 174 (150)
[205.] ADDENDA LIB. I.
Page: 175 (151)
[206.] Pag. 74. ad finem Prim. Coroll.
Page: 175 (151)
[207.] Ad calcem Pag. 78. COROLL. II.
Page: 175 (151)
[208.] Pag. 87. ad finem Moniti.
Page: 175 (151)
[209.] Pag. 123. poſt Prop. 77. Aliter idem, ac Vniuerſaliùs.
Page: 175 (151)
[210.] COROLL.
Page: 177 (153)
[211.] Pag. 131. poſt Prop. 84.
Page: 177 (153)
[212.] Pag. 144. ad calcem Prop. 93.
Page: 177 (153)
[213.] SCHOLIVM.
Page: 177 (153)
[214.] Pag. 147. ad finem Prop. 97.
Page: 178 (154)
[215.] FINIS.
Page: 178 (154)
[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.
Page: 179
[217.] FLORENTIÆ MDCLIX. Apud Ioſeph Cocchini, Typis Nouis, ſub Signo STELLÆ. _SVPERIORVM PERMISSV._
Page: 179
[218.] SERENISSIMO PRINCIPI LEOPOLODO AB ETRVRIA.
Page: 181
[219.] VINCENTII VIVIANI DE MAXIMIS, ET MINIMIS Geometrica diuinatio in V. conic. Apoll. Pergæi. LIBER SECVNDVS. LEMMA I. PROP. I.
Page: 183 (1)
[220.] LEMMA II. PROP. II.
Page: 183 (1)
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          <head xml:id="echoid-head311" xml:space="preserve">PROBL. XI. PROP. LX.</head>
          <p>
            <s xml:id="echoid-s7240" xml:space="preserve">A puncto intra ſphæram dato, ad eius concauam ſuperficiem,
              <lb/>
            _MAXIMAM, & </s>
            <s xml:id="echoid-s7241" xml:space="preserve">MINIMAM rectam lineam ducere._</s>
            <s xml:id="echoid-s7242" xml:space="preserve"/>
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            <s xml:id="echoid-s7243" xml:space="preserve">ESto ſphæra, cuius centrum A, & </s>
            <s xml:id="echoid-s7244" xml:space="preserve">oporteat per datum intra ipſam pun-
              <lb/>
            ctum B ad concauam ſphæræ ſuperficiem _MAXIMAM_, & </s>
            <s xml:id="echoid-s7245" xml:space="preserve">_MINIMAM_
              <lb/>
            rectam lineam ducere.</s>
            <s xml:id="echoid-s7246" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7247" xml:space="preserve">Si punctum B fuerit in centro ſphæræ, patet tunc neque _MAXIMAM,_
              <lb/>
            neque _MINIMAM_ dari, cum omnes eductæ à centro ad ſphærę ſuperficiem
              <lb/>
            ſint æquales.</s>
            <s xml:id="echoid-s7248" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7249" xml:space="preserve">Si autem datum punctum fuerit præter cen-
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            trum: </s>
            <s xml:id="echoid-s7250" xml:space="preserve">iungatur cum centro A recta B A, quæ
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            hinc inde producta occurrat ſphęricæ ſuperficiei
              <lb/>
            in punctis C, D. </s>
            <s xml:id="echoid-s7251" xml:space="preserve">Dico B D, in quà eſt centrum,
              <lb/>
            eſſe _MAXIMAM_, reliquam B C _MINIMAM_.</s>
            <s xml:id="echoid-s7252" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7253" xml:space="preserve">Si enim circà axim C D intelligatur quicun-
              <lb/>
            que _MAXIMVS_ ſphæræ circulus C D F: </s>
            <s xml:id="echoid-s7254" xml:space="preserve">patet
              <lb/>
            linearum ex B ad peripheriam C D F ducibi-
              <lb/>
            lium, B D in qua centrum A, eſſe _MAXIMAM_,
              <lb/>
            & </s>
            <s xml:id="echoid-s7255" xml:space="preserve">B C _MINIMAM_.</s>
            <s xml:id="echoid-s7256" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7257" xml:space="preserve">Siverò ducta ſit quælibet alia B E extra peri-
