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

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[271.] THEOR. XXIII. PROP. XXXX.
Page: 235 (51)
[272.] COROLL. I.
Page: 237 (53)
[273.] COROLL. II.
Page: 237 (53)
[274.] COROLL. III.
Page: 237 (53)
[275.] PROBL. VI. PROP. XXXXI.
Page: 238 (54)
[276.] PROBL. VII. PROP. XXXXII.
Page: 238 (54)
[277.] COROLL.
Page: 239 (55)
[278.] THEOR. XXIV. PROP. XXXXIII.
Page: 240 (56)
[279.] THEOR. XXV. PROP. XXXXIV.
Page: 240 (56)
[280.] SCHOLIVM.
Page: 242 (58)
[281.] THEOR. XXVI. PROP. XLV.
Page: 242 (58)
[282.] COROLL.
Page: 243 (59)
[283.] THEOR. XXVII. PROP. XLVI.
Page: 243 (59)
[284.] COROLL. I.
Page: 245 (61)
[285.] COROLL. II.
Page: 245 (61)
[286.] THEOR. XXVIII. PROP. XLVII.
Page: 245 (61)
[287.] THEOR. XXIX. PROP. XLVIII.
Page: 247 (63)
[288.] THEOR. XXX. PROP. XLIX.
Page: 248 (64)
[289.] THEOR. XXXI. PROP. L.
Page: 249 (65)
[290.] COROLL.
Page: 250 (66)
[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)
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          <head xml:id="echoid-head319" xml:space="preserve">LEMMA XIII. PROP. LXVII.</head>
          <p>
            <s xml:id="echoid-s7658" xml:space="preserve">Si in angulo A B C applicatæ ſint duæ rectæ lineæ D E, A
              <lb/>
            C, quæ ab eadem recta B G per verticem B ducta proportio-
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            naliter ſecentur, ita vt ſit A G ad G C, homologè, vt D F ad
              <lb/>
            F E. </s>
            <s xml:id="echoid-s7659" xml:space="preserve">Dico ipſas A C, D F inter ſe æquidiſtare.</s>
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            <s xml:id="echoid-s7661" xml:space="preserve">SI enim A C non eſt ipſi D E parallela, ſit alia
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            applicata A H, ſecans B G in I: </s>
            <s xml:id="echoid-s7662" xml:space="preserve">erit ergo
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            (ob parallelas) A I ad I H, vt D F ad F E; </s>
            <s xml:id="echoid-s7663" xml:space="preserve">vel
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            ob hypotheſim, vt A G ad G C, ergo in trian-
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            gulo A C H erit I G parallela ad H C, ſed ipſæ
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            conueniunt in B. </s>
            <s xml:id="echoid-s7664" xml:space="preserve">Quare non erit alia ex A ipſi
              <lb/>
            D E parallela, quàm A C. </s>
            <s xml:id="echoid-s7665" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s7666" xml:space="preserve">c.</s>
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          <head xml:id="echoid-head320" xml:space="preserve">THEOR. XLII. PROP. LXVIII.</head>
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            <s xml:id="echoid-s7668" xml:space="preserve">Baſes æqualium portionum, ex eodem angulo, ſiue ex eadem
              <lb/>
              <note position="left" xlink:label="note-0274-01" xlink:href="note-0274-01a" xml:space="preserve">Conuer-
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              ſum Pro-
                <lb/>
              p. 45. h.</note>
            quacunque coni- ſectione, vel circulo abſciſſarum, eandem in-
              <lb/>
            ſcriptam eiuſdem nominis ſectionem ſimilem, & </s>
            <s xml:id="echoid-s7669" xml:space="preserve">concentricam
              <lb/>
            ad puncta media contingunt.</s>
            <s xml:id="echoid-s7670" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7671" xml:space="preserve">SInt de angulo rectilineo, vt in prima figura, vel de qualibet alia coni- ſe-
              <lb/>
            ctione, vel circulo, vt in ſecunda, abſciſſæ duæ æquales portiones A
              <lb/>
            B C, D E F, quarum baſes A C, D F ſint bifariam ſectæ in G, H, & </s>
            <s xml:id="echoid-s7672" xml:space="preserve">per G
              <lb/>
            inſcribatur eiuſdem nominis ſectio ſimilis, & </s>
            <s xml:id="echoid-s7673" xml:space="preserve">concentrica exteriori A B
              <note symbol="a" position="left" xlink:label="note-0274-02" xlink:href="note-0274-02a" xml:space="preserve">4. ſec.
                <lb/>
              conic &
                <lb/>
              5 6.7. p. h.</note>
            quæ ſit I G H. </s>
            <s xml:id="echoid-s7674" xml:space="preserve">Dico baſim A C ſectionem I G H contingere in G, & </s>
            <s xml:id="echoid-s7675" xml:space="preserve">ba-
              <lb/>
            ſim quoque D F eandem ſectionem contingere in H.</s>
            <s xml:id="echoid-s7676" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7677" xml:space="preserve">Iungatur, in prima, B G, & </s>
            <s xml:id="echoid-s7678" xml:space="preserve">producatur, nam ipſa erit diameter Hyper-
              <lb/>
            bolæ I G H (cum ſit B eius centrum) bifariam ſecans omnes in ea applica-
              <lb/>
            tas, quæ ſi vſque ad aſymptotos producantur, erunt, & </s>
            <s xml:id="echoid-s7679" xml:space="preserve">ipſarum ſegmenta
              <lb/>
            inter aſymptotos, & </s>
            <s xml:id="echoid-s7680" xml:space="preserve">ſectionem æqualia inter ſe, quare ſi ipſa
              <note symbol="b" position="left" xlink:label="note-0274-03" xlink:href="note-0274-03a" xml:space="preserve">8. ſecũd.
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              conic.</note>
            concipiantur addita æqualibus ſemi- applicatis in ſectione eis in directum
              <lb/>
            poſitis, prouenient totæ applicatæ in angulo A B E biſariam ſectæ à dia-
              <lb/>
            metro B G producta, ſed ponitur quoque applicata A C bifariam ſecta in
              <lb/>
            G, quare A C ipſis applicatis in ſectione æquidiſtabit, ac ideò
              <note symbol="c" position="left" xlink:label="note-0274-04" xlink:href="note-0274-04a" xml:space="preserve">67. h.</note>
            I G H continget in G.</s>
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          <note symbol="d" position="left" xml:space="preserve">32. pri-
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          mi conic.</note>
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            <s xml:id="echoid-s7682" xml:space="preserve">In ſecunda autem figura quaſcunque coni- ſectiones exhibente ducatur
              <lb/>
            ex G diameter G B, quæ vtriuſque ſectionis A B E, I G H erit communis
              <lb/>
            diameter (cumipſæ ponantur ſectiones concentricæ, &</s>
            <s xml:id="echoid-s7683" xml:space="preserve">c.) </s>
            <s xml:id="echoid-s7684" xml:space="preserve">ad applicatas </s>
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