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

Table of contents

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[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)
[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)
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            BGL erit diameter, tum datæ Hyperbolæ, tum deſcripti anguli; </s>
            <s xml:id="echoid-s3839" xml:space="preserve">& </s>
            <s xml:id="echoid-s3840" xml:space="preserve">cum GH,
              <lb/>
            GI, per punctum G, in Hyperbola ſumptum, ductæ ſint aſymptotis æquidi-
              <lb/>
            ſtantes, ipſæ, ad partes B productæ, Hyperbolæ occurrent, cum aſymptotos
              <lb/>
            ſecent, ſed ad partes H, I, nunquam cum ſectione conuenient, at
              <note symbol="a" position="left" xlink:label="note-0138-01" xlink:href="note-0138-01a" xml:space="preserve">Coroll.
                <lb/>
              11. huius.</note>
            que ducatur ex G extra angulum HGI, ſecabit producta alteram aſympto-
              <lb/>
            ton (cum ſecet in G ipſi parallelam GH) ac ideò priùs Hyperbolen datam:
              <lb/>
            </s>
            <s xml:id="echoid-s3841" xml:space="preserve">eſt igitur HGI _MAXIMV S_ inſcriptus angulus, vti quærebatur. </s>
            <s xml:id="echoid-s3842" xml:space="preserve">Quod primò
              <lb/>
            erat, &</s>
            <s xml:id="echoid-s3843" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3844" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3845" xml:space="preserve">IAM ſit datus angulus HGI, & </s>
            <s xml:id="echoid-s3846" xml:space="preserve">datum punctum ſit B, in angulo tamen, qui
              <lb/>
            ei eſt ad verticem: </s>
            <s xml:id="echoid-s3847" xml:space="preserve">oportet per B _MINIMAM_ Hyperbolen circumſcribe-
              <lb/>
            re, cum dato ſemi- tranſuerſo R.</s>
            <s xml:id="echoid-s3848" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3849" xml:space="preserve">Iungatur GB, & </s>
            <s xml:id="echoid-s3850" xml:space="preserve">producatur, ſu-
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                <image file="0138-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0138-01"/>
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            maturque B D æqualis R; </s>
            <s xml:id="echoid-s3851" xml:space="preserve">& </s>
            <s xml:id="echoid-s3852" xml:space="preserve">per D
              <lb/>
            agantur DE, DF, ipſis GH, GI pa-
              <lb/>
            rallelæ, & </s>
            <s xml:id="echoid-s3853" xml:space="preserve">per B cum afymptotis
              <lb/>
            DE, DF deſcribatur
              <note symbol="b" position="left" xlink:label="note-0138-02" xlink:href="note-0138-02a" xml:space="preserve">4. ſec.
                <lb/>
              conic.</note>
            ABC, Dico hanc eſſe _MINIMAM_
              <lb/>
            circumſcriptam quæſitam.</s>
            <s xml:id="echoid-s3854" xml:space="preserve"/>
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            <s xml:id="echoid-s3855" xml:space="preserve">Nam eadem ratione, vt ſupra.</s>
            <s xml:id="echoid-s3856" xml:space="preserve">,
              <lb/>
            oſtendetur DBGL eſſe diametrum
              <lb/>
            ſectionis, & </s>
            <s xml:id="echoid-s3857" xml:space="preserve">dati anguli, & </s>
            <s xml:id="echoid-s3858" xml:space="preserve">rectas
              <lb/>
            GH, GI, ad partes H, I productas (cum aſymptotis æquidiſtent) nunquam
              <lb/>
            cum ſectione conuenire; </s>
            <s xml:id="echoid-s3859" xml:space="preserve">ideoque Hyperbolen ABC dato angulo eſſe circũ-
              <lb/>
            ſcriptam: </s>
            <s xml:id="echoid-s3860" xml:space="preserve">ſed eſt quoque _MINIMA_, quoniam, quæ cum eodem tranſuerſo
              <lb/>
