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

Page concordance

< >
Scan Original
151 131
152 132
153 133
154 134
155 135
156 136
157 137
158 138
159 139
160 140
161 141
162 142
163 143
164 144
165 145
166 146
167 147
168 148
169 149
170 150
171 151
172 152
173 153
174 154
175 155
176 156
177 157
178 158
179 159
180 160
< >
page |< < (258) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div616" type="section" level="1" n="358">
          <p style="it">
            <s xml:id="echoid-s6454" xml:space="preserve">
              <pb o="258" file="0278" n="278" rhead="GEOMETRIÆ"/>
            logrammo, FP, quod dicimus ſimilare, ſemper eſſe cylindricum, geni-
              <lb/>
            tum verò ex triangulo, DEP, ſemper eſſe conicum, vt etiam accidit in
              <lb/>
            omni parallelogrammo, & </s>
            <s xml:id="echoid-s6455" xml:space="preserve">triangulo, dummodò regula ſit vnum laterum
              <lb/>
            eorundem, ſolida igitur ſimilariagenita ex parallelogrammis ſunt cy-
              <lb/>
            lindrici, genita verò ex triangulis ſunt conici, genita inquam, regula,
              <lb/>
            vno laterum eorundem exiſtente; </s>
            <s xml:id="echoid-s6456" xml:space="preserve">quod ſi figuræ quæ dicuntur omnes fi-
              <lb/>
            guræ ſimiles par allelogrammidati, regula vno laterum, ſint eirculi, ille
              <lb/>
            cylindricus erit cylindrus; </s>
            <s xml:id="echoid-s6457" xml:space="preserve">& </s>
            <s xml:id="echoid-s6458" xml:space="preserve">ſi, quæ dicuntur omnes figuræ ſimiles dati
              <lb/>
            trianguli ſint pariter cirouli, regula vno laterum, conicus erit conus;
              <lb/>
            </s>
            <s xml:id="echoid-s6459" xml:space="preserve">nomine ergo communi bic cylindrus, & </s>
            <s xml:id="echoid-s6460" xml:space="preserve">conus dicti ſunt ſolida ſimila-
              <lb/>
            ria nomine particulari dicti ſunt cylindricus, & </s>
            <s xml:id="echoid-s6461" xml:space="preserve">conicus, ſed nomine,
              <lb/>
            magis particulari, & </s>
            <s xml:id="echoid-s6462" xml:space="preserve">proprio dicuntur cylindrus, & </s>
            <s xml:id="echoid-s6463" xml:space="preserve">conus, quotieſcun-
              <lb/>
              <note position="left" xlink:label="note-0278-01" xlink:href="note-0278-01a" xml:space="preserve">_34. Lib. 2._</note>
            que dictæ figuræ ſint circuli, iuxta alibi à me oſtenſa.</s>
            <s xml:id="echoid-s6464" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6465" xml:space="preserve">Pariter ſi figuræ genitrices ſolidorum ſint circuli, vel ellipſes, illæ
              <lb/>
            autem, quæ dicuntur @omnes figuræ ſimiles earundem ſumptæ cum datis
              <lb/>
            regulis) ſint pariter circuli, quorum deſcribentes rectæ lineæ in figuris
              <lb/>
            genitricibus ſint eorundem diametri, ſolida ſimilaria genita ex eiſdem,
              <lb/>
            iuxta eaſdem regulas, erunt, alterum ſpbæra, quod ſcilicet gignitur ex
              <lb/>
              <note position="left" xlink:label="note-0278-02" xlink:href="note-0278-02a" xml:space="preserve">_@6. Lib. 1._</note>
            circulo, alterum ſphæroides quod ſcilicet gignitur ex ellipſi, ſi figuræ
              <lb/>
            ſimiles rectè ſecent axem ellipſis, & </s>
            <s xml:id="echoid-s6466" xml:space="preserve">ſint erectæ tum circulo, tum ellipſi;
              <lb/>
            </s>
            <s xml:id="echoid-s6467" xml:space="preserve">
              <note position="left" xlink:label="note-0278-03" xlink:href="note-0278-03a" xml:space="preserve">_47. Eiuſd._
                <lb/>
              _lib. 1._</note>
