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

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[141.] THEOR. XXIX. PROP. LIIX.
Page: 126 (102)
[142.] ALITER.
Page: 126 (102)
[143.] THEOR. XXX. PROP. LIX.
Page: 127 (103)
[144.] THEOR. XXXI. PROP. LX.
Page: 127 (103)
[145.] THEOR. XXXII. PROP. LXI.
Page: 128 (104)
[146.] THEOR. XXXIII. PROP. LXII.
Page: 129 (105)
[147.] SCHOLIVM.
Page: 130 (106)
[148.] THEOR. XXXIV. PROP. LXIII.
Page: 131 (107)
[149.] THEOR. XXXV. PROP. LXIV.
Page: 131 (107)
[150.] PROBL. XXIV. PROP. LXV.
Page: 132 (108)
[151.] LEMMA VII. PROP. LXVI.
Page: 133 (109)
[152.] SCHOLIVM.
Page: 133 (109)
[153.] PROBL. XXV. PROP. LXVII.
Page: 134 (110)
[154.] MONITVM.
Page: 134 (110)
[155.] PROBL. XXVI. PROP. LXVIII.
Page: 135 (111)
[156.] PROBL. XXVII. PROP. LXIX.
Page: 137 (113)
[157.] PROBL. XXVIII. PROP. LXX.
Page: 138 (114)
[158.] LEMMA VIII. PROP. LXXI.
Page: 139 (115)
[159.] LEMMA IX. PROP. LXXII.
Page: 140 (116)
[160.] PROBL. XXIX. PROP. LXXIII.
Page: 141 (117)
[161.] LEMMA X. PROP. LXXIV.
Page: 141 (117)
[162.] PROBL. XXX. PROP. LXXV.
Page: 142 (118)
[163.] COROLL. I.
Page: 143 (119)
[164.] COROLL. II.
Page: 143 (119)
[165.] MONITVM.
Page: 143 (119)
[166.] THEOR. XXXVI. PROP. LXXVI.
Page: 144 (120)
[167.] SCHOLIVM.
Page: 145 (121)
[168.] THEOR. XXXVII. PROP. LXXVII.
Page: 146 (122)
[169.] PROBL. XXXI. PROP. LXXVIII.
Page: 147 (123)
[170.] MONITVM.
Page: 148 (124)
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          <head xml:id="echoid-head165" xml:space="preserve">PROBL. XXIX. PROP. LXXIII.</head>
          <p>
            <s xml:id="echoid-s3944" xml:space="preserve">Dato angulo rectilineo, per punctum in qualibet eius diametro
              <lb/>
            datum, MAXIMAM Ellipſim inſcribere, cuius latera datam ha-
              <lb/>
            beant rationem.</s>
            <s xml:id="echoid-s3945" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3946" xml:space="preserve">SIt datus angulus ABC, diameter BD, & </s>
            <s xml:id="echoid-s3947" xml:space="preserve">datum punctum D, per quod
              <lb/>
            oporteat Ellipſim inſcribere, cuius tranſuerſum latus ad rectum, datam
              <lb/>
            quamcunque habeat rationem E ad F, & </s>
            <s xml:id="echoid-s3948" xml:space="preserve">ſit _MAXIMA_.</s>
            <s xml:id="echoid-s3949" xml:space="preserve"/>
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            <s xml:id="echoid-s3950" xml:space="preserve">Applicetur per D, ordinatim GDH, &</s>
            <s xml:id="echoid-s3951" xml:space="preserve">
              <note symbol="a" position="right" xlink:label="note-0141-01" xlink:href="note-0141-01a" xml:space="preserve">66. h.</note>
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            per H ducatur HIL diametrum ſecans in I, & </s>
            <s xml:id="echoid-s3952" xml:space="preserve">
              <lb/>
            BA in L, ita vt ex I, & </s>
            <s xml:id="echoid-s3953" xml:space="preserve">L ductis A I, LM ipſi
              <lb/>
            DH parallelis, rectangulum DIM, ad quadra-
              <lb/>
            tum AI, rationem habeat E ad F, & </s>
            <s xml:id="echoid-s3954" xml:space="preserve">cum
              <note symbol="b" position="right" xlink:label="note-0141-02" xlink:href="note-0141-02a" xml:space="preserve">72. h.</note>
            uerſo DM, per extrema applicatæ AC, Elli-
              <lb/>
            pſis deſcribatur DAMC. </s>
            <s xml:id="echoid-s3955" xml:space="preserve">Dico hanc
              <note symbol="c" position="right" xlink:label="note-0141-03" xlink:href="note-0141-03a" xml:space="preserve">Coroll.
