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

Table of contents

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[311.] THEOREMA VIII. PROPOS. IX.
Page: 230 (210)
[312.] COROLLARIVM.
Page: 231 (211)
[313.] THEOREMA IX. PROPOS. X.
Page: 231 (211)
[314.] COROLLARIVM.
Page: 232 (212)
[315.] THEOREMAX. PROPOS. XI.
Page: 233 (213)
[316.] COROLLARIVM I.
Page: 234 (214)
[317.] COROLL II. A. SECTIO I.
Page: 235 (215)
[318.] B. SECTIO II.
Page: 235 (215)
[319.] C. SECTIO III.
Page: 235 (215)
[320.] D. SECTIO IV.
Page: 235 (215)
[321.] E. SECTIO V.
Page: 236 (216)
[322.] F. SECTIO VI.
Page: 236 (216)
[323.] THEOREMA XI. PROPOS. XII.
Page: 236 (216)
[324.] THEOREMA XII. PROPOS. XIII.
Page: 237 (217)
[325.] COROLLARIVM.
Page: 239 (219)
[326.] THEOREMA XIII. PROPOS. XIV.
Page: 239 (219)
[327.] COROLLARIVM.
Page: 242 (222)
[328.] THEOREMA XIV. PROPOS. XV.
Page: 242 (222)
[329.] ALITER.
Page: 244 (224)
[330.] THEOREMA XV. PROPOS. XVI.
Page: 244 (224)
[331.] THEOREMA XVI. PROPOS. XVII.
Page: 247 (227)
[332.] COROLLARIVM I.
Page: 248 (228)
[333.] COROLLARIVM II.
Page: 249 (229)
[334.] THEOREMA XVII. PROPOS. XVIII.
Page: 249 (229)
[335.] COROLLARIVM.
Page: 251 (231)
[336.] THEOREMA XVIII. PROPOS. XIX.
Page: 251 (231)
[337.] COROLLARIVM.
Page: 252 (232)
[338.] THEOREMA XIX. PROPOS. XX.
Page: 252 (232)
[339.] COROLLARIVM.
Page: 254 (234)
[340.] THEOREMA XX. PROPOS. XXI.
Page: 254 (234)
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          <head xml:id="echoid-head436" xml:space="preserve">THEOREMA VIII. PROPOS. VIII.</head>
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            <s xml:id="echoid-s7171" xml:space="preserve">SI ad baſim datæ parabolæ ordinatim applicetur recta li-
              <lb/>
            nea, ſub qua, & </s>
            <s xml:id="echoid-s7172" xml:space="preserve">ſub portione baſis abſciſſa, ac earum ex-
              <lb/>
            trema iungente, fiattriangulum, portio parabolæ abſciſſa ad
              <lb/>
            triangulum ſibi inſcriptum erit, vt ad reliquam baſis, dempta
              <lb/>
            abſciſſa, eadem reliqua cum, {1/3}, ipſius abſciſſæ.</s>
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            <s xml:id="echoid-s7174" xml:space="preserve">Sit parabola, HGA, in baſi, HA, ad quam ordinatim applicetur
              <lb/>
            vtcunque recta linea, ST, fiat autem triangulum ſub, ST, & </s>
            <s xml:id="echoid-s7175" xml:space="preserve">vtrauis
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              <figure xlink:label="fig-0316-01" xlink:href="fig-0316-01a" number="210">
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            duarum, HT, TA, vt ſub, HT, & </s>
            <s xml:id="echoid-s7176" xml:space="preserve">ſub, SH,
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            quod ſit, HST. </s>
            <s xml:id="echoid-s7177" xml:space="preserve">Dico portionem, HST, ad
              <lb/>
            triangulum, HST, eſſe vt compoſitam ex, A
              <lb/>
            T, &</s>
            <s xml:id="echoid-s7178" xml:space="preserve">, {1/3}, TH; </s>
            <s xml:id="echoid-s7179" xml:space="preserve">ad, AT, compleatur paralle-
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            logrammum, CT, eſt ergo parallelogrammum,
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              <note position="left" xlink:label="note-0316-01" xlink:href="note-0316-01a" xml:space="preserve">5. Huius.</note>
            CT, ad portionem, HST, vt, AT, ad com-
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            poſitam ex, {1/2}, AT, &</s>
            <s xml:id="echoid-s7180" xml:space="preserve">, {1/6}, TH, & </s>
            <s xml:id="echoid-s7181" xml:space="preserve">anteceden-
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            tium dimidia ſcilicet triangulum, HST, ad
              <lb/>
            portionem, HST, erit vt dimidia, AT, ad
              <lb/>
            compoſitam ex, {1/2}, AT, &</s>
            <s xml:id="echoid-s7182" xml:space="preserve">, {1/6}, TH, ideſt vt,
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            AT, ad, AT, cum, {1/3}, HT, & </s>
            <s xml:id="echoid-s7183" xml:space="preserve">conuertendo,
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            portio, HST, ad triangulum, HST, erit vt
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            compoſita ex, {1/3}, HT, & </s>
            <s xml:id="echoid-s7184" xml:space="preserve">tota, TA, ad, TA,
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            quod oſtendendum nobis erat.</s>
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          <head xml:id="echoid-head437" xml:space="preserve">SCHOLIV M.</head>
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            <s xml:id="echoid-s7186" xml:space="preserve">_P_Oteſt autem, & </s>
            <s xml:id="echoid-s7187" xml:space="preserve">dicta ratio ſic conſtitui, triplicatis terminis, ſcili-
              <lb/>
            cet, quod portio, HST, ad triangulum, HST, ſit bt bna, HA,
              <lb/>
            cum duabus, AT, ad tres, AT, bel ſic, quod ſit, bt dimidia, HA, cum,
              <lb/>
            AT, ad ipſam, AT.</s>
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          <head xml:id="echoid-head438" xml:space="preserve">PROBLEMA I. PROPOS. IX.</head>
          <p>
            <s xml:id="echoid-s7189" xml:space="preserve">A Data parabola portionem abſcindere per lineam ab
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            eiuſdem baſim ordinatim ductam, quę ad triangulum
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            ſub eadem ordinatim ducta, & </s>
            <s xml:id="echoid-s7190" xml:space="preserve">abſciſſa per eandem à baſi pa-
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            rabolæ ad eandem partem, ad quam abſcinditur portio, ha-
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            beat datam rationem, dummodò hæc ſit maior ſexquialtera.</s>
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