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
291 279
292 280
293 281
294 288
295 283
296 284
297 285
298 286
299 287
300 288
301 289
302 290
303 291
304 292
305 293
306 294
307 295
308 296
309 297
310 298
311 299
312 300
313 301
314 302
315 303
316 304
317 305
318 306
319 307
320 308
< >
page |< < (376) 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-div730" type="section" level="3" n="41">
              <div xml:id="echoid-div730" type="letter" level="4" n="1">
                <pb o="376" rhead="IO. BABPT. BENED." n="388" file="0388" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0388"/>
                <p>
                  <s xml:id="echoid-s4447" xml:space="preserve">Poſſumus etiam probare quod periferia quadrati æqualis triangulo æquilatero
                    <lb/>
                  minor ſit periferia ipſius trianguli æquilateri. </s>
                  <s xml:id="echoid-s4448" xml:space="preserve">Cogita triangulum æquilaterum hic
                    <lb/>
                  ſubſcriptum
                    <var>.d.l.q.</var>
                  cuius baſis
                    <var>.l.q.</var>
                  diuiſa ſit per æqualia à perpendiculari
                    <var>.d.o.</var>
                    <reg norm="deſcri- ptumque" type="context simple">deſcri­
                      <lb/>
                    ptũq́;</reg>
                  ſit rectangulum
                    <var>.o.g.</var>
                  quod æquale erit triangulo
                    <var>.d.l.q.</var>
                  ſed periferia trianguli
                    <lb/>
                  maior eſt periferia rectanguli, nam
                    <var>.l.q.</var>
                  æqualis eſt
                    <var>.o.q.</var>
                  cum
                    <var>.d.g.</var>
                  ſed
                    <var>.q.d.</var>
                  maior eſt
                    <var>.o.
                      <lb/>
                    d.</var>
                  ex .18. primi, vnde
                    <var>.l.d.</var>
                  maior etiam
                    <var>.q.g.</var>
                  cum ex .34. dicti latera oppoſita ipſius re
                    <lb/>
                  ctanguli ſint inuicem æqualia, accipiamus poſtea
                    <var>.e.c.</var>
                  æqualem
                    <var>.o.d.</var>
                  et
                    <var>.c.h.</var>
                  indire-
                    <lb/>
                  ctum æqualem
                    <var>.o.q.</var>
                  circa quem diametrum
                    <var>.e.h.</var>
                  intelligatur circulus
                    <var>.e.i.h.k.</var>
                  et. à pun­
                    <lb/>
                  cto
                    <var>.c.</var>
                  dirigatur perpendicularis
                    <var>.k.i.</var>
                  ad
                    <var>.e.h.</var>
                  vnde ex .3. tertij
                    <var>.c.i.</var>
                  æqualis erit
                    <var>.c.k.</var>
                  & ex
                    <lb/>
                  34. quod fit ex
                    <var>.c.i.</var>
                  in
                    <var>.c.k.</var>
                  hoc eſt quadratum ipſius
                    <var>.c.i.</var>
                  æquale erit ei quod fit .ex
                    <var>.e.c.</var>
                    <lb/>
                  in
                    <var>.c.h.</var>
                  hoc eſt rectangulo
                    <var>.g.o.</var>
                  hoc eſt triangulo
                    <var>.d.l.q.</var>
                  ſed
                    <var>.e.h.</var>
                  eſt dimidium perife-
                    <lb/>
                  rię ipſius rectanguli
                    <var>.g.o.</var>
                  quæ minor eſt di midio periferiæ trianguli
                    <var>.d.l.q.</var>
                  vt vidimus
                    <lb/>
                  et
                    <var>.i.k.</var>
                  eſt dimidium periferię quadrati ipſius
                    <var>.i.c.</var>
                  & minor etiam ipſa
                    <var>.e.h.</var>
                  ex .14. tertij
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4449" xml:space="preserve">quare verum eſt propoſitum.</s>
                </p>
                <figure position="here" number="429">
                  <image file="0388-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0388-01"/>
                </figure>
                <p>
                  <s xml:id="echoid-s4450" xml:space="preserve">Sed quando periferiæ ſunt inuicem æquales, poſſumus etiam breuiter videre id
                    <lb/>
                  quod ſupradiximus, hoc eſt, quod quadratum, maius ſit triangulo æquilatero. </s>
                  <s xml:id="echoid-s4451" xml:space="preserve">Nam
                    <lb/>
                  cum
                    <var>.b.g.</var>
                  ſeſquitertia ſit ad
                    <var>.b.a.</var>
                  ergo
                    <var>.b.g.</var>
                  erit vt .4. et
                    <var>.b.a.</var>
                  ut .3. vnde
                    <var>.b.q.</var>
                  erit vt .16
                    <lb/>
                  et
                    <var>.b.l.</var>
                  vt .9. et
                    <var>.c.q.</var>
                  vt .8. </s>
                  <s xml:id="echoid-s4452" xml:space="preserve">quare
                    <var>.b.l.</var>
                  maius erit ipſo
                    <reg norm="rectangulo" type="context">rectãgulo</reg>
                    <var>.c.q.</var>
                  ſed
                    <var>.c.q.</var>
                  maius eſt
                    <reg norm="triam" type="context">triã</reg>
                    <lb/>
                  gulo
                    <var>.b.o.g.</var>
                  cum
                    <var>.q.g.</var>
                  quæ æqualis eſt
                    <var>.o.g.</var>
                  maior ſit
                    <var>.o.c.</var>
                  ex .18. vel penultima primi,
                    <lb/>
                  nam ſi
                    <var>.q.g.</var>
                  æqualis eſſet
                    <var>.o.c.</var>
                  </s>
                  <s xml:id="echoid-s4453" xml:space="preserve">tunc
                    <var>.c.q.</var>
                  æqualis eſſet triangulo
                    <var>.b.o.g.</var>
                  ex .41. primi.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4454" xml:space="preserve">Alia etiam via maiores noſtri vſi ſunt quæ generalis eſt vt in Theone ſupra Al-
                    <lb/>
                  mageſtum videre eſt, medijs perpendicularibus à centris ad latera figurarum, ſed
                    <lb/>
                  quia
                    <reg norm="differentia" type="context">differẽtia</reg>
                  longitudinum ipſarum perpendicularium alio medio inueniri poteſt,
                    <lb/>
                  eo quo ipſi vſi ſunt, prætermittere nolo quin tibi ſcribam.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4455" xml:space="preserve">Ego enim ita diſcurro.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4456" xml:space="preserve">Sint duæ figuræ iſoperimetrę æquilaterę & æquiangulæ, puta primò trian-
                    <lb/>
                  gulum & quadratum quorum centra ſint
                    <var>.e.</var>
                  et
                    <var>.o.</var>
                  à quibus centris ad latera ſint per-
                    <lb/>
                  pendiculares
                    <var>.e.n.</var>
                  et
                    <var>.o.u.</var>
                  vnde
                    <var>.n.</var>
                  et
                    <var>.u.</var>
                  diuident latera per æqualia vt ſcis, ducantur
                    <lb/>
                  poſtea
                    <var>.e.t.</var>
                  et
                    <var>.o.a.</var>
                  ad angulos dictorum laterum, vnde habebimus angulum
                    <var>.o.a.u.</var>
                    <reg norm="di- midium" type="context">di-
                      <lb/>
                    midiũ</reg>
                  recti, et
                    <var>.e.t.n.</var>
                  tertia pars vnius recti, vt ex te ipſo videre potes, </s>
                  <s xml:id="echoid-s4457" xml:space="preserve">quare angulus </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>