Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

Table of figures

< >
[Figure 141]
Page: 176
[Figure 142]
Page: 179
[Figure 143]
Page: 183
[Figure 144]
Page: 184
[Figure 145]
Page: 184
[Figure 146]
Page: 185
[Figure 147]
Page: 186
[Figure 148]
Page: 188
[Figure 149]
Page: 189
[Figure 150]
Page: 190
[Figure 151]
Page: 191
[Figure 152]
Page: 192
[Figure 153]
Page: 193
[Figure 154]
Page: 194
[Figure 155]
Page: 195
[Figure 156]
Page: 196
[Figure 157]
Page: 197
[Figure 158]
Page: 198
[Figure 159]
Page: 199
[Figure 160]
Page: 200
[Figure 161]
Page: 201
[Figure 162]
Page: 202
[Figure 163]
Page: 203
[Figure 164]
Page: 204
[Figure 165]
Page: 205
[Figure 166]
Page: 205
[Figure 167]
Page: 206
[Figure 168]
Page: 207
[Figure 169]
Page: 208
[Figure 170]
Page: 208
< >
page |< < (48) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div671" type="section" level="1" n="267">
          <pb o="48" file="0230" n="230" rhead=""/>
        </div>
        <div xml:id="echoid-div673" type="section" level="1" n="268">
          <head xml:id="echoid-head277" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s6429" xml:space="preserve">EX hac facilè elicietur methodus, qua precipuas quorumlibet Acumi-
              <lb/>
            natorum paſſiones oſtendi poſſint, nempe: </s>
            <s xml:id="echoid-s6430" xml:space="preserve">ipſa Acuminata à diame-
              <lb/>
            tris bifariam ſecari: </s>
            <s xml:id="echoid-s6431" xml:space="preserve">& </s>
            <s xml:id="echoid-s6432" xml:space="preserve">Proportionalia Acuminata ęqualium altitudinum
              <lb/>
            inter ſe eſſe vt baſes: </s>
            <s xml:id="echoid-s6433" xml:space="preserve">& </s>
            <s xml:id="echoid-s6434" xml:space="preserve">(tanquam Corollarium) Acuminata proportio-
              <lb/>
            nalia æqualium baſium eſſe inter ſe vt altitudines: </s>
            <s xml:id="echoid-s6435" xml:space="preserve">item duo quæcunque
              <lb/>
            Acuminata proportionalia habere inter ſe rationem compoſitam ex ratio-
              <lb/>
            ne baſium, & </s>
            <s xml:id="echoid-s6436" xml:space="preserve">ex ratione altitudinum: </s>
            <s xml:id="echoid-s6437" xml:space="preserve">& </s>
            <s xml:id="echoid-s6438" xml:space="preserve">ad inſcripta triangula, vel cir-
              <lb/>
            cumſcripta parallelogramma eandem retinere rationem, aliaque his ſimi-
              <lb/>
            lia: </s>
            <s xml:id="echoid-s6439" xml:space="preserve">& </s>
            <s xml:id="echoid-s6440" xml:space="preserve">quod de proportionalibus Acuminatis, idem penitus euenire de ſi-
              <lb/>
            milibus menſalibus proportionalium Acuminatorum, præmiſſa priùs ha-
              <lb/>
            rum menſalium definitione, &</s>
            <s xml:id="echoid-s6441" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6442" xml:space="preserve">quæ omnia infinitas figurarum ſpecies
              <lb/>
              <gap/>
            , ne dum hactenus tractatis Parabolis, Hyperbolis, &</s>
            <s xml:id="echoid-s6443" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6444" xml:space="preserve">maximè con-
              <lb/>
            ducunt. </s>
            <s xml:id="echoid-s6445" xml:space="preserve">Sed hæc aliàs, quę tamen cum ſint haud obſcurę indagationis,
              <lb/>
            & </s>
            <s xml:id="echoid-s6446" xml:space="preserve">huic noſtro inſtituto prorſus aliena, erudito Lectori ſic præmonſtraſſe
              <lb/>
