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

Page concordance

< >
Scan Original
271 85
272 86
273 87
274 88
275 89
276 90
277 91
278 92
279 93
280 94
281 95
282 96
283 97
284 98
285 99
286 100
287 101
288 102
289 103
290 104
291 105
292 106
293 107
294 108
295 109
296 110
297 111
298 112
299 113
300 114
< >
page |< < (69) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div224" type="section" level="1" n="102">
          <pb o="69" file="0093" n="93" rhead=""/>
          <p>
            <s xml:id="echoid-s2385" xml:space="preserve">Productis enim contingentibus EB, NI vſque ad aſymptotos in S, T, fiat
              <lb/>
            vt DB ad MI, ita BQ ad IV, & </s>
            <s xml:id="echoid-s2386" xml:space="preserve">per V applicetur VXY: </s>
            <s xml:id="echoid-s2387" xml:space="preserve">cum ſit DB maior
              <lb/>
            MI, erit BQ, & </s>
            <s xml:id="echoid-s2388" xml:space="preserve">IR maior IV, eſtque FB maior OI (cum duplum DB ſit maior
              <lb/>
            duplo MI) ergo tota FQ erit maior tota OV, & </s>
            <s xml:id="echoid-s2389" xml:space="preserve">QA ad VX erit vt DB
              <note symbol="a" position="right" xlink:label="note-0093-01" xlink:href="note-0093-01a" xml:space="preserve">38. h.</note>
            MI, & </s>
            <s xml:id="echoid-s2390" xml:space="preserve">quoniam QB ad VI, eſt vt BD ad IM, vel vt dimidium BF ad dimi-
              <lb/>
            dium IO, erit per-
              <lb/>
              <figure xlink:label="fig-0093-01" xlink:href="fig-0093-01a" number="63">
                <image file="0093-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0093-01"/>
              </figure>
            mutando, compo-
              <lb/>
            nendo, & </s>
            <s xml:id="echoid-s2391" xml:space="preserve">iterum
              <lb/>
            permutando QF ad
              <lb/>
            VO, vt BF ad IO,
              <lb/>
            vel vt DB ad MI; </s>
            <s xml:id="echoid-s2392" xml:space="preserve">& </s>
            <s xml:id="echoid-s2393" xml:space="preserve">
              <lb/>
            cum ſit quadratum
              <lb/>
            SB ad TI, vt rectan-
              <lb/>
            gulũ DBE ad MIN,
              <lb/>
            vtrunque enim eſt
              <lb/>
            quarta pars ſuæ fi-
              <lb/>
            guræ) vel vt qua-
              <lb/>
            dratum DB ad qua-
              <lb/>
            dratum MI; </s>
            <s xml:id="echoid-s2394" xml:space="preserve">ob rectangulorum ſimilitudinem) vel ſumptis ſubquadruplis, vt
              <lb/>
            quadratum FB ad OI, erit quoque linea SB ad TI, vt linea FB ad OI, & </s>
            <s xml:id="echoid-s2395" xml:space="preserve">per-
              <lb/>
            mutando SB ad BF, vt TI ad IO, ſed anguli SBF, TIO ſunt æquales per ſex-
              <lb/>
            tam ſecundarum definitionum, & </s>
            <s xml:id="echoid-s2396" xml:space="preserve">per conſtructionem, quare triangula SBF,
              <lb/>
            TIO erunt ſimilia, vti etiam triangula GQF, YVO, obidque homologa eo-
              <lb/>
            rum latera proportionalia erunt, hoc eſt GQ ad YV, vt FQ ad OV, ſed eſt
              <lb/>
            FQ maior OV, ergo, & </s>
            <s xml:id="echoid-s2397" xml:space="preserve">GQ erit maior YV, ſed FQ ad OV, eſt vt DB ad MI,
              <lb/>
            item AQ ad XV, vt DB ad MI, vt ſupra oſtendimus, quare GQ ad YV erit
              <lb/>
            vt AQ ad XV, & </s>
            <s xml:id="echoid-s2398" xml:space="preserve">permutando, & </s>
            <s xml:id="echoid-s2399" xml:space="preserve">per conuerſionem rationis, & </s>
            <s xml:id="echoid-s2400" xml:space="preserve">iterum per-
              <lb/>
            mutando GQ ad YV, vt GA ad YX, ſed eſt GQ maior YV, ergo, & </s>
            <s xml:id="echoid-s2401" xml:space="preserve">G A
              <lb/>
            maior YX, eſt autem YX maior PH, ergo eò magis GA erit maior PH. </s>
            <s xml:id="echoid-s2402" xml:space="preserve">Quod
              <lb/>
            erat demonſtrandum.</s>
            <s xml:id="echoid-s2403" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div226" type="section" level="1" n="103">
          <head xml:id="echoid-head108" xml:space="preserve">COROLL.</head>
          <p>
            <s xml:id="echoid-s2404" xml:space="preserve">EX hac patet, in ſimilibus Hyperbolis aſymptotos ad partes æqualium in-
              <lb/>
            clinationum ductas, æquales angulos cum diametris efficere, ac ideo
              <lb/>
            angulos ab aſymptotis factos eſſe inter ſe æquales. </s>
            <s xml:id="echoid-s2405" xml:space="preserve">Cum enim demonſtrata
              <lb/>
            ſint triangula SFB, TOI ſimilia, erunt anguli ad F, O, æquales; </s>
            <s xml:id="echoid-s2406" xml:space="preserve">eademque
              <lb/>
            ratione æquales etiam anguli ab alijs aſymptotis cum diametris ad alteram
              <lb/>
            partem conſtitutis; </s>
            <s xml:id="echoid-s2407" xml:space="preserve">vnde eorum aggregata, nempe anguli ab aſymptotis fa-
              <lb/>
            cti in ſimilibus Hyperbolis inter ſe æquales erunt.</s>
            <s xml:id="echoid-s2408" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum