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

Table of contents

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[151.] Finis Primi Libri.
Page: 118 (98)
[152.] CAVALER II LIBER SECVNDVS.
Page: 119 (99)
[153.] DIFINITIONES. I.
Page: 119 (99)
[154.] COROLLARIVM.
Page: 120 (100)
[155.] II.
Page: 120 (100)
[156.] COROLLARIVM.
Page: 120 (100)
[157.] III.
Page: 120 (100)
[158.] COROLLARIVM.
Page: 121 (101)
[159.] IV.
Page: 121 (101)
[160.] V.
Page: 121 (101)
[161.] COROLLARIVM.
Page: 122 (102)
[162.] VI.
Page: 122 (102)
[163.] COROLLARIVM.
Page: 122 (102)
[164.] VII.
Page: 122 (102)
[165.] A. VIII.
Page: 123 (103)
[166.] B.
Page: 123 (103)
[167.] C.
Page: 123 (103)
[168.] D.
Page: 124 (104)
[169.] E.
Page: 124 (104)
[170.] APPENDIX. Pro antecedentium Definitionum explicatione.
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[171.] POSTVLATA I.
Page: 128 (108)
[172.] II.
Page: 128 (108)
[173.] THEOREMA I. PROPOS. I.
Page: 128 (108)
[174.] SCHOLIVM.
Page: 131 (111)
[175.] THEOREMA II. PROPOS. II.
Page: 132 (112)
[176.] COROLLARIV M.
Page: 133 (113)
[177.] THEOREMA III. PROPOS. III.
Page: 133 (113)
[178.] COROLLARIVM.
Page: 135 (115)
[179.] THEOREMA IV. PROPOS. IV.
Page: 135 (115)
[180.] COROLLARIVM.
Page: 136 (116)
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          <pb o="102" file="0122" n="122" rhead="GEOMETRIE"/>
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        <div xml:id="echoid-div247" type="section" level="1" n="161">
          <head xml:id="echoid-head174" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s2473" xml:space="preserve">_H_Inc liquet cuilibet abſciſſæ in proximis definitionibus propoſitæ li-
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            neæ reſpondere vnam ex reſiduis, ita vt tot ſint illæ, quæ dicun-
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            tur reſiduæ omnium abſciſſarum propoſitæ lineæ quot illæ, quæ dicun-
              <lb/>
            tur eiuſdem omnes abſciſſæ, ſiue recti, ſiue eiuſdem obliqui tranſitus, nam
              <lb/>
            reſiduæ omnium abſciſſarum propoſitælineæ interiacent inter reliquum
              <lb/>
            extremum eiuſdem punctum, & </s>
            <s xml:id="echoid-s2474" xml:space="preserve">eadem illa puncta, inter quæ, & </s>
            <s xml:id="echoid-s2475" xml:space="preserve">ex-
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            tremum primò dictum, interiacent omnes abſciſſæ.</s>
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          <head xml:id="echoid-head175" xml:space="preserve">VI.</head>
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            <s xml:id="echoid-s2477" xml:space="preserve">SI pro qualibet earum, quæ dicuntur omnes abſciſſæ pro-
              <lb/>
            poſitæ rectæ lineæ, ipſa propoſita linea, ſiue eidem æ-
              <lb/>
            qualis, ſemel aſſumpta intelligatur, iſtæ ſimul collectæ di-
              <lb/>
            centur: </s>
            <s xml:id="echoid-s2478" xml:space="preserve">Maximæ omnium abſciſſarum propoſitæ lineæ, vel
              <lb/>
            ſubintelligentur ſemper eſſe omnium, etiam ſi dicerentur ſo-
              <lb/>
            lummodò: </s>
            <s xml:id="echoid-s2479" xml:space="preserve">Maximæ abſciſſarum.</s>
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          <head xml:id="echoid-head176" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s2481" xml:space="preserve">_E_T quia omnes abſciſſæ tot ſunt, quot omnes reſidue, maximè verò
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            omnium abſciſſtrum tot ſunt, quot omnes abſciſſæ, nam cuilibet
              <lb/>
            abſciſſæ reſpondet vna maximarum, ideò maximæ omnium abſciſſarum
              <lb/>
            propoſitæ lineæ tot erunt, quot etiam reſiduæ omnium abſciſſarum, quot-
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            cumque ſint omnes abſciſſæ, vel reſiduæ : </s>
            <s xml:id="echoid-s2482" xml:space="preserve">ideſt pro qualibet reſidua ha-
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            bebimus quoque vnam maximarum; </s>
            <s xml:id="echoid-s2483" xml:space="preserve">ijs ſemper recti, vel eiuſdem obli-
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            qui tranſitus aſſumptis.</s>
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          <head xml:id="echoid-head177" xml:space="preserve">VII.</head>
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            <s xml:id="echoid-s2485" xml:space="preserve">SI cuilibet omnium abſciſſarum propoſitæ rectæ lineæ ad-
              <lb/>
            iuncta intelligatur alia recta linea cuidam equalis, com-
              <lb/>
            poſitæ ex omnibus abſciſſis, & </s>
            <s xml:id="echoid-s2486" xml:space="preserve">adiunctis, ſinul colle ctæ di-
              <lb/>
            centur : </s>
            <s xml:id="echoid-s2487" xml:space="preserve">Omnes abſciſſæ propoſitæ lineæ adiuncta tali, nem-
              <lb/>
            pè adiuncta illa, cui, quę adiunguntur, ſunt ęquales. </s>
            <s xml:id="echoid-s2488" xml:space="preserve">Sive-
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            rò fieret hęc adiunctio reſiduis, vel maximis omnium abſciſ-
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            ſarum, pariter dicerentur : </s>
            <s xml:id="echoid-s2489" xml:space="preserve">Reſiduæ, vel Maximæ omnium
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            abſciſſarum adiuncta eadem; </s>
            <s xml:id="echoid-s2490" xml:space="preserve">rectiſemper, veleiuſdem ob-
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            liqui tranſitus.</s>
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