            ſuſſiciat.</s>
            <s xml:id="echoid-s6447" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div674" type="section" level="1" n="269">
          <head xml:id="echoid-head278" xml:space="preserve">LEMMA XI. PROP. XXXVIII.</head>
          <p>
            <s xml:id="echoid-s6448" xml:space="preserve">Si duæ rectæ lineæ inter ſe æquales fuerint, & </s>
            <s xml:id="echoid-s6449" xml:space="preserve">parallelæ, & </s>
            <s xml:id="echoid-s6450" xml:space="preserve">
              <lb/>
            ab earum extremis terminis ducantur lineæ quemlibet angulum
              <lb/>
            efficientes, ab alteris autem terminis aliæ ipſis æquidiſtantes;
              <lb/>
            </s>
            <s xml:id="echoid-s6451" xml:space="preserve">hæ quoque angulum inter datas conſtituent, & </s>
            <s xml:id="echoid-s6452" xml:space="preserve">recta angulo-
              <lb/>
            rum vertices coniungens erit vtrique datarum æqualis, & </s>
            <s xml:id="echoid-s6453" xml:space="preserve">pa-
              <lb/>
            rallela.</s>
            <s xml:id="echoid-s6454" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6455" xml:space="preserve">Si verò datæ rectæ lineæ terminatæ ad quemcunque angulum
              <lb/>
            applicatæ fuerint, & </s>
            <s xml:id="echoid-s6456" xml:space="preserve">vbicunque proportionaliter ſectę, aut pro-
              <lb/>
            ductæ, atque ab homologis earum punctis, hoc eſt, vel ab ex-
              <lb/>
            tremis terminis, vel ab inter-ſectionum, aut productionum pun-
              <lb/>
            ctis, ductæ fuerint intra datum angulum aliæ rectæ lineæ, quæ
              <lb/>
            item angulum quemlibet conſtituant, à reliquis verò punctis aliæ
              <lb/>
            ipſis æquidiſtanter ducantur, hæ pariter tertium angulum effi-
              <lb/>
            cient intra datum, & </s>
            <s xml:id="echoid-s6457" xml:space="preserve">horum trium angulorum vertices in vna
              <lb/>
            eademque recta linea reperientur.</s>
            <s xml:id="echoid-s6458" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6459" xml:space="preserve">SIt, in prima figura, recta A B æqualis, & </s>
            <s xml:id="echoid-s6460" xml:space="preserve">parallela ad C D, & </s>
            <s xml:id="echoid-s6461" xml:space="preserve">exter-
              <lb/>
            minis A, C inter eas conſtituatur angulus quicunque A E C ducta-
              <lb/>
            que B F parallela ad A E, D F verò ad C E. </s>
            <s xml:id="echoid-s6462" xml:space="preserve">Dico B F, D F inter datas
              <lb/>
            æquidiſtantes conuenire, & </s>
            <s xml:id="echoid-s6463" xml:space="preserve">E F iungentem angulorum vertices, alteri A
              <lb/>
            B, vel C D eſſe æqualem, & </s>
            <s xml:id="echoid-s6464" xml:space="preserve">parallelam.</s>
            <s xml:id="echoid-s6465" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6466" xml:space="preserve">Iungantur A C, B D: </s>
            <s xml:id="echoid-s6467" xml:space="preserve">& </s>
            <s xml:id="echoid-s6468" xml:space="preserve">quoniam B F eſt parallela ad A E, erit angu-
              <lb/>
            lus G B F æqualis angulo B A E; </s>
            <s xml:id="echoid-s6469" xml:space="preserve">cumque A B ſit æqualis, & </s>
            <s xml:id="echoid-s6470" xml:space="preserve">parallela </s>
          </p>
        </div>
      </text>
    </echo>
Impressum