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

Table of contents

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[121.] THEOR. XXVI. PROP. XXXXVIII.
Page: 108 (84)
[122.] MONITVM.
Page: 111 (87)
[123.] THEOR. XXVII. PROP. XXXXIX.
Page: 112 (88)
[124.] THEOR. XXVIII. PROP. L.
Page: 113 (89)
[125.] COROLL.
Page: 113 (89)
[126.] PROBL. XVII. PROP. LI.
Page: 114 (90)
[127.] PROBL. XVIII. PROP. LII.
Page: 115 (91)
[128.] ALITER.
Page: 116 (92)
[129.] ALITER breuiùs.
Page: 117 (93)
[130.] PROBL. XIX. PROP. LIII.
Page: 117 (93)
[131.] ALITER.
Page: 118 (94)
[132.] ALITER breuiùs.
Page: 119 (95)
[133.] PROBL. XX. PROP. LIV.
Page: 119 (95)
[134.] ALITER breuiùs.
Page: 120 (96)
[135.] PROBL. XXI. PROP. LV.
Page: 121 (97)
[136.] PROBL. XXII. PROP. LVI.
Page: 123 (99)
[137.] COROLL. I.
Page: 125 (101)
[138.] COROLL. II.
Page: 125 (101)
[139.] PROBL. XXIII. PROP. LVII.
Page: 125 (101)
[140.] COROLL.
Page: 126 (102)
[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)
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          <head xml:id="echoid-head140" xml:space="preserve">PROBL. XXI. PROP. LV.</head>
          <p>
            <s xml:id="echoid-s3268" xml:space="preserve">Datæ Hyperbolæ, per punctum intra ipſam datum, cum dato
              <lb/>
            ſemi-tranſuerſo latere, quodtamen non excedat diſtantiam inter
              <lb/>
            datum punctum, & </s>
            <s xml:id="echoid-s3269" xml:space="preserve">datæ ſectionis centrum, MAXIMAM Hyper-
              <lb/>
            bolen inſcribere: </s>
            <s xml:id="echoid-s3270" xml:space="preserve">& </s>
            <s xml:id="echoid-s3271" xml:space="preserve">è contra.</s>
            <s xml:id="echoid-s3272" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3273" xml:space="preserve">Datæ Hyperbolæ, per punctum extra ipſam datum, cum dato
              <lb/>
            ſemi-tranſuerſo latere MINIMAM Hyperbolen circumſcribere.</s>
            <s xml:id="echoid-s3274" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3275" xml:space="preserve">Oportet autem datum punctum, vel eſſe in angulo aſymptotali,
              <lb/>
            vel in eo, qui eſt ad verticem; </s>
            <s xml:id="echoid-s3276" xml:space="preserve">& </s>
            <s xml:id="echoid-s3277" xml:space="preserve">ſi in primò caſu, neceſſe eſt, vt ſe-
              <lb/>
            mi-tranſuerſum excedat interuallum inter datum punctum, & </s>
            <s xml:id="echoid-s3278" xml:space="preserve">cen-
              <lb/>
            trum datæ ſectionis: </s>
            <s xml:id="echoid-s3279" xml:space="preserve">in ſecundò verò ſit cuiuslibet longitudinis.</s>
            <s xml:id="echoid-s3280" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3281" xml:space="preserve">ESto Hyperbole ABC, cuius centrum D, & </s>
            <s xml:id="echoid-s3282" xml:space="preserve">datum intra ipſam punctum
              <lb/>
            ſit E: </s>
            <s xml:id="echoid-s3283" xml:space="preserve">oporret primò per E, cum dato ſemi-tranſuerſo EF (quod ſit mi-
              <lb/>
            nus interuallo ED) _MAXIMAM_ Hyperbolen inſcribere.</s>
            <s xml:id="echoid-s3284" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3285" xml:space="preserve">Iungatur E D
              <lb/>
              <figure xlink:label="fig-0121-01" xlink:href="fig-0121-01a" number="86">
                <image file="0121-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0121-01"/>
              </figure>
            ſecans ABC in B,
              <lb/>
            & </s>
            <s xml:id="echoid-s3286" xml:space="preserve">ex ipſa ED de-
              <lb/>
            matur EF æ qualis
              <lb/>
            dato ſemi- tranſ-
              <lb/>
            uerſo, & </s>
            <s xml:id="echoid-s3287" xml:space="preserve">per ver-
              <lb/>
            ticem E, cum cẽ-
              <lb/>
            tro F adſeribatur
              <lb/>
            ſectioni A B
              <note symbol="a" position="right" xlink:label="note-0121-01" xlink:href="note-0121-01a" xml:space="preserve">6. huius.</note>
            Hyperbole EG ſi-
              <lb/>
            milis datæ ABC;
              <lb/>
            </s>
            <s xml:id="echoid-s3288" xml:space="preserve">quæ (cum habeat
              <lb/>
            centrum F, velin
              <lb/>
            ipſo D, ſinempe datum ſemi-tran ſuerſum EF æquale fuerit iunctæ ED, vel
              <lb/>
            infra idem centrum D, ſi datum fuerit ipſa ED minus) erit datæ
              <note symbol="b" position="right" xlink:label="note-0121-02" xlink:href="note-0121-02a" xml:space="preserve">48. h.</note>
            læ ABC inſcripta. </s>
            <s xml:id="echoid-s3289" xml:space="preserve">Dico hanc eſſe _MAXIMAM_ quæſitam.</s>
            <s xml:id="echoid-s3290" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3291" xml:space="preserve">Quoniam quælibet alia per verticem E, cum eodem tranſuerſo EF adſcri-
              <lb/>
            pta, ſed cum recto, quod ſit minus recto ſectionis EG, ipſa EG minor eſt;</s>
            <s xml:id="echoid-s3292" xml:space="preserve">
              <note symbol="c" position="right" xlink:label="note-0121-03" xlink:href="note-0121-03a" xml:space="preserve">2. Co-
                <lb/>
              roll. 19. h.</note>
            quæ verò cum recto, quod ipſum excedat qualis eſt EL eſt quidem
              <note symbol="d" position="right" xlink:label="note-0121-04" xlink:href="note-0121-04a" xml:space="preserve">ibidem.</note>
            eadem EG, ſed omnino ſecat circumſcriptam ABC. </s>
            <s xml:id="echoid-s3293" xml:space="preserve">Nam ducta FI aſym-
              <lb/>
            ptoto ſectionis EG, & </s>
            <s xml:id="echoid-s3294" xml:space="preserve">FM ſectionis EL, (quæ FM cadet extra E I, vt patet
              <lb/>
            ex vltima parte 37. </s>
            <s xml:id="echoid-s3295" xml:space="preserve">huius) ac DH ſectionis ABC: </s>
            <s xml:id="echoid-s3296" xml:space="preserve">erunt DH, FI inter ſe
              <note symbol="e" position="right" xlink:label="note-0121-05" xlink:href="note-0121-05a" xml:space="preserve">48. h.</note>
            rallelę, ſed FM aſymptotos EL producta ſecatur à DH, cum ſecetur quoque
              <lb/>
            ab altera parallelarum in F, quare ipſa DH ſecabit Hyperbolen EL; </s>
            <s xml:id="echoid-s3297" xml:space="preserve">
              <note symbol="f" position="right" xlink:label="note-0121-06" xlink:href="note-0121-06a" xml:space="preserve">35. h.</note>
            DH tota cadit extra ABC, cum ſit eius aſymptotos, ideò occurſus rectę DH
              <lb/>
            cum ſectione EL, erit extra ipſam ABC, vnde EL neceſſariò ſecabit priùs
              <lb/>
            circumſcriptam ABC. </s>
            <s xml:id="echoid-s3298" xml:space="preserve">Erit ergo EG _MAXIMA_ inſcripta quæſita, cum da-
              <lb/>
            to ſemi tranſuerſo EF. </s>
            <s xml:id="echoid-s3299" xml:space="preserve">Quod primò erat, &</s>
            <s xml:id="echoid-s3300" xml:space="preserve">c.</s>
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