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

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            <s xml:id="echoid-s3476" xml:space="preserve">
              <pb o="147" file="0167" n="167" rhead="LIBER II."/>
            BM, angulus, HFE, æqualis eſt angulo illi coalterno, BCM, &</s>
            <s xml:id="echoid-s3477" xml:space="preserve">,
              <lb/>
            HEF, ipſi, FDC, qui eſt æqualis angulo illi oppoſito, FAC, qui
              <lb/>
            tandem æquatur angulo, MBC; </s>
            <s xml:id="echoid-s3478" xml:space="preserve">interior exteriori, ideò anguius,
              <lb/>
            FEH, æquatur angulo, MBC, ſunt igitur in triangulis, FEH, M
              <lb/>
            BC, duo anguli duobus angulis æquales, & </s>
            <s xml:id="echoid-s3479" xml:space="preserve">latera illis adiacentia
              <lb/>
            ſunt æqualia, nempè, FE, ipſi, BC, ergo reliqua latera erunt æ-
              <lb/>
              <note position="right" xlink:label="note-0167-01" xlink:href="note-0167-01a" xml:space="preserve">26. Primi
                <lb/>
              Elem.</note>
            qualia, .</s>
            <s xml:id="echoid-s3480" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s3481" xml:space="preserve">HE, ipſi, BM, eodem modo oſtendemus de cæteris pa-
              <lb/>
            rallelis ipſi, CD, eas nempè, quæ verſus puncta, F, C, abſcindunt
              <lb/>
            à lateribus, FD, CA, partes æquales, eſſe pariter inter ſe æquales,
              <lb/>
            veiuti ſunt extremæ, AF, CD, æquales, ergo omnes lineæ trian-
              <lb/>
            guli, CAF, æquabuntur omnibus lineis trianguli, FDC, ſumptis
              <lb/>
              <note position="right" xlink:label="note-0167-02" xlink:href="note-0167-02a" xml:space="preserve">3. huius.</note>
            in vtriſq; </s>
            <s xml:id="echoid-s3482" xml:space="preserve">omnibus lineis regula, CD, ergo triangulus, ACF, erit
              <lb/>
            æqualis triangulo, FDC, ergo duo trianguli, ACF, FDC, ſcili-
              <lb/>
            cet parallelogrammum, AD, erit duplum cuiuſuis triangulorum, A
              <lb/>
            CF, FCD, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s3483" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div361" type="section" level="1" n="220">
          <head xml:id="echoid-head235" xml:space="preserve">COROLLARIVM I.</head>
          <p style="it">
            <s xml:id="echoid-s3484" xml:space="preserve">_H_Inc patet, quæcunq; </s>
            <s xml:id="echoid-s3485" xml:space="preserve">de parallelogrammis in Prop. </s>
            <s xml:id="echoid-s3486" xml:space="preserve">5.</s>
            <s xml:id="echoid-s3487" xml:space="preserve">6.</s>
            <s xml:id="echoid-s3488" xml:space="preserve">7. </s>
            <s xml:id="echoid-s3489" xml:space="preserve">& </s>
            <s xml:id="echoid-s3490" xml:space="preserve">8.
              <lb/>
            </s>
            <s xml:id="echoid-s3491" xml:space="preserve">huius Librioſtenſaſunt, eadem de triangulis vt verarecipi poſſe,
              <lb/>
            ſi in triangulis conditiones ibi oppoſitæ repertæ fuerint, nam in vnoquo-
              <lb/>
            que expoſitorum triangulorum ſumptis duobus quibuſuis lateribus ſieri
              <lb/>
            poteſt ſub illis in eodem angulo parallelogr ammum, cuius triangulum
              <lb/>
            erit dimidium. </s>
            <s xml:id="echoid-s3492" xml:space="preserve">Triangula ergo, quæ in eadem ſunt altitudine inter ſe
              <lb/>
            ſunt, vt baſes: </s>
            <s xml:id="echoid-s3493" xml:space="preserve">Et quæ in eadem baſi mierſe ſunt, vt altitudines, vel vt
              <lb/>
            latera æqualiter baſibus inclinata; </s>
            <s xml:id="echoid-s3494" xml:space="preserve">Item babent rationem compoſitam ex
              <lb/>
            ratione baſium, & </s>
            <s xml:id="echoid-s3495" xml:space="preserve">altitudinum, ſine laterum æqualiter baſibus inclina-
              <lb/>
            torum, cum ſunt æquiangulæ: </s>
            <s xml:id="echoid-s3496" xml:space="preserve">Item triangula, quorum baſes altitudi-
              <lb/>
            nibus, vel lateribus æqualiter baſibus inclinatis, reciprocantur ſunt æ-
              <lb/>
            qualia; </s>
            <s xml:id="echoid-s3497" xml:space="preserve">& </s>
            <s xml:id="echoid-s3498" xml:space="preserve">quæ ſunt æqualia baſes habent altitudinibus, vel lateribus
              <lb/>
            æqualiter baſibus inclmatis, reciprocas: </s>
            <s xml:id="echoid-s3499" xml:space="preserve">Et tandem habetur ſimilia trian-
              <lb/>
              <note position="right" xlink:label="note-0167-03" xlink:href="note-0167-03a" xml:space="preserve">_Iux. diff._
                <lb/>
              _1. Sexti_
                <lb/>
              _Elem._</note>
            gula eſſe in dupla ratione laterum homologorum, quæ omnia ex præſenti
              <lb/>
            Propoſ. </s>
            <s xml:id="echoid-s3500" xml:space="preserve">pendent.</s>
            <s xml:id="echoid-s3501" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div363" type="section" level="1" n="221">
          <head xml:id="echoid-head236" xml:space="preserve">COROLLARIVM II.</head>
          <p style="it">
            <s xml:id="echoid-s3502" xml:space="preserve">_C_Olligitur in ſuper, ſi ſupponamur, CD, eſſe æqualem ipſi, DF,
              <lb/>
            quamlibet ductam in triangulo, FCD, parallelam ipſi, CD, æqua-
              <lb/>
            lem eſſe ei, quam ipſa abſcindit ab, FD, verſus, F, nempè ipſi abſciſſæ,
              <lb/>
            FE, & </s>
            <s xml:id="echoid-s3503" xml:space="preserve">producta, EH, verjus, AC, cui incidat in, N, ipſam, HN,
              <lb/>
            æquari reſiduæ abſciſſæ, FE, .</s>
            <s xml:id="echoid-s3504" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s3505" xml:space="preserve">ipſi, ED, &</s>
            <s xml:id="echoid-s3506" xml:space="preserve">, NE, integram </s>
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