Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

Page concordance

< >
Scan Original
331 319
332 320
333 321
334 322
335 323
336 324
337 325
338 326
339 327
340 328
341 329
342 330
343 331
344 332
345 333
346 334
347 335
348 336
349 337
350 338
351 339
352 340
353 341
354 342
355 343
356 344
357 345
358 346
359 347
360 348
< >
page |< < (351) of 445 > >|
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div670" type="section" level="3" n="29">
              <div xml:id="echoid-div673" type="letter" level="4" n="2">
                <pb o="351" rhead="EPISTOL AE." n="363" file="0363" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0363"/>
                <p>
                  <s xml:id="echoid-s4222" xml:space="preserve">Volo etiam quod ad partem
                    <var>.c.l.s.</var>
                  quadrilateri conſtituta ſit alia parallela ad
                    <var>.z.
                      <lb/>
                    r.</var>
                  & in æquali diſtantia ab ipſa quemadmodum
                    <var>.u.n.</var>
                  diſtat ad eademmet
                    <var>.z.r.</var>
                  ad ean
                    <lb/>
                  dem operationem faciendam. </s>
                  <s xml:id="echoid-s4223" xml:space="preserve">Vnde in vno tantummodo itinere puncti
                    <var>.s.</var>
                  ab
                    <var>.r.</var>
                    <reg norm="vſque" type="simple">vſq;</reg>
                    <lb/>
                  ad
                    <var>.c.</var>
                  deſignabimus quartam partem ſectionis, conuerſo poſtea inſtrumento, hoc eſt
                    <lb/>
                  poſito puncto
                    <var>.r.</var>
                  vbi prius erat
                    <var>.z.</var>
                  et
                    <var>.z.</var>
                  vbi erat
                    <var>.r.</var>
                  aliam delineabimus quartam, &
                    <lb/>
                  ſic ad oppoſitam partem ipſius
                    <var>.z.r.</var>
                  faciendum erit. </s>
                  <s xml:id="echoid-s4224" xml:space="preserve">Hoc inſtrumentum poſſumus
                    <lb/>
                  etiam ita conſtruere, vt puncta
                    <var>.o.</var>
                  et
                    <var>.K.</var>
                  poſſint collocari in laterihus
                    <var>.c.e.</var>
                  et
                    <var>.e.s.</var>
                  vbi no
                    <lb/>
                  bis magis libuerit, ita vt licebit in qualibet proportione
                    <reg norm="axium" type="context">axiũ</reg>
                  propoſita, oxygoniam
                    <lb/>
                  deſignare. </s>
                  <s xml:id="echoid-s4225" xml:space="preserve">Nam
                    <var>.c.o.</var>
                  erit longitudo dimidij axis minoris, et
                    <var>.c.e.</var>
                  dimidij maioris.</s>
                </p>
              </div>
            </div>
            <div xml:id="echoid-div676" type="section" level="3" n="30">
              <div xml:id="echoid-div676" type="letter" level="4" n="1">
                <head xml:id="echoid-head515" xml:space="preserve">DE CONSTITVTIONE TRIANGVLI
                  <lb/>
                orthogonij conditionati.</head>
                <head xml:id="echoid-head516" style="it" xml:space="preserve">Domino Ludouico de Rocchaforte.</head>
                <p>
                  <s xml:id="echoid-s4226" xml:space="preserve">
                    <emph style="sc">QVod</emph>
                  à me poſtulas, non eſt admodum difficile, cupis enim triangulum
                    <lb/>
                  orthogonium, exempli gratia
                    <var>.o.i.e.</var>
                  in figura
                    <var>.A.</var>
                  ita conſtituere, vt di-
                    <lb/>
                  uiſum ſit à perpendiculari
                    <var>.a.i.</var>
                  & quod proportio
                    <var>.o.e.</var>
                  ad
                    <var>.o.i.</var>
                  ſit vt
                    <var>.o.i.</var>
                  ad
                    <lb/>
                    <var>i.e.</var>
                  & quod quadrati
                    <var>.o.i.</var>
                  ad quadratum
                    <var>.o.a.</var>
                  ſit vt
                    <var>.e.i.</var>
                  ad
                    <var>.e.a.</var>
                  & quadra
                    <lb/>
                  tum
                    <var>.o.i.</var>
                  ad quadratum
                    <var>.e.i.</var>
                  ſit .ut
                    <var>.o.a.</var>
                  ad
                    <var>.e.a</var>
                  . </s>
                  <s xml:id="echoid-s4227" xml:space="preserve">Quæ omnia in promptu veniunt, quo
                    <lb/>
                  tieſcunque
                    <var>.o.e.</var>
                  fuerit diameter alicuius circuli,
                    <reg norm="diuiſaque" type="simple">diuiſaq́;</reg>
                  in puncto
                    <var>.a.</var>
                  ſecundum pro
                    <lb/>
                  portionem habentem medium
                    <reg norm="duoque" type="simple">duoq́;</reg>
                  extrema, protracta deinde perpendiculari
                    <var>.a.
                      <lb/>
                    i.</var>
                  ad
                    <var>o.e.</var>
                  uſque ad circunferentiam,
                    <reg norm="coniunctæque" type="simple">coniunctæq́;</reg>
                    <var>.o.i.</var>
                  et
                    <var>.i.e</var>
                  : tale triangulum, omnia
                    <lb/>
                  ſupradicta in ſe continebit.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4228" xml:space="preserve">Nam ex .30. tertij angulus
                    <var>.i.</var>
                  rectus erit, & ex .8. ſexti
                    <var>.o.i.</var>
                  erit media proportio-
                    <lb/>
                  nalis inter
                    <var>.o.e.</var>
                  et
                    <var>.o.a.</var>
                  et
                    <var>.e.i.</var>
                  inter
                    <var>.o.e.</var>
                    <lb/>
                    <figure xlink:label="fig-0363-01" xlink:href="fig-0363-01a" number="400">
                      <image file="0363-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0363-01"/>
                    </figure>
                  et
                    <var>.a.e.</var>
                  ſed quia ex diuiſione facta in
                    <reg norm="pum" type="context">pũ</reg>
                    <lb/>
                  cto
                    <var>.a.</var>
                  etiam
                    <var>.o.a.</var>
                  erit media proportio-
                    <lb/>
                  nalis inter totum & reſiduum, ideo ex
                    <num value="11">.
                      <lb/>
                    11.</num>
                  quinti ita erit
                    <var>.o.e.</var>
                  ad
                    <var>.e.i.</var>
                  vt
                    <var>.o.e.</var>
                  ad
                    <var>.
                      <lb/>
                    o.a.</var>
                  vnde ex .9. eiuſdem
                    <var>.a.o.</var>
                  erit æqua-
                    <lb/>
                  lis
                    <var>.e.i.</var>
                  & ideo
                    <var>.o.i.</var>
                  erit media proportio
                    <lb/>
                  nalis inter
                    <var>.o.e.</var>
                  et
                    <var>.e.i</var>
                  . </s>
                  <s xml:id="echoid-s4229" xml:space="preserve">Sed quia propor-
                    <lb/>
                  tio
                    <var>.e.i.</var>
                  ad
                    <var>.a.e.</var>
                    <reg norm="eadem" type="context">eadẽ</reg>
                  eſt, quę ipſius
                    <var>.o.e.</var>
                  ad
                    <lb/>
                    <var>o.a</var>
                  . </s>
                  <s xml:id="echoid-s4230" xml:space="preserve">tunc videbis ex .18. ſexti, quod pro
                    <lb/>
                  portio quadrati
                    <var>.o.i.</var>
                  ad quadratum
                    <var>.o.a.</var>
                    <lb/>
                  erit vt
                    <var>.e.i.</var>
                  ad
                    <var>.e.a.</var>
                  cum vero duo trian-
                    <lb/>
                  guli
                    <var>.o.i.a.</var>
                  et
                    <var>.a.i.e.</var>
                  ſint inuicem ſimiles
                    <lb/>
                  ex ſupradicta .8. ſexti, </s>
                  <s xml:id="echoid-s4231" xml:space="preserve">tunc videbis ex
                    <lb/>
                  18. et .17. eiuſdem dictos
                    <reg norm="triangulos" type="context">triãgulos</reg>
                  ean
                    <lb/>
                  dem habere inter ſe proportionem, quę
                    <lb/>
                  eſt inrer quadrata ipſius
                    <var>.o.i.</var>
                  et
                    <var>.i.e.</var>
                  vnde
                    <lb/>
                  ex prima ſexti ita ſe inuicem habebunt
                    <var>.
                      <lb/>
                    a.o.</var>
                  et
                    <var>.a.e</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4232" xml:space="preserve">Circa eam verò difficultatem quam </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>