            adſcribitur, ſed cum recto maiori, maioreſt ipſa ABC; </s>
            <s xml:id="echoid-s3861" xml:space="preserve">quæ verò cum
              <note symbol="c" position="left" xlink:label="note-0138-03" xlink:href="note-0138-03a" xml:space="preserve">2. Co-
                <lb/>
              roll. 19. h.</note>
            cto minori, qualis eſt MBN, eſt quidem minor ABC, ſed omnino ſecat
              <note symbol="d" position="left" xlink:label="note-0138-04" xlink:href="note-0138-04a" xml:space="preserve">ibidem.</note>
            tera dati anguli: </s>
            <s xml:id="echoid-s3862" xml:space="preserve">quoniam ducta DO, quæ ſit aſymptotos inſcriptæ MBN,
              <lb/>
            ipſa cadet infra DE, ſed eam ſecat in D, quare producta, alteram
              <note symbol="e" position="left" xlink:label="note-0138-05" xlink:href="note-0138-05a" xml:space="preserve">ex 37. h.</note>
            lam ſecabit GH, ſed DO tota cadit extra BM, vnde occurſus DO cum GH
              <lb/>
            erit extra BM; </s>
            <s xml:id="echoid-s3863" xml:space="preserve">ſiue GH neceſſariò ſecabit priùs ſectionem BM. </s>
            <s xml:id="echoid-s3864" xml:space="preserve">Eſt igitur ſe-
              <lb/>
            ctio MBN _MINIMA_ circumſcripta quæſita dato angulo HGI, per datum
              <lb/>
            punctum B, & </s>
            <s xml:id="echoid-s3865" xml:space="preserve">cum dato ſemi-tranſuerſo R. </s>
            <s xml:id="echoid-s3866" xml:space="preserve">Quod vltimò faciendum erat.</s>
            <s xml:id="echoid-s3867" xml:space="preserve"/>
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        <div xml:id="echoid-div372" type="section" level="1" n="157">
          <head xml:id="echoid-head162" xml:space="preserve">PROBL. XXVIII. PROP. LXX.</head>
          <p>
            <s xml:id="echoid-s3868" xml:space="preserve">Dato angulo rectilineo, per punctum intra ipſum datum, cum
              <lb/>
            dato tranſuerſo latere, MAXIMAM Ellipſim inſcribere: </s>
            <s xml:id="echoid-s3869" xml:space="preserve">& </s>
            <s xml:id="echoid-s3870" xml:space="preserve">è con-
              <lb/>
            tra.</s>
            <s xml:id="echoid-s3871" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3872" xml:space="preserve">SIt datus angulus ABC, & </s>
            <s xml:id="echoid-s3873" xml:space="preserve">punctum intra ipſum ſit D, per quod ei opor-
              <lb/>
            teat, cum dato tranſuerſo R, _MAXIMAM_ Ellipſim inſcribere.</s>
            <s xml:id="echoid-s3874" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3875" xml:space="preserve">Sumatur DE ęqualis R, & </s>
            <s xml:id="echoid-s3876" xml:space="preserve">per D, & </s>
            <s xml:id="echoid-s3877" xml:space="preserve">E in angulo ABC applicentur
              <note symbol="a" position="left" xlink:label="note-0138-06" xlink:href="note-0138-06a" xml:space="preserve">66. h.</note>
            HEL, & </s>
            <s xml:id="echoid-s3878" xml:space="preserve">iungatur HG diametrum ſecans in M, per quod applicetur AMD,
              <lb/>
            & </s>
            <s xml:id="echoid-s3879" xml:space="preserve">circa diametrum DE, ac per terminos applicatæ AC, deſcribatur
              <note symbol="b" position="left" xlink:label="note-0138-07" xlink:href="note-0138-07a" xml:space="preserve">Coroll.
                <lb/>
              57. h.</note>
            DAEC. </s>
            <s xml:id="echoid-s3880" xml:space="preserve">Dico hanc eſſe _MAXIMAM_ quæſitam. </s>
            <s xml:id="echoid-s3881" xml:space="preserve">Quoniam, ipſa ADCE eſt
              <lb/>
            menſali HFGL, ſiue dato angulo inſcripta, & </s>
            <s xml:id="echoid-s3882" xml:space="preserve">quælibet alia Ellipſis
              <note symbol="c" position="left" xlink:label="note-0138-08" xlink:href="note-0138-08a" xml:space="preserve">Schol.
                <lb/>
              62. h.</note>
            </s>
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