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

Page concordance

< >
Scan Original
121 101
122 102
123 103
124 104
125 105
126 106
127 107
128 108
129 109
130 110
131 111
132 112
133 113
134 114
135 115
136 116
137 117
138 118
139 119
140 120
141 121
142 122
143 123
144 124
145 125
146 126
147 127
148 128
149 129
150 130
< >
page |< < (91) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div219" type="section" level="1" n="142">
          <p>
            <s xml:id="echoid-s2247" xml:space="preserve">
              <pb o="91" file="0111" n="111" rhead="LIBER I."/>
            tantum ſui parte, velin vno puncto tantum, prędictas figuras, tan-
              <lb/>
            gant in punctis tantum, P, R, & </s>
            <s xml:id="echoid-s2248" xml:space="preserve">ab ipſis ducantur parallelę regulis,
              <lb/>
            dO, gY, ipſæ, PN, RT, occurrentes incidentibus, LO, uY, in
              <lb/>
            punctis, N, T, dico, LN, uY, ſimiliter ad eandem partem ſecari
              <lb/>
            in, N, T, ſi.</s>
            <s xml:id="echoid-s2249" xml:space="preserve">n. </s>
            <s xml:id="echoid-s2250" xml:space="preserve">hoc non ſit, diuidatur, LO, in, M, ſimiliter ad ean-
              <lb/>
            dem partem, acdiuiditur, uY, in, T, & </s>
            <s xml:id="echoid-s2251" xml:space="preserve">per, M, extendatur, MI,
              <lb/>
            parallela, dO, incidentes ambitui figuræ in, I, & </s>
            <s xml:id="echoid-s2252" xml:space="preserve">rurſus ſecetur, u
              <lb/>
            Y, in, V, ſimiliter ad eandem partem, vt ſecatur, LO, in, N, quia
              <lb/>
            ergo, N, eſt intra puncta, M, O, etiam, V, erit inter puncta, T,
              <lb/>
            Y; </s>
            <s xml:id="echoid-s2253" xml:space="preserve">ducatur tandem, VS, parallela, gY, incidens ambitui figurę in,
              <lb/>
            S. </s>
            <s xml:id="echoid-s2254" xml:space="preserve">Quia igitur, MI, non incidit in punctum contactus rectæ, H o,
              <lb/>
            cum figura, erit, MI, maior, NP, eadem ratione oſtendemus, SV,
              <lb/>
            fore maiorem ipſa, RT, eſt enim, RT, minima earum, quæ abin-
              <lb/>
            cidente, uY, ad ambitum figuræ duci poſſunt æquidiſtanter ipſi, g
              <lb/>
            Y. </s>
            <s xml:id="echoid-s2255" xml:space="preserve">Cum verò, IM, RT, ſimiliter diuidant, & </s>
            <s xml:id="echoid-s2256" xml:space="preserve">ad eandem partem
              <lb/>
            ipſas incidentes, LO, uY, erit, IM, ad, RT, vt, LO, ad, uY,
              <lb/>
              <note position="right" xlink:label="note-0111-01" xlink:href="note-0111-01a" xml:space="preserve">Defin. 10.
                <lb/>
              huius.</note>
            ideſt vt, PN, ad, SV, ergo, permutando, IM, ad, PN, erit vt,
              <lb/>
            RT, ad, SV, eſt autem, IM, maior, PN, ergo etiam, RT, erit
              <lb/>
            maior, SV, ſed etiam minor, quod eſt abſurdum, ergo falſum eſt ip-
              <lb/>
            ſas, PN, RT, non ſecare ſimiliter ad eandem partem ipſas, LO,
              <lb/>
            uY, ſic igitur eaſdem diuidunt, eritque, PN, ad, RT, hoc eſt, H
              <lb/>
            L, ad, Xu, vt, LO, ad, uY, idem oſtendemus etiam ſi contactus
              <lb/>
            eſſet in parte linearum, Ho, XZ, ſeu in totis eiſdem lineis, vt conſi-
              <lb/>
            deranti facilè innoteſcet. </s>
            <s xml:id="echoid-s2257" xml:space="preserve">Eadem autem methodo probabimus etiam,
              <lb/>
            DL, pu, eſſe vt ipſas, LO, uY, ergo reſiduæ, DH, pX, hoc eſt,
              <lb/>
            AC, FK, erunt vt, LO, uY, ideſt vt, E4, ℟ &</s>
            <s xml:id="echoid-s2258" xml:space="preserve">, ſed, AC, FK,
              <lb/>
            ſimiliter ſunt diuiſę ab homologis, sl, 7 4, productis, in punctis, B,
              <lb/>
              <note position="right" xlink:label="note-0111-02" xlink:href="note-0111-02a" xml:space="preserve">Defin. 10.
                <lb/>
              huius.</note>
            G, ergo, AB, ad, FG, ideſt, DE, ad, p℟, erit vt, AC, ad, F
              <lb/>
            K, ideſt vt, E 4, ad, ℟ &</s>
            <s xml:id="echoid-s2259" xml:space="preserve">. Extendantur, NP, TR, quę diuidunt,
              <lb/>
            LO, uY, ſimiliter ad eandem partem, ſecentque ipſos, E4, ℟ &</s>
            <s xml:id="echoid-s2260" xml:space="preserve">,
              <lb/>
            in punctis, 2, 3, incidat autem, NQ, in, Q, punctum contactus
              <lb/>
            lineæ, Ad, cum figura, oſtendemus, vt factum eſt circa ipſas, NP,
              <lb/>
            TR, etiam, T8, incidere in punctum contactus rectę, p g, cum fi-
              <lb/>
            gura, quod ſit ipſum, 8, quoniam ergo probatum eſt, DE, ad, p
              <lb/>
            ℟, eſſe vt, E4, ad, ℟ &</s>
            <s xml:id="echoid-s2261" xml:space="preserve">, erit etiam, Q2, ad, 83, vt, E4, ad,
              <lb/>
            ℟ &</s>
            <s xml:id="echoid-s2262" xml:space="preserve">. Similiter probabimus, 2P, ad, 3R, eſſe vt, E4, ad, ℟ &</s>
            <s xml:id="echoid-s2263" xml:space="preserve">,
              <lb/>
            & </s>
            <s xml:id="echoid-s2264" xml:space="preserve">diuidunt ipſas, E4, ℟ &</s>
            <s xml:id="echoid-s2265" xml:space="preserve">, ſimiliter ad eandem partem, à quibus
              <lb/>
            viciſſim ſecantur ad eundem angulum ex eadem parte, cum, E4, ℟
              <lb/>
            &</s>
            <s xml:id="echoid-s2266" xml:space="preserve">, ſint parallelæ ipſis, LO, uY, ergo, E4, ℟ &</s>
            <s xml:id="echoid-s2267" xml:space="preserve">, erunt incidentes
              <lb/>
            ſimilium figurarum, PlQs, R487, & </s>
            <s xml:id="echoid-s2268" xml:space="preserve">oppoſitarum tangentium,
              <lb/>
              <note position="right" xlink:label="note-0111-03" xlink:href="note-0111-03a" xml:space="preserve">24, huius.</note>
            DH, do, pX, gZ, quod etiam veriſicaretur de ipſis homologis, ls,
              <lb/>
            47, ſi fuiſſent ad oppoſitas tangentes terminatę in punctis, E, 4, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum