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

Table of contents

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[281.] L. SECTIO XI.
Page: 206 (186)
[282.] M. SECTIO XII.
Page: 206 (186)
[283.] N. SECTIO XIII.
Page: 207 (187)
[284.] THEOREMA XXXV. PROPOS. XXXV.
Page: 207 (187)
[285.] SCHOLIV M.
Page: 208 (188)
[286.] THEOREMA XXXVI. PROPOS. XXXVI.
Page: 208 (188)
[287.] THEOREMA XXXVII. PROPOS. XXXVII.
Page: 209 (189)
[288.] COROLLARIVM.
Page: 210 (190)
[289.] THEOREMA XXXVIII. PROPOS. XXXVIII.
Page: 210 (190)
[290.] SCHOLIVM.
Page: 211 (191)
[291.] THEOREMA XXXIX. PROPOS. XXXIX:
Page: 211 (191)
[292.] THEOREMA XL. PROPOS. XL.
Page: 212 (192)
[293.] COROLLARIVM.
Page: 212 (192)
[294.] THEOREMA XLI. PROPOS. XLI.
Page: 212 (192)
[295.] THEOREMA XLII. PROPOS. XLII.
Page: 213 (193)
[296.] COROLLARIVM.
Page: 214 (194)
[297.] SCHOLIVM.
Page: 215 (195)
[298.] Finis Secundi Libri.
Page: 215 (195)
[299.] CAVALERII LIBER TERTIVS. In quo de circulo, & Ellipſi, ac ſolidis ab eiſdem genitis, traditur doctrina.
Page: 217 (197)
[300.] THEOREMA I. PROPOS. I.
Page: 217 (197)
[301.] COROLLARIVM.
Page: 219 (199)
[302.] THEOREMA II. PROPOS. II.
Page: 220 (200)
[303.] THEOREMA III. PROPOS. III.
Page: 221 (201)
[304.] THEOREMA IV. PROPOS. IV.
Page: 223 (203)
[305.] THEOREMA V. PROPOS. V.
Page: 224 (204)
[306.] COROLLARIV M.
Page: 225 (205)
[307.] THEOREMA VI. PROPOS. VI.
Page: 226 (206)
[308.] COROLLARIVM.
Page: 228 (208)
[309.] THEOREMA VII. PROPOS. VII.
Page: 228 (208)
[310.] PROBLEMA I PROPOS. VIII.
Page: 229 (209)
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        <div xml:id="echoid-div639" type="section" level="1" n="372">
          <head xml:id="echoid-head389" xml:space="preserve">SECTIO III.</head>
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            <s xml:id="echoid-s6631" xml:space="preserve">ITem colligimus ſolida ſimilaria genita excirculo, & </s>
            <s xml:id="echoid-s6632" xml:space="preserve">ellipſi, vel
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            ellipſibus, vtcunque iuxta datas regulas .</s>
            <s xml:id="echoid-s6633" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6634" xml:space="preserve">ſphæram, & </s>
            <s xml:id="echoid-s6635" xml:space="preserve">ſphæroi-
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            des, & </s>
            <s xml:id="echoid-s6636" xml:space="preserve">alia quæcunque ſolida ſimilaria genita ex dictis figuris, ha-
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            bere inter ſe rationem ex eorum axibus, vel diametris coniugatis
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            compoſitam.</s>
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        <div xml:id="echoid-div640" type="section" level="1" n="373">
          <head xml:id="echoid-head390" xml:space="preserve">SECTIO IV.</head>
          <p>
            <s xml:id="echoid-s6638" xml:space="preserve">ITem colligimus ſolida ſimilaria genita ex circulo, vel ellipſi, vel
              <lb/>
            ellipſibus, quæ habeant axes, vel diametros reciprocè quadratis
              <lb/>
            axium illis coniugatorum relpondentes iuxta quæ genita, intelligan-
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            tur, effe æqualia, dummodo vel vna in vtriſque ſumantur axes, vel
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            vna diametri æqualiter ad inuicem inclinatæ: </s>
            <s xml:id="echoid-s6639" xml:space="preserve">& </s>
            <s xml:id="echoid-s6640" xml:space="preserve">ſi hæc ſint æqualia,
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            illa eſſe reciprocè reſpondentia.</s>
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          <head xml:id="echoid-head391" xml:space="preserve">SECTIO V.</head>
          <p>
            <s xml:id="echoid-s6642" xml:space="preserve">ITem habemus, quod ſphæræ, & </s>
            <s xml:id="echoid-s6643" xml:space="preserve">ſimilia ſphæroideia, & </s>
            <s xml:id="echoid-s6644" xml:space="preserve">in vni-
              <lb/>
            uerſum, quod ſolida ſimilaria genita ex circulis, vel ellipſibus ha-
              <lb/>
            bentibus axes, vel diametros in ratione ſecundorum axium, vel dia-
              <lb/>
            metrorum, cum quibus æqualiter ſintinclinati, quod, inquam, ſint
              <lb/>
            in tripla ratione axium, vel diametrorum. </s>
            <s xml:id="echoid-s6645" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6646" xml:space="preserve">vt cubi eorundem. </s>
            <s xml:id="echoid-s6647" xml:space="preserve">Hæc
              <lb/>
            enim demonſtrata de omnibus quadratis parallelogrammorum pro
              <lb/>
            omnibus quadratis circulorum, vel ellipſium, tamquam eorundem
              <lb/>
            partibus proportionalibus (dum illis inſcripta intelliguntur) recipi
              <lb/>
            poſiunt.</s>
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          <head xml:id="echoid-head392" xml:space="preserve">COROLLARIVM XI.</head>
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            <s xml:id="echoid-s6649" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s6650" xml:space="preserve">13. </s>
            <s xml:id="echoid-s6651" xml:space="preserve">colligemus ſolidum ſimilare genitum ex, OV, quod
              <lb/>
            poteſt eſſe vel cylindrus, vel prima, ad ſibi ſimilare genitum ex
              <lb/>
            trilineo, DCV, eſſe vt, OV, ad reliquum ſpatium, dempta quarta
              <lb/>
            circuli, vel ellipſis, OCD, cum exceſſu dicti quadrantis ſuper duas
              <lb/>
            tertias, rectanguli, OV, ideſt proximè, vt 21. </s>
            <s xml:id="echoid-s6652" xml:space="preserve">ad 2. </s>
            <s xml:id="echoid-s6653" xml:space="preserve">Exponatur de
              <lb/>
            huius Theor. </s>
            <s xml:id="echoid-s6654" xml:space="preserve">figura tantum rectangulum, OV, cum quarta, OCD,
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            dimiffa, EF, ſi igitur intelligemus, OV, circa, DV, manentem re-
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            uolui, quoad redeat, vnde diſceſſit, defcribetur, ab, OV, cylindrus,
              <lb/>
            OA, ideſt ſolidum ſimilare genitum ex, OV, cuius omnes </s>
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