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

Table of contents

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[291.] THEOR. XXXII. PROP. LI.
Page: 251 (67)
[292.] SCHOLIVM.
Page: 252 (68)
[293.] THEOR. XXXIII. PROP. LII.
Page: 253 (69)
[294.] THEOR. XXXIV. PROP. LIII.
Page: 253 (69)
[295.] ALITER.
Page: 254 (70)
[296.] THEOR. XXXV. PROP. LIV.
Page: 255 (71)
[297.] THEOR. XXXIV. PROP. LV.
Page: 256 (72)
[298.] THEOR. XXXVII. PROP. LVI.
Page: 257 (73)
[299.] PROBL. VIII. PROP. LVII.
Page: 259 (75)
[300.] PROBL. IX. PROP. LVIII.
Page: 260 (76)
[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)
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          <head xml:id="echoid-head345" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s8138" xml:space="preserve">HIs peractis, patet baſes A C, I L æqualium portionum de eodem an-
              <lb/>
            gulo A B C neceſſariò ſe mutuò ſecare intra angulum. </s>
            <s xml:id="echoid-s8139" xml:space="preserve">Nam I M,
              <lb/>
            quæ ex puncto I inter H, & </s>
            <s xml:id="echoid-s8140" xml:space="preserve">C ſumpto æquidiſtans ducitur rectæ A H
              <lb/>
            neceſſariò occurrit cum A C, vt in M.</s>
            <s xml:id="echoid-s8141" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8142" xml:space="preserve">Dico ampliùs earum baſium occurſum M cadere omninò inter diame-
              <lb/>
            tros B D, B E; </s>
            <s xml:id="echoid-s8143" xml:space="preserve">hoc eſt inter puncta E, D; </s>
            <s xml:id="echoid-s8144" xml:space="preserve">atque rectas N D, A I, L C
              <lb/>
            harũ baſim tùm puncta media, tùm extrema iungẽtes eſſe inter ſe parallelas.</s>
            <s xml:id="echoid-s8145" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8146" xml:space="preserve">Si enim per E agatur O
              <lb/>
              <figure xlink:label="fig-0291-01" xlink:href="fig-0291-01a" number="237">
                <image file="0291-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0291-01"/>
              </figure>
            E P ipſis A H, L I æquidi-
              <lb/>
            ſtans, & </s>
            <s xml:id="echoid-s8147" xml:space="preserve">per P recta P Q
              <lb/>
            parallela ad A B, erit (ob
              <lb/>
            ipſarum æquidiſtantiam) O
              <lb/>
            E æqualis E P, itemque A
              <lb/>
            E ęqualis E Q (ob triangu-
              <lb/>
            lorum ſimilitudinem A E
              <lb/>
            O, Q E P) atque anguli ad
              <lb/>
            E ſunt æquales, quare & </s>
            <s xml:id="echoid-s8148" xml:space="preserve">
              <lb/>
            ipſa triangula ęqualia erunt,
              <lb/>
            quibus communi addito tra-
              <lb/>
            petio A B P E, fiet triangu-
              <lb/>
            lum O B P æquale menſali
              <lb/>
            A B P Q, hoc eſt minus triangulo A B C, vel triangulo L B I, quare L I
              <lb/>
            eſt infra æquidiſtantem baſim O P, ſiue baſis L I ſecat baſim A C vltra E,
              <lb/>
            verſus D. </s>
            <s xml:id="echoid-s8149" xml:space="preserve">Præterea cum ſit C B ad B I, vt C I ad I H, vel vt C M
              <note symbol="a" position="right" xlink:label="note-0291-01" xlink:href="note-0291-01a" xml:space="preserve">Coroll.
                <lb/>
              12. primi
                <lb/>
              huius.</note>
            ad M A, ſitque C B maior B I erit C M maior M A, hoc eſt punctum M
              <lb/>
            cadet vltra D, verſus E. </s>
            <s xml:id="echoid-s8150" xml:space="preserve">Itaque harum baſium occurſus eſt inter diame-
              <lb/>
            tros B N, B D. </s>
            <s xml:id="echoid-s8151" xml:space="preserve">Quod idem eſt, ac ſi dicatur nullam ipſarum baſium tranſi-
              <lb/>
            re per medium punctum alterius.</s>
            <s xml:id="echoid-s8152" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8153" xml:space="preserve">Tandem cum triangula A B C, L B I ſint æqualia, dempto com-
              <lb/>
            munitriangulo A B I, remanebit triangulum A C I ęquale trian-
              <lb/>
            gulo A L I, ſuntque ſuper eadem baſi A I, quare A I ipſi
              <lb/>
            L C æquidiſtabit; </s>
            <s xml:id="echoid-s8154" xml:space="preserve">& </s>
            <s xml:id="echoid-s8155" xml:space="preserve">cum inter parallelas A I, L C
              <lb/>
            interceptæ ſint duæ C A, L I proportionaliter
              <lb/>
            ſectæ in N, D, (ibi enim bifariam ſectæ
              <lb/>
            ſunt ex hypotheſi) erit quoque iun-
              <lb/>
            cta N D ipſi L C, vel A I æqui-
              <lb/>
            diſtans; </s>
            <s xml:id="echoid-s8156" xml:space="preserve">vt patet ex Ele-
              <lb/>
            mentis.</s>
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