            poterit etiam eſſe ſpbæroides, etiamſi figuræ ſimiles non ſint circuli, ſed
              <lb/>
            ellipſes iuxta alibi oſtenſa; </s>
            <s xml:id="echoid-s6468" xml:space="preserve">quæ igitur in boc caſu nomine communi di-
              <lb/>
            cuntur, ſolida ſimilaria genita ex circulo, vel ellipſi, iuxta datas regu-
              <lb/>
            las, nomine particulari, & </s>
            <s xml:id="echoid-s6469" xml:space="preserve">proprio, dicuntur ſphæra, vel ſphæroides:
              <lb/>
            </s>
            <s xml:id="echoid-s6470" xml:space="preserve">Et quæ pariter dicerentur nomine communi ſolida ſimilaria genita ex
              <lb/>
            portione tali, vel tali, iuxta talem regulam, portione inquam circuli,
              <lb/>
            vel ellipſis, quotieſcunque figuræ, quæ dicuntur, omnes figuræ ſimiles
              <lb/>
            talis portionis iuxta eandem regulam, ſint circuli erecti genitricibus,
              <lb/>
            & </s>
            <s xml:id="echoid-s6471" xml:space="preserve">figura genitrix pontio circuli, erit, & </s>
            <s xml:id="echoid-s6472" xml:space="preserve">dicetur nomine particulari, & </s>
            <s xml:id="echoid-s6473" xml:space="preserve">
              <lb/>
            proprio, portio ſphæræ; </s>
            <s xml:id="echoid-s6474" xml:space="preserve">ſi verò ſigura genitrix ſit ellipſis portio, & </s>
            <s xml:id="echoid-s6475" xml:space="preserve">ſi-
              <lb/>
              <note position="left" xlink:label="note-0278-04" xlink:href="note-0278-04a" xml:space="preserve">_46. Lib. 1._</note>
            guræ ſimiles ſint circuli erecti genitricibus, rectè axem portionis ſecan-
              <lb/>
              <note position="left" xlink:label="note-0278-05" xlink:href="note-0278-05a" xml:space="preserve">_47. Lib. 1._</note>
            tes, ſiet portio ſphæroidis, quod ſi ſint ellipſes erectæ genitricibus, dia-
              <lb/>
            metros habentes, vt poſtulat Propoſ. </s>
            <s xml:id="echoid-s6476" xml:space="preserve">47. </s>
            <s xml:id="echoid-s6477" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s6478" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6479" xml:space="preserve">fiet etiam portio ſphæ-
              <lb/>
            roidis: </s>
            <s xml:id="echoid-s6480" xml:space="preserve">Sic igitur nommibus particularibus hæc ſolida vocari conſuene-
              <lb/>
            runt. </s>
            <s xml:id="echoid-s6481" xml:space="preserve">Cum verò figuræ ſimiles non ſunt neq; </s>
            <s xml:id="echoid-s6482" xml:space="preserve">circuli, neq; </s>
            <s xml:id="echoid-s6483" xml:space="preserve">ellipſes ſum-
              <lb/>
            ptæ, vt dictum eſt, ſufficiet eadem vocare nomine communi ſolidi ſimi-
              <lb/>
            Laris, &</s>
            <s xml:id="echoid-s6484" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6485" xml:space="preserve">licet ad variationem, & </s>
            <s xml:id="echoid-s6486" xml:space="preserve">nominationem ſimilium figurarum,
              <lb/>
            conſequenter & </s>
            <s xml:id="echoid-s6487" xml:space="preserve">eadem varia ſolida, variè nominari poſſent; </s>
            <s xml:id="echoid-s6488" xml:space="preserve">fortè autem
              <lb/>
            in ſequentibus ex genitricium figurarum variatione varia nomina com-
              <lb/>
            ponemus, interim hæc teneantur, hoc animaduerſo, quod in ſuperiori-
              <lb/>
            bus, dum ſit ſphæra, vel ſphæroides, vel eorundem portio, ſuppono li-
              <lb/>
            neas, quæ ſunt in genitricibus ſiguris, & </s>
            <s xml:id="echoid-s6489" xml:space="preserve">circulos, vel ellipſes </s>
          </p>
        </div>
      </text>
    </echo>
Impressum