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

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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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          <head xml:id="echoid-head241" xml:space="preserve">THEOR. X. PROP. XIV.</head>
          <p>
            <s xml:id="echoid-s5574" xml:space="preserve">Si in Hyperbola ſumpta fuerint duo quælibet puncta, è quo-
              <lb/>
            rum vno ducta ſit recta linea, alteri aſymptoto æquidiſtans,
              <lb/>
            aliamque ſecans; </s>
            <s xml:id="echoid-s5575" xml:space="preserve">ex reliquo verò alia vtranque aſymptoton di-
              <lb/>
            uidens in angulo, qui aſymptotali deinceps eſt, à qua, producta
              <lb/>
            in angulo ad verticem aſymptotalis, ſumatur ęqualis ei, quę ex
              <lb/>
            ipſa inter prædictum punctum, & </s>
            <s xml:id="echoid-s5576" xml:space="preserve">alteram aſymptoton interci-
              <lb/>
            pitur, atque ex ſumptæ termino ducta ſit parallela ei aſympto-
              <lb/>
            to, cui prima eductarum occurrit, hanc ipſam ſecans: </s>
            <s xml:id="echoid-s5577" xml:space="preserve">recta li-
              <lb/>
            nea huiuſmodi interſectionem iungens cum puncto, in quo ſe-
              <lb/>
            cunda eductarum eam aſymptoton ſecat, cui prima æquidiſtat,
              <lb/>
            rectæ data puncta iungenti æquidiſtabit.</s>
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            <s xml:id="echoid-s5579" xml:space="preserve">SInt in Hyperbola A B, cuius aſymptoti C D, C E, ſumpta duo
              <lb/>
            quæcunque puncta A, B, è quorum altero A ducta ſit A E I alteri
              <lb/>
            aſymptoto C D æquidiſtans, ex B verò quælibet B G F vtranque ſecans
              <lb/>
            in G, & </s>
            <s xml:id="echoid-s5580" xml:space="preserve">F; </s>
            <s xml:id="echoid-s5581" xml:space="preserve">ſectaque G H in directum, & </s>
            <s xml:id="echoid-s5582" xml:space="preserve">æquali ipſi B F, ducatur ex H
              <lb/>
            recta H I parallela ad C E occurrens cum productis D C, A E in L, & </s>
            <s xml:id="echoid-s5583" xml:space="preserve">
              <lb/>
            I. </s>
            <s xml:id="echoid-s5584" xml:space="preserve">Dico iunctas A B, F I eſſe inter ſe parallelas.</s>
            <s xml:id="echoid-s5585" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s5586" xml:space="preserve">Ducta enim B D parallela ad C E, iunctaque D E, cum ſit B F æqua-
              <lb/>
            lis G H, erit quoque D F æqualis C L, ob parallelas D B, G E, HI, ſed
              <lb/>
            eſt C L æqualis ipſi E I, quare D F, & </s>
            <s xml:id="echoid-s5587" xml:space="preserve">E I æquales erunt, ſuntque etiam
              <lb/>
            parallelæ, ergo F I æquidiſtat ipſi D E, ſed eſt A B æquidiſtans
              <note symbol="a" position="right" xlink:label="note-0199-01" xlink:href="note-0199-01a" xml:space="preserve">13. h.</note>
            D E, quare F I, & </s>
            <s xml:id="echoid-s5588" xml:space="preserve">A B ſunt quoque inter ſe parallelæ. </s>
            <s xml:id="echoid-s5589" xml:space="preserve">Quod, &</s>
            <s xml:id="echoid-s5590" xml:space="preserve">c.</s>
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