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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          <head xml:id="echoid-head277" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s6429" xml:space="preserve">EX hac facilè elicietur methodus, qua precipuas quorumlibet Acumi-
              <lb/>
            natorum paſſiones oſtendi poſſint, nempe: </s>
            <s xml:id="echoid-s6430" xml:space="preserve">ipſa Acuminata à diame-
              <lb/>
            tris bifariam ſecari: </s>
            <s xml:id="echoid-s6431" xml:space="preserve">& </s>
            <s xml:id="echoid-s6432" xml:space="preserve">Proportionalia Acuminata ęqualium altitudinum
              <lb/>
            inter ſe eſſe vt baſes: </s>
            <s xml:id="echoid-s6433" xml:space="preserve">& </s>
            <s xml:id="echoid-s6434" xml:space="preserve">(tanquam Corollarium) Acuminata proportio-
              <lb/>
            nalia æqualium baſium eſſe inter ſe vt altitudines: </s>
            <s xml:id="echoid-s6435" xml:space="preserve">item duo quæcunque
              <lb/>
            Acuminata proportionalia habere inter ſe rationem compoſitam ex ratio-
              <lb/>
            ne baſium, & </s>
            <s xml:id="echoid-s6436" xml:space="preserve">ex ratione altitudinum: </s>
            <s xml:id="echoid-s6437" xml:space="preserve">& </s>
            <s xml:id="echoid-s6438" xml:space="preserve">ad inſcripta triangula, vel cir-
              <lb/>
            cumſcripta parallelogramma eandem retinere rationem, aliaque his ſimi-
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            lia: </s>
            <s xml:id="echoid-s6439" xml:space="preserve">& </s>
            <s xml:id="echoid-s6440" xml:space="preserve">quod de proportionalibus Acuminatis, idem penitus euenire de ſi-
              <lb/>
            milibus menſalibus proportionalium Acuminatorum, præmiſſa priùs ha-
              <lb/>
            rum menſalium definitione, &</s>
            <s xml:id="echoid-s6441" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6442" xml:space="preserve">quæ omnia infinitas figurarum ſpecies
              <lb/>
              <gap/>
            , ne dum hactenus tractatis Parabolis, Hyperbolis, &</s>
            <s xml:id="echoid-s6443" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6444" xml:space="preserve">maximè con-
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            ducunt. </s>
            <s xml:id="echoid-s6445" xml:space="preserve">Sed hæc aliàs, quę tamen cum ſint haud obſcurę indagationis,
              <lb/>
            & </s>
            <s xml:id="echoid-s6446" xml:space="preserve">huic noſtro inſtituto prorſus aliena, erudito Lectori ſic præmonſtraſſe
              <lb/>
            ſuſſiciat.</s>
            <s xml:id="echoid-s6447" xml:space="preserve"/>
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          <head xml:id="echoid-head278" xml:space="preserve">LEMMA XI. PROP. XXXVIII.</head>
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            <s xml:id="echoid-s6448" xml:space="preserve">Si duæ rectæ lineæ inter ſe æquales fuerint, & </s>
            <s xml:id="echoid-s6449" xml:space="preserve">parallelæ, & </s>
            <s xml:id="echoid-s6450" xml:space="preserve">
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            ab earum extremis terminis ducantur lineæ quemlibet angulum
              <lb/>
            efficientes, ab alteris autem terminis aliæ ipſis æquidiſtantes;
              <lb/>
            </s>
            <s xml:id="echoid-s6451" xml:space="preserve">hæ quoque angulum inter datas conſtituent, & </s>
            <s xml:id="echoid-s6452" xml:space="preserve">recta angulo-
              <lb/>
            rum vertices coniungens erit vtrique datarum æqualis, & </s>
            <s xml:id="echoid-s6453" xml:space="preserve">pa-
              <lb/>
            rallela.</s>
            <s xml:id="echoid-s6454" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6455" xml:space="preserve">Si verò datæ rectæ lineæ terminatæ ad quemcunque angulum
              <lb/>
            applicatæ fuerint, & </s>
            <s xml:id="echoid-s6456" xml:space="preserve">vbicunque proportionaliter ſectę, aut pro-
              <lb/>
            ductæ, atque ab homologis earum punctis, hoc eſt, vel ab ex-
              <lb/>
            tremis terminis, vel ab inter-ſectionum, aut productionum pun-
              <lb/>
            ctis, ductæ fuerint intra datum angulum aliæ rectæ lineæ, quæ
              <lb/>
            item angulum quemlibet conſtituant, à reliquis verò punctis aliæ
              <lb/>
            ipſis æquidiſtanter ducantur, hæ pariter tertium angulum effi-
              <lb/>
            cient intra datum, & </s>
            <s xml:id="echoid-s6457" xml:space="preserve">horum trium angulorum vertices in vna
              <lb/>
            eademque recta linea reperientur.</s>
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            <s xml:id="echoid-s6459" xml:space="preserve">SIt, in prima figura, recta A B æqualis, & </s>
            <s xml:id="echoid-s6460" xml:space="preserve">parallela ad C D, & </s>
            <s xml:id="echoid-s6461" xml:space="preserve">exter-
              <lb/>
            minis A, C inter eas conſtituatur angulus quicunque A E C ducta-
              <lb/>
            que B F parallela ad A E, D F verò ad C E. </s>
            <s xml:id="echoid-s6462" xml:space="preserve">Dico B F, D F inter datas
              <lb/>
            æquidiſtantes conuenire, & </s>
            <s xml:id="echoid-s6463" xml:space="preserve">E F iungentem angulorum vertices, alteri A
              <lb/>
            B, vel C D eſſe æqualem, & </s>
            <s xml:id="echoid-s6464" xml:space="preserve">parallelam.</s>
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            <s xml:id="echoid-s6466" xml:space="preserve">Iungantur A C, B D: </s>
            <s xml:id="echoid-s6467" xml:space="preserve">& </s>
            <s xml:id="echoid-s6468" xml:space="preserve">quoniam B F eſt parallela ad A E, erit angu-
              <lb/>
            lus G B F æqualis angulo B A E; </s>
            <s xml:id="echoid-s6469" xml:space="preserve">cumque A B ſit æqualis, & </s>
            <s xml:id="echoid-s6470" xml:space="preserve">parallela </s>
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