Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

Table of contents

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[121.] THEOREMA XXX. PROPOS. XXXIII.
Page: 95 (75)
[122.] THEOREMA XXXI. PROPOS. XXXIV.
Page: 96 (76)
[123.] COROLLARIVM.
Page: 97 (77)
[124.] THEOREMA XXXII. PROPOS. XXXV.
Page: 97 (77)
[125.] COROLLARIVM.
Page: 98 (78)
[126.] THEOREMA XXXIII. PROPOS. XXXVI.
Page: 98 (78)
[127.] THEOREMA XXXIV. PROPOS. XXXVII.
Page: 99 (79)
[128.] COROLLARIVM.
Page: 101 (81)
[129.] THEOREMA XXXV. PROPOS. XXXVIII.
Page: 101 (81)
[130.] THEOREMA XXXVI. PROPOS. XXXIX.
Page: 103 (83)
[131.] THEOREMA XXXVII. PROPOS. XL.
Page: 103 (83)
[132.] SCHOLIVM.
Page: 104 (84)
[133.] THEOREMA XXXVIII. PROPOS. XLI.
Page: 105 (85)
[134.] THEOREMA XXXIX PROPOS. XLII.
Page: 105 (85)
[135.] THEOREMA XL. PROPOS. XLIII.
Page: 105 (85)
[136.] THEOREMA XLI. PROPOS. XLIV.
Page: 106 (86)
[137.] THEOREMA XLII. PROPOS. XLV.
Page: 107 (87)
[138.] THEOREMA XLIII. PROPOS. XLVI.
Page: 107 (87)
[139.] THEOREMA XLIV. PROPOS. XLVII.
Page: 108 (88)
[140.] COROLLARIVM.
Page: 109 (89)
[141.] SCHOLIVM.
Page: 109 (89)
[142.] LEMMA.
Page: 110 (90)
[143.] COROLLARIVM.
Page: 112 (92)
[144.] THEOREMA XLV. PROPOS. XLVIII.
Page: 112 (92)
[145.] COROLLARIVM.
Page: 113 (93)
[146.] THEOREMA XLVI. PROPOS. XLIX.
Page: 114 (94)
[147.] THEOREMA XLVII. PROPOS. L:
Page: 115 (95)
[148.] COROLLARIVM I.
Page: 117 (97)
[149.] COROLLARIVM II.
Page: 117 (97)
[150.] SCHOLIVM.
Page: 118 (98)
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            tera omnium quadratorum parallelogrammi, AD, regula eadem,
              <lb/>
              <note position="right" xlink:label="note-0231-01" xlink:href="note-0231-01a" xml:space="preserve">Iuxt. 1.
                <lb/>
              lib. 1.</note>
            MC, omnia verò quadrata eiuſdem circuli, vel ellipſis, regula, PF,
              <lb/>
            ſunt ſubſexquialtera omnium quadratorum parallelogrammi, AD,
              <lb/>
              <note position="right" xlink:label="note-0231-02" xlink:href="note-0231-02a" xml:space="preserve">Coroll. 1.
                <lb/>
              huius.</note>
            regula eadem, PF, ergo omnia quadrata circuli, vel ellipſis, MP
              <lb/>
            CF, regula, MC, ad omnia quadrata eiuſdem regula, PF, erunt,
              <lb/>
            vt omnia quadrata parallelogrammi, AD, regula, MC, ad omnia
              <lb/>
              <note position="right" xlink:label="note-0231-03" xlink:href="note-0231-03a" xml:space="preserve">29.Lib.2.</note>
            quadrata eiuſdem, regula, PF, ſed omnia quadrata parallelogram-
              <lb/>
            mi, AD, regula, MC, ad omnia quadrata eiuſdem, regula, PF,
              <lb/>
            ſunt, vt, MC, ad, PF, ergo omnia quadrata circuli, vel ellipſis, M
              <lb/>
            PCF, regula, MC, ad omnia quadrata eiuſdem, regula, PF, erunt,
              <lb/>
            vt, MC, ad, PF, quod oſten ler oportebat.</s>
            <s xml:id="echoid-s5165" xml:space="preserve"/>
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        <div xml:id="echoid-div522" type="section" level="1" n="312">
          <head xml:id="echoid-head329" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s5166" xml:space="preserve">_H_INC patet, ſi ad, MC, PF, ordinatim applicentur rectæ lineæ
              <lb/>
            portiones abſcindentes à dicto circulo, vel ellipſi, quoniam oſten-
              <lb/>
            ſa eſtratio omnium quadratorum abſciſſæ portionis, regulabaſi, ad omnia
              <lb/>
              <note position="right" xlink:label="note-0231-04" xlink:href="note-0231-04a" xml:space="preserve">_6. Huius._</note>
            quadrata circuli, vel ellipſis, MPCF, & </s>
            <s xml:id="echoid-s5167" xml:space="preserve">item oſtenſa eſt ratio om-
              <lb/>
              <note position="right" xlink:label="note-0231-05" xlink:href="note-0231-05a" xml:space="preserve">_Exantec._</note>
            nium quadratorum circuli, vel ellipſis, MPCF, regula altero axium,
              <lb/>
            vel diametrorum, ad omnia quadrata eiuſdem, regula reliquo axi, vel
              <lb/>
            diametro, & </s>
            <s xml:id="echoid-s5168" xml:space="preserve">deniq; </s>
            <s xml:id="echoid-s5169" xml:space="preserve">oſtenſa eſt ratio omnium quadratorum eiuſdem cir-
              <lb/>
            culi, vel ellipſis, ad omnia quadrata portionis per aliam ordinatim ap-
              <lb/>
            plicatam abſciſſæ, regula baſi dictæ portionis, quod ideo nota erit ratio
              <lb/>
              <note position="right" xlink:label="note-0231-06" xlink:href="note-0231-06a" xml:space="preserve">_6. Huius._</note>
            omnium quadratorum duarum portionum per dictas applicatas abſciſſa-
              <lb/>
            rum, regulis dictarum portionum baſibus, quod, &</s>
            <s xml:id="echoid-s5170" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5171" xml:space="preserve"/>
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        <div xml:id="echoid-div524" type="section" level="1" n="313">
          <head xml:id="echoid-head330" xml:space="preserve">THEOREMA IX. PROPOS. X.</head>
          <p>
            <s xml:id="echoid-s5172" xml:space="preserve">SI circulus, & </s>
            <s xml:id="echoid-s5173" xml:space="preserve">ellipſis, vel duæ ellipſes ſuerint circa eun-
              <lb/>
            dem axim, vel diametrum, illi erunt interſe, vt eorum
              <lb/>
            ſecundiaxes, vel diametri.</s>
            <s xml:id="echoid-s5174" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5175" xml:space="preserve">Sint circulus, & </s>
            <s xml:id="echoid-s5176" xml:space="preserve">ellipſis, vel duæ ellipſes, AFVT, AGVS, cir-
              <lb/>
              <note position="right" xlink:label="note-0231-07" xlink:href="note-0231-07a" xml:space="preserve">Vide d-
                <lb/>
              cta lib. 7.
                <lb/>
              Annot.
                <lb/>
              Prop. 21.</note>
            ca eundem axim, vel diametrum, AV, ſint verò ſecundi axes, vel
              <lb/>
            diametri, FT, GS. </s>
            <s xml:id="echoid-s5177" xml:space="preserve">Dico circulum, vel ellipſim, AFVT, ad cir-
              <lb/>
            culum, vel ellipſim, AGVS, eſſe, vt, FT, ad, GS; </s>
            <s xml:id="echoid-s5178" xml:space="preserve">duæ igitur,
              <lb/>
            DA, DF, tangentes eaſdem in terminis coniugatarum axium, vel
              <lb/>
            diametrorum, inter ſe conueniant in, D, erit ergo, DH, paralle-
              <lb/>
            logrammum, ducatur etiam per, G, ipſa, GC, parallela ipſi, AV,
              <lb/>
            quæ tanget ellipſim, AGVS, in, G, erit ergo etiam, CH, paral-
              <lb/>
              <note position="right" xlink:label="note-0231-08" xlink:href="note-0231-08a" xml:space="preserve">17. 1. Co-
                <lb/>
              nicorum.</note>
            lelogrammum in eadem baſi, & </s>
            <s xml:id="echoid-s5179" xml:space="preserve">altitudine cum ſemiportione, </s>
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