              <lb/>
            pheriam C D F, ſphæricæ ſuperficiei occurrens
              <lb/>
            in E; </s>
            <s xml:id="echoid-s7258" xml:space="preserve">per rectas C D, & </s>
            <s xml:id="echoid-s7259" xml:space="preserve">B E intelligatur pla-
              <lb/>
            num, cuius communis ſectio cum ſphæræ ſuperficie erit cuiuſdam _MAXIMI_
              <lb/>
            circuli peripheria C E D, & </s>
            <s xml:id="echoid-s7260" xml:space="preserve">eius diameter C D: </s>
            <s xml:id="echoid-s7261" xml:space="preserve">quare B D, in qua eſt
              <lb/>
            centrum, cum ſit _MAXIMA_, erit maior B E; </s>
            <s xml:id="echoid-s7262" xml:space="preserve">& </s>
            <s xml:id="echoid-s7263" xml:space="preserve">B C, cum ſit _MINIMA_
              <lb/>
            minor erit eadem B E, & </s>
            <s xml:id="echoid-s7264" xml:space="preserve">hoc ſemper vbicunque pertingat ducta B E: </s>
            <s xml:id="echoid-s7265" xml:space="preserve">ideo-
              <lb/>
            que B D eſt _MAXIMA_ ad vniuerſam ſphæræ ſuperficiem ducibilium ex da-
              <lb/>
            to puncto B, & </s>
            <s xml:id="echoid-s7266" xml:space="preserve">B C _MINIMA_. </s>
            <s xml:id="echoid-s7267" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s7268" xml:space="preserve"/>
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          <head xml:id="echoid-head312" xml:space="preserve">PROBL. XII. PROP. LXI.</head>
          <p>
            <s xml:id="echoid-s7269" xml:space="preserve">A puncto intra Conum rectum, vel Conoides Parabolicum,
              <lb/>
            aut Hyperbolicum dato, ad eius concauam ſuperficiem, MI-
              <lb/>
            NIMAM rectam lineam ducere.</s>
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          <p>
            <s xml:id="echoid-s7271" xml:space="preserve">ESto Conus rectus; </s>
            <s xml:id="echoid-s7272" xml:space="preserve">vt in prima ſigura, vel Conoides Parabolicum, aut
              <lb/>
            Hyperbolicum, vt in ſecunda, cuius axis A B, & </s>
            <s xml:id="echoid-s7273" xml:space="preserve">oporteat per punctum
              <lb/>
            intra ipſum datum ad concauam ſolidi ſuperficiem _MINIMAM_ rectam li-
              <lb/>
            neam ducere.</s>
            <s xml:id="echoid-s7274" xml:space="preserve"/>
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          <note symbol="a" position="left" xml:space="preserve">ex Com
            <lb/>
          ment. Có-
            <lb/>
          mand. in
            <lb/>
          12. Arch.
            <lb/>
          de Co.
            <lb/>
          noid. &
            <lb/>
          Spheroid,</note>
          <p>
            <s xml:id="echoid-s7275" xml:space="preserve">Secetur ſolidum plano per axem A B, ac per datum punctum ducto effi-
              <lb/>
            ciente in ſolidi ſuperficie ſectionem D A E, quæ eadem erit, ac ipſius ſo- lidi genitrix ſectio, & </s>
            <s xml:id="echoid-s7276" xml:space="preserve">in Cono angulum rectilineum conſtituet.</s>
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            <s xml:id="echoid-s7278" xml:space="preserve">Iam ſi datum punctum fuerit in axe; </s>
            <s xml:id="echoid-s7279" xml:space="preserve">vt in H; </s>
            <s xml:id="echoid-s7280" xml:space="preserve">ducta H D, quæ in </s>
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