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

Table of contents

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[301.] PROBL. X. PROP. LIX.
Page: 261 (77)
[302.] PROBL. XI. PROP. LX.
Page: 262 (78)
[303.] PROBL. XII. PROP. LXI.
Page: 262 (78)
[304.] PROBL. XIII. PROP. LXII.
Page: 265 (79)
[305.] MONITVM.
Page: 268 (82)
[306.] THEOR. XXXVIII. PROP. LXIII.
Page: 268 (82)
[307.] THEOR. XXXIX. PROP. LXIV.
Page: 270 (84)
[308.] THEOR. XL. PROP. LXV.
Page: 271 (85)
[309.] THEOR. XLI. PROP. LXVI.
Page: 273 (87)
[310.] LEMMA XIII. PROP. LXVII.
Page: 274 (88)
[311.] THEOR. XLII. PROP. LXVIII.
Page: 274 (88)
[312.] COROLL. I.
Page: 276 (90)
[313.] COROLL. II.
Page: 276 (90)
[314.] MONITVM.
Page: 276 (90)
[315.] DEFINITIONES. I.
Page: 278 (92)
[316.] II.
Page: 278 (92)
[317.] III.
Page: 279 (93)
[318.] IIII.
Page: 279 (93)
[319.] PROBL. XIV. PROP. LXIX.
Page: 280 (94)
[320.] SCHOLIVM I.
Page: 282 (96)
[321.] COROLL. I.
Page: 282 (96)
[322.] SCHOLIVM II.
Page: 282 (96)
[323.] COROLL. II.
Page: 282 (96)
[324.] SCHOLIVM III.
Page: 283 (97)
[325.] COROLL. III.
Page: 283 (97)
[326.] THEOR. XLIII. PROP. LXX.
Page: 284 (98)
[327.] COROLL.
Page: 286 (100)
[328.] THEOR. XLIV. PROP. LXXI.
Page: 286 (100)
[329.] COROLL.
Page: 287 (101)
[330.] THEOR. XLV. PROP. LXXII.
Page: 288 (102)
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          <head xml:id="echoid-head405" xml:space="preserve">LEMMA IV. PROP. VIII.</head>
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            <s xml:id="echoid-s9407" xml:space="preserve">Si in triangulo A B C, cuius baſis A B, ex vertice C ducta ſit
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            C E ipſi B A parallela, vel ad eaſdem, vel ad oppoſitas partes, & </s>
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            ducatur quælibet A D E vtranque B C, C E ſecans in D, & </s>
            <s xml:id="echoid-s9409" xml:space="preserve">E:
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            <s xml:id="echoid-s9410" xml:space="preserve">dico aggregatum triangulorum A D B, D C E ad triangulum A
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            C B eſſe vt aggregatum extremarum poſt B D, D C, ad B C.</s>
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            <s xml:id="echoid-s9412" xml:space="preserve">SVmatur D F tertia proportionalis poſt B D, D C.</s>
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            <s xml:id="echoid-s9414" xml:space="preserve">Iam triangulum D C E ad A D C eſt vt E D ad D A, vel vt C D ad
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            D B, vel vt D F ad D C; </s>
            <s xml:id="echoid-s9415" xml:space="preserve">& </s>
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            triangulum A D C ad trian-
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            gulum A B C, eſt vt D C
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            ad C B, ergo ex æquali triã-
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            gulum D C E ad A B C, erit
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            vt D F ad C B; </s>
            <s xml:id="echoid-s9417" xml:space="preserve">ſed triangu-
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            lum A D B ad idem A B C
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            eſt vt B D ad B C, quare
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            duo ſimul triangula D C E,
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            A D B, ad triangulum A C
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            B, erunt vt duæ ſimul lineæ
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            D F, D B, hoc eſt tota B F,
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            aggregatum extremarum poſt B D, D C, ad B C. </s>
            <s xml:id="echoid-s9418" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s9419" xml:space="preserve">c.</s>
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          <head xml:id="echoid-head406" xml:space="preserve">PROBL. III. PROP. IX.</head>
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            <s xml:id="echoid-s9421" xml:space="preserve">Duabus datis rectis lineis terminatis ad quemlibet angulum
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            conſtitutis, & </s>
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            æquidiſtanter ducta, ad contrarias tamen partes, & </s>
            <s xml:id="echoid-s9423" xml:space="preserve">in infinitum
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            producta: </s>
            <s xml:id="echoid-s9424" xml:space="preserve">oportet per extremum terminum alterius, rectam duce-
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            re ęquidiſtanti occurrentem, ita vt, cum ipſa bina ſimilia triangula
              <lb/>
            ad verticem conſtituat, horũ aggregatum ſit MINIMA quantitas.</s>
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          </p>
          <p>
            <s xml:id="echoid-s9426" xml:space="preserve">SInt A B, B C rectæ lineæ terminatæ ad quemcunque angulum A B C
              <lb/>
            compoſitæ, ſitque C D in infinitum producta ipſi B A parallela, ſed ad
              <lb/>
            oppoſit as partes rectæ C B: </s>
            <s xml:id="echoid-s9427" xml:space="preserve">oportet ex A rectam ducere, qualis eſt A D,
              <lb/>
            ita vt aggregatum ſimilium triangulorum A E B, C E D ad verticem E
              <lb/>
            ſit _MINIMVM_.</s>
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            <s xml:id="echoid-s9429" xml:space="preserve">Diuidatur B C in E, ita vt B E ad E C ſit vt latus cuiuſdam quadrati ad
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            exceſſum diametri ſuper latus: </s>
            <s xml:id="echoid-s9430" xml:space="preserve">dico punctum E eſſe quæſitum.</s>
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            <s xml:id="echoid-s9432" xml:space="preserve">Nam ducta qualibet alia A F G; </s>
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            tremarum proportionalium poſt B E, E C ſit _MINIMVM_ (per </s>
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