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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          <pb o="154" file="0178" n="178" rhead=""/>
          <p>
            <s xml:id="echoid-s5094" xml:space="preserve">In ſingulis enim figuris iuncta recta C D: </s>
            <s xml:id="echoid-s5095" xml:space="preserve">erit in tribus primis circa maio-
              <lb/>
            rem axim, recta C D maior C A (cum circulus ex C A ſit ſectioni
              <note symbol="a" position="left" xlink:label="note-0178-01" xlink:href="note-0178-01a" xml:space="preserve">92. h</note>
            ptus, ac propterea ſecet C D) ſed C A maior eſt G D, v thìc ad numeros
              <lb/>
            2, 3, & </s>
            <s xml:id="echoid-s5096" xml:space="preserve">5. </s>
            <s xml:id="echoid-s5097" xml:space="preserve">oſtenſum eſt, ergo C D eò ampliùs maior erit ipſa G D, ſiue
              <lb/>
            quadratum C D maius quadrato G D, vel duo ſimul C I, I D maiora
              <lb/>
            duobus ſimul G I, I D, quare dempto communi D I, erit quadratum C I
              <lb/>
            maius quadrato G I, vnde punctum C cadet infra G: </s>
            <s xml:id="echoid-s5098" xml:space="preserve">ſed A C, D G ſi-
              <lb/>
            mul conueniunt ad partes axis B R, vt ad num. </s>
            <s xml:id="echoid-s5099" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5100" xml:space="preserve">oſtendimus, ergo ipſa-
              <lb/>
            rum occurſus erit vltra axim B R.</s>
            <s xml:id="echoid-s5101" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5102" xml:space="preserve">In quarta demum figura, eſt C D minor C A (cum circulus ex C A ſit
              <lb/>
            Ellipſi circumſcriptus ) & </s>
            <s xml:id="echoid-s5103" xml:space="preserve">C A minor G D, prout ad num. </s>
            <s xml:id="echoid-s5104" xml:space="preserve">6. </s>
            <s xml:id="echoid-s5105" xml:space="preserve">huius
              <note symbol="b" position="left" xlink:label="note-0178-02" xlink:href="note-0178-02a" xml:space="preserve">ibidem.</note>
            monſtrauimus, quare C D erit omnino minor G D, ſiue quadratum C D
              <lb/>
            minus quadrato G D, vel duo ſimul C I, I D minora duobus ſimul G I,
              <lb/>
            I D; </s>
            <s xml:id="echoid-s5106" xml:space="preserve">quamobré dempto I D, erit C I minus G I, ſiue punctum C occurſus
              <lb/>
            inferioris perpendicularis A C cadet ſupra G occurſum ſuperioris D G;
              <lb/>
            </s>
            <s xml:id="echoid-s5107" xml:space="preserve">ſed tales perpendiculares A C, D G ſe mutuò ſecant (vt ſuperiùs oſten-
              <lb/>
            dimus ad num. </s>
            <s xml:id="echoid-s5108" xml:space="preserve">1.) </s>
            <s xml:id="echoid-s5109" xml:space="preserve">ad partes axis B R, quare ipſarum occurſus erit inter
              <lb/>
            contactus, & </s>
            <s xml:id="echoid-s5110" xml:space="preserve">minorem axim, ſed reſpectu maiorem axim M L ſe mutuò
              <lb/>
            ſecant vltra M L, vti paulò ante demonſtrauimus. </s>
            <s xml:id="echoid-s5111" xml:space="preserve">Quare in Ellipſi oc-
              <lb/>
            curſus huiuſmodi perpendicularium A C, D G cadet in angulo quadran-
              <lb/>
            tis M L G, qui deinceps eſt quadranti M L B, ad cuius peripheriam M A
              <lb/>
            B ductæ ſunt perpendiculares A C, D G, &</s>
            <s xml:id="echoid-s5112" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5113" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div520" type="section" level="1" n="214">
          <head xml:id="echoid-head219" xml:space="preserve">Pag. 147. ad finem Prop. 97.</head>
          <p>
            <s xml:id="echoid-s5114" xml:space="preserve">quodque de _MAXIMIS_ ſimilibus Ellipſibus angulo rectilineo inſcriptis
              <lb/>
            facillimùm eſt demonſtrare.</s>
            <s xml:id="echoid-s5115" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div521" type="section" level="1" n="215">
          <head xml:id="echoid-head220" xml:space="preserve">FINIS.</head>
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