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

List of thumbnails

< >
441
441 (421) 		442
442 (422)
443
443 (423) 		444
444 (424)
445
445 (425) 		446
446 (426)
447
447 (427) 		448
448 (428)
449
449 (429) 		450
450 (428)
< >
page |< < (429) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1025" type="section" level="1" n="616">
          <pb o="429" file="0449" n="449" rhead="LIBER VI."/>
        </div>
        <div xml:id="echoid-div1026" type="section" level="1" n="617">
          <head xml:id="echoid-head647" xml:space="preserve">THEOREMA I. PROPOS. I.</head>
          <p>
            <s xml:id="echoid-s11188" xml:space="preserve">CIrculorum æqualium, necnon ſectorum æqualium,
              <lb/>
            & </s>
            <s xml:id="echoid-s11189" xml:space="preserve">ab eodem, vel æqualibus circulis abſciſſorum,
              <lb/>
            omnes circumferentiæ ſunt æquales.</s>
            <s xml:id="echoid-s11190" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11191" xml:space="preserve">Hæc Propoſitio facilè per ſuperpoſitionem oſtendetur. </s>
            <s xml:id="echoid-s11192" xml:space="preserve">Si
              <lb/>
            enim circuli æquales ad inuicem ſuperponantur, ita vt centrum
              <lb/>
            centro congruat, etiam ipſi circuli congruent, cum ſupponantur
              <lb/>
            æquales, vnde & </s>
            <s xml:id="echoid-s11193" xml:space="preserve">eorum radij ſint æquales, congruentibus autem
              <lb/>
            circulis, etiam omnes vnius circumferentiæ congruent omnibus
              <lb/>
            alterius circumferentijs, & </s>
            <s xml:id="echoid-s11194" xml:space="preserve">ideò inter ſe æquales erunt. </s>
            <s xml:id="echoid-s11195" xml:space="preserve">Eadem
              <lb/>
            pariter ſuperpoſitionis adhibita via, oſtendemus ſectorum æqua-
              <lb/>
            lium, ab eodem, vel æqualibus circulis abſciſſorum omnes circum-
              <lb/>
            ferentias inter ſe æquales eſſe, quod erat demonſtrandum.</s>
            <s xml:id="echoid-s11196" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1027" type="section" level="1" n="618">
          <head xml:id="echoid-head648" xml:space="preserve">THEOREMA II. PROPOS. II.</head>
          <p>
            <s xml:id="echoid-s11197" xml:space="preserve">OMnis circulus æqualis eſt triangulo rectangulo, cu-
              <lb/>
            ius radius eſt par vni eorum, quæ ſunt circa rectum
              <lb/>
            angulum, circumferentia verò baſi.</s>
            <s xml:id="echoid-s11198" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11199" xml:space="preserve">Hæc oſtenditur ab Archimede lib. </s>
            <s xml:id="echoid-s11200" xml:space="preserve">de Dimenſione Circuli, Pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s11201" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11202" xml:space="preserve">propterea ibirecolatur.</s>
            <s xml:id="echoid-s11203" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1028" type="section" level="1" n="619">
          <head xml:id="echoid-head649" xml:space="preserve">THEOREMA III. PROPOS. III.</head>
          <p>
            <s xml:id="echoid-s11204" xml:space="preserve">OMnis ſector circuli æqualis eſt triangulo rectangu-
              <lb/>
            lo, cuius circuli radius eſt par vni eorum, quæ ſunt
              <lb/>
            circa rectum, circumferentia verò baſi illius ſectoris.</s>
            <s xml:id="echoid-s11205" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11206" xml:space="preserve">Si circulus, ABCD, cuius radius, ED, & </s>
            <s xml:id="echoid-s11207" xml:space="preserve">ſector, EDC, expo
              <lb/>
            ſito vero triangulo, HOM, cuius angulus, HMO, ſit rectus, & </s>
            <s xml:id="echoid-s11208" xml:space="preserve">
              <lb/>
            letus, HM, æquale ipſi, ED, &</s>
            <s xml:id="echoid-s11209" xml:space="preserve">, MO, circumferentiæ, ABCD,
              <lb/>
              <note position="right" xlink:label="note-0449-01" xlink:href="note-0449-01a" xml:space="preserve">33. Sexti
                <lb/>
              Blem.
                <lb/>
              Exantec.</note>
            ſit, MN, æqualis circumferentiæ, CD; </s>
            <s xml:id="echoid-s11210" xml:space="preserve">& </s>
            <s xml:id="echoid-s11211" xml:space="preserve">iungatur, HN. </s>
            <s xml:id="echoid-s11212" xml:space="preserve">Dico
              <lb/>
            ergo ſectorem, ECD, æquari triangulo, HNM,. </s>
            <s xml:id="echoid-s11213" xml:space="preserve">Nam circulus,
              <lb/>
            ABCD, ad ſectorem, CED, eſt vt circumferentia, ABCD, ad </s>
          </p>
        </div>
      </text>
    </echo>
Impressum