                <lb/>
              57. h.</note>
            _MAXIMAM_ quæſitam.</s>
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            <s xml:id="echoid-s3957" xml:space="preserve">Eſt enim LB ad BG, ſiue MB ad BD,
              <note symbol="d" position="right" xlink:label="note-0141-04" xlink:href="note-0141-04a" xml:space="preserve">71. h.</note>
            LA ad AG, ſiue vt MI ad ID, quare BA, BC
              <lb/>
            Ellipſim contingent, ideoque ipſa erit
              <note symbol="e" position="right" xlink:label="note-0141-05" xlink:href="note-0141-05a" xml:space="preserve">34. pri.
                <lb/>
              conic.</note>
            lo inſcripta, eritque _MAXIMA_, vt in præce-
              <lb/>
            dentibus oſtenſum fuit. </s>
            <s xml:id="echoid-s3958" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s3959" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3960" xml:space="preserve"/>
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          <head xml:id="echoid-head166" xml:space="preserve">LEMMA X. PROP. LXXIV.</head>
          <p>
            <s xml:id="echoid-s3961" xml:space="preserve">Datis medijs proportionalibus, Arithmetica nempe, & </s>
            <s xml:id="echoid-s3962" xml:space="preserve">Geo-
              <lb/>
            metrica inter eaſdem ignotas extremas; </s>
            <s xml:id="echoid-s3963" xml:space="preserve">ipſas extremas inuenire.</s>
            <s xml:id="echoid-s3964" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3965" xml:space="preserve">SIt AB media arithmetica, & </s>
            <s xml:id="echoid-s3966" xml:space="preserve">AC media
              <lb/>
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            geometrica inter duas eaſdem ignotas
              <lb/>
            extremas, quarum idem ſit terminus A, & </s>
            <s xml:id="echoid-s3967" xml:space="preserve">
              <lb/>
            ſimul congruere intelligantur: </s>
            <s xml:id="echoid-s3968" xml:space="preserve">patet primò
              <lb/>
            AB ſuperare ipſam AC, cum media ari-
              <lb/>
            thmetica ſit maior media geometrica. </s>
            <s xml:id="echoid-s3969" xml:space="preserve">Iam
              <lb/>
            oporteat datis AC, AB ignotas extremas
              <lb/>
            proportionales inuenire.</s>
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          <p>
            <s xml:id="echoid-s3971" xml:space="preserve">Fiat centro A interuallo A C circulus
              <lb/>
            CF, cui ex puncto B contingens ducatur
              <lb/>
            BF, quæ eum radio FA rectum efficiet an-
              <lb/>
            gulum, vnde ſubtenſa BA erit maior ipſa
              <lb/>
            BF; </s>
            <s xml:id="echoid-s3972" xml:space="preserve">ſi ergo cum centro B, interuallo BF
              <lb/>
            deſcribatur ſemi- circulus DFE, ipſæ ſeca-
              <lb/>
            bit BA infra A, ſed tamen vltra C (cum ſit
              <lb/>
            BC minor BF, eo quod AC æquatur AF,
              <lb/>
            &</s>
            <s xml:id="echoid-s3973" xml:space="preserve">tota AB minor eſt duobus AF, FB) ſecabitque productam AB in E; </s>
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