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

Table of contents

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[151.] LEMMA VII. PROP. LXVI.
[152.] SCHOLIVM.
[153.] PROBL. XXV. PROP. LXVII.
[154.] MONITVM.
[155.] PROBL. XXVI. PROP. LXVIII.
[156.] PROBL. XXVII. PROP. LXIX.
[157.] PROBL. XXVIII. PROP. LXX.
[158.] LEMMA VIII. PROP. LXXI.
[159.] LEMMA IX. PROP. LXXII.
[160.] PROBL. XXIX. PROP. LXXIII.
[161.] LEMMA X. PROP. LXXIV.
[162.] PROBL. XXX. PROP. LXXV.
[163.] COROLL. I.
[164.] COROLL. II.
[165.] MONITVM.
[166.] THEOR. XXXVI. PROP. LXXVI.
[167.] SCHOLIVM.
[168.] THEOR. XXXVII. PROP. LXXVII.
[169.] PROBL. XXXI. PROP. LXXVIII.
[170.] MONITVM.
[171.] LEMMA XI. PROP. LXXIX.
[172.] LEMMA XII. PROP. LXXX.
[173.] THEOR. XXXVIII. PROP. LXXXI.
[174.] PROBL. XXXII. PROP. LXXXII.
[175.] COROLL.
[176.] THEOR. XXXIX. PROP. LXXXIII.
[177.] ALITER affirmatiuè.
[178.] PROBL. XXXIII. PROP. LXXXIV.
[179.] SCHOLIVM.
[180.] THEOR. XL. PROP. LXXXV.
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        <div xml:id="echoid-div505" type="section" level="1" n="205">
          <head xml:id="echoid-head210" xml:space="preserve">ADDENDA LIB. I.</head>
          <p style="it">
            <s xml:id="echoid-s4984" xml:space="preserve">IN huius operis contextu, vel etiam in ipſa perſcriptione, quædam
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            ſunt, quæ aut mentem noſtram, aut Amanuenſis, quamuis accura-
              <lb/>
            tiſsimi, oculum effugerant: </s>
            <s xml:id="echoid-s4985" xml:space="preserve">itaque ſub calcem vniuſcuiuſque libri eadem ſic
              <lb/>
            addere liceat.</s>
            <s xml:id="echoid-s4986" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div506" type="section" level="1" n="206">
          <head xml:id="echoid-head211" xml:space="preserve">Pag. 74. ad finem Prim. Coroll.</head>
          <p>
            <s xml:id="echoid-s4987" xml:space="preserve">Quapropter huiuſmodi Parabolæ iuxta has interceptas lineas diametro B
              <lb/>
            E parallelas, ſunt ſemper inter ſe ęquidiſtantes, licet iuxta intercepta appli-
              <lb/>
            catarum ſegmenta A E, I D, L M, & </s>
            <s xml:id="echoid-s4988" xml:space="preserve">ad eaſdem partes A I, E D ſint ſem-
              <lb/>
            per ſimul accedentes, nunquam verò coeuntes.</s>
            <s xml:id="echoid-s4989" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div507" type="section" level="1" n="207">
          <head xml:id="echoid-head212" xml:space="preserve">Ad calcem Pag. 78.
            <lb/>
          COROLL. II.</head>
          <p>
            <s xml:id="echoid-s4990" xml:space="preserve">PAtet denique congruentes Hyperbolas per diuerſos vèrtices ſimul ad-
              <lb/>
            ſcriptas, & </s>
            <s xml:id="echoid-s4991" xml:space="preserve">ad eaſdem partes productas, eſſe inter ſe, & </s>
            <s xml:id="echoid-s4992" xml:space="preserve">ſimul ſemper ma-
              <lb/>
            gis accedentes, & </s>
            <s xml:id="echoid-s4993" xml:space="preserve">ſemper æquidiſtantes. </s>
            <s xml:id="echoid-s4994" xml:space="preserve">Nam iuxta intercepta applicata-
              <lb/>
            rum ſegmenta A E, S D, X Y, in præcedentibus figuris huiuſmodi Hyper-
              <lb/>
            bolæ ſemper fiunt propiores, licet nunquam ſimul conueniant; </s>
            <s xml:id="echoid-s4995" xml:space="preserve">iuxta autem
              <lb/>
            rectas B E, M D, Z Y, ad eaſdem partes A S, E D, perpetuam ſeruant ęqui-
              <lb/>
            diſtantiam, cum ipſæ B E, M D, Z Y inter ſe æquales ſint oſtenſæ, &</s>
            <s xml:id="echoid-s4996" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4997" xml:space="preserve"/>
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        <div xml:id="echoid-div508" type="section" level="1" n="208">
          <head xml:id="echoid-head213" xml:space="preserve">Pag. 87. ad finem Moniti.</head>
          <p style="it">
            <s xml:id="echoid-s4998" xml:space="preserve">atque item congruentes Hyperbolæ, &</s>
            <s xml:id="echoid-s4999" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5000" xml:space="preserve">prout in 2. </s>
            <s xml:id="echoid-s5001" xml:space="preserve">Coroll. </s>
            <s xml:id="echoid-s5002" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s5003" xml:space="preserve">quadrageſi-
              <lb/>
            quartæ monuimus.</s>
            <s xml:id="echoid-s5004" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div509" type="section" level="1" n="209">
          <head xml:id="echoid-head214" xml:space="preserve">Pag. 123. poſt Prop. 77.
            <lb/>
          Aliter idem, ac Vniuerſaliùs.</head>
          <p>
            <s xml:id="echoid-s5005" xml:space="preserve">MAXIMÆ ſimiles Ellipſes, Parabolæ inſcriptę, & </s>
            <s xml:id="echoid-s5006" xml:space="preserve">à vertice
              <lb/>
            ſucceſſiuè ſe mutuò contingentes, ſunt inter ſe in ratione quadra-
              <lb/>
            torum, diſparium numerorum ab vnitate incipientium.</s>
            <s xml:id="echoid-s5007" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5008" xml:space="preserve">ESto Parabole A B C, cuius diameter B D, latus rectum B E, & </s>
            <s xml:id="echoid-s5009" xml:space="preserve">circa
              <lb/>
            quodlibet diametri ſegmentum B F ſit ipſi Parabolæ per verticem E
              <lb/>
            inicripta _MAXIMA_ Ellipſis B F (quę erit illa, cuius rectum latus idem
              <note symbol="*" position="right" xlink:label="note-0175-01" xlink:href="note-0175-01a" xml:space="preserve">20. h.</note>
            ac rectum B E) & </s>
            <s xml:id="echoid-s5010" xml:space="preserve">applicata ex F ad diametrum recta H F G, ſumptaque
              <lb/>
            F I æquali ipſi F B, ducatur diagonalis G I L, ex L applicetur L M </s>
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