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
361 349
362 350
363 351
364 352
365 353
366 354
367 355
368 356
369 357
370 358
371 359
372 360
373 361
374 362
375 363
376 364
377 365
378 366
379 367
380 368
381 369
382 370
383 371
384 372
385 373
386 374
387 375
388 376
389 377
390 378
< >
page |< < (377) 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">
                <p>
                  <s xml:id="echoid-s4457" xml:space="preserve">
                    <pb o="377" rhead="EPISTOLAE." n="389" file="0389" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0389"/>
                  a. ſeſquialter erit angulo
                    <var>.t.</var>
                  quod vt clarius videas cogita lineam
                    <var>.b.d.</var>
                  cuius medietas
                    <lb/>
                  ſit
                    <var>.c.d.</var>
                  tertia verò pars illius ſit
                    <var>.g.d.</var>
                  </s>
                  <s xml:id="echoid-s4458" xml:space="preserve">tunc dico
                    <var>.c.d.</var>
                  ſeſquialteram eſſe ipſi
                    <var>.g.d.</var>
                  ſit enim
                    <lb/>
                    <var>f.d.</var>
                  duplum ipſius
                    <var>.g.d.</var>
                  </s>
                  <s xml:id="echoid-s4459" xml:space="preserve">quare
                    <var>.f.d.</var>
                  erunt duæ tertiæ totius lineę
                    <var>.b.d.</var>
                  & quia eadem pro
                    <lb/>
                  portio eſt totius
                    <var>.b.d.</var>
                  ad
                    <var>.c.d.</var>
                  quæ
                    <var>.f.d.</var>
                  ad
                    <var>.g.d.</var>
                  ergo permutando eadem erit totius
                    <var>.b.
                      <lb/>
                    d.</var>
                  ad
                    <var>.f.d.</var>
                  quæ
                    <var>.c.d.</var>
                  ad
                    <var>.g.d</var>
                  . </s>
                  <s xml:id="echoid-s4460" xml:space="preserve">Sed
                    <var>.b.d.</var>
                  ad
                    <var>.f.d.</var>
                  ſeſquialtera eſt, verum igitur erit quod an-
                    <lb/>
                  gulus
                    <var>.a.</var>
                  ſeſquialter ſit ipſi
                    <var>.t.</var>
                  deinde
                    <var>.t.n.</var>
                  eſt ſeſquitertia ipſi
                    <var>.a.u.</var>
                  vt ſuperius vidimus .
                    <lb/>
                  in eorum duplis. </s>
                  <s xml:id="echoid-s4461" xml:space="preserve">ſcimus etiam
                    <var>.n.e.</var>
                  eſſe dimidium ipſius
                    <var>.t.e.</var>
                  co quod cum
                    <var>.e.t.n.</var>
                  ſit
                    <lb/>
                  tertia pars vnius recti, angulus,
                    <var>t.e.n.</var>
                  erit duo tertia vnius recti, vnde
                    <var>.e.n.</var>
                  erit latus.
                    <lb/>
                  exagoni æquilateris inſcriptibilis circulo cuius diameter ſit
                    <var>.e.t.</var>
                  </s>
                  <s xml:id="echoid-s4462" xml:space="preserve">quare
                    <var>.e.t.</var>
                  dupla erit
                    <lb/>
                  ipſi
                    <var>.e.n.</var>
                  in longitudine, ſed quadrupla in potentia: </s>
                  <s xml:id="echoid-s4463" xml:space="preserve">t.n. vero tripla in potentia ipſi
                    <var>.n.
                      <lb/>
                    e.</var>
                  ex penultima primi, quæ omnia etiam ex .8. tertijdecimi. Eucli. elicere potes, ſed
                    <lb/>
                    <var>c.n.</var>
                  erat ſexquitertia ipſi
                    <var>.a.u.</var>
                  in longitudine, hoc eſt ipſi
                    <var>.o.u.</var>
                  nam
                    <var>.o.u.</var>
                  æqualis eſt ipſi
                    <lb/>
                    <var>a.u</var>
                  . </s>
                  <s xml:id="echoid-s4464" xml:space="preserve">quare
                    <var>.n.t.</var>
                  erit minus quam dupla in potentia ipſi
                    <var>.o.u.</var>
                  hoc eſt, vt .16. ad .9. ergo
                    <lb/>
                  maior proportio erit ipſius
                    <var>.t.n.</var>
                  in potentia ad
                    <var>.n.e.</var>
                  quam ad
                    <var>.o.u.</var>
                  </s>
                  <s xml:id="echoid-s4465" xml:space="preserve">quare etiam in lon
                    <lb/>
                  gitudine, maior proportio erit ipſius
                    <var>.t.n.</var>
                  ad
                    <var>.n.e.</var>
                  quam ad
                    <var>.o.u.</var>
                  vnde
                    <var>.o.u.</var>
                  longior erit
                    <lb/>
                  ipſa
                    <var>.n.e.</var>
                  quod eſt propoſitum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4466" xml:space="preserve">Sed ſi
                    <var>.o.a.u.</var>
                  eſſet pentagonus æquilaterus & æquiangulus, ſimiliter probabo per-
                    <lb/>
                  pendicularem
                    <var>.o.u.</var>
                  longiorem eſſe
                    <var>.n.e.</var>
                  ipſius trianguli æquilateri, dummodo ſint iſo-
                    <lb/>
                  perimetrę. </s>
                  <s xml:id="echoid-s4467" xml:space="preserve">Sit enim
                    <var>.a.u.</var>
                  dimidium lateris pentagoni ex ſuppoſito, cuius centrum ſit
                    <lb/>
                  o. </s>
                  <s xml:id="echoid-s4468" xml:space="preserve">tunc proportio
                    <var>.t.n.</var>
                  ad
                    <var>.a.u.</var>
                  erit ſuperbipartienstertias, vt ex ordine iam hic ſupradi
                    <lb/>
                  cto à te facillimè elicere potes, hoc eſt, vt .5. ad .3. et
                    <var>.a.u.</var>
                  minor erit
                    <var>.o.u.</var>
                  eo quod
                    <lb/>
                  angulus
                    <var>.o.</var>
                  minor erit angulo
                    <var>.a.</var>
                  nam angulus
                    <var>.o.</var>
                  erit quinta pars
                    <reg norm="duorum" type="context">duorũ</reg>
                  rectorum, hoc
                    <lb/>
                  eſt duæ quintæ vnius recti, vnde angulus
                    <var>.a.</var>
                  reſiduum vnius recti erit tres quin-
                    <lb/>
                  tæ vnius recti, </s>
                  <s xml:id="echoid-s4469" xml:space="preserve">quare angulus
                    <var>.a.</var>
                  maior ericangulo
                    <var>.o.</var>
                  & conſequenter latus
                    <var>.o.u.</var>
                  ma-
                    <lb/>
                  ius latere
                    <var>.a.u.</var>
                  ſed
                    <var>.t.n.</var>
                  minor eſt quam tripla in potentia ad
                    <var>.a.u.</var>
                  eo quod erit vt .25.
                    <lb/>
                  ad .9. cum in longitudine ſit vt .5. ad .3. ſed dicta
                    <var>.t.n.</var>
                  tripla eſt in potentia ad
                    <var>.e.n.</var>
                  qua-
                    <lb/>
                  re
                    <var>.a.u.</var>
                  maior erit ipſa
                    <var>.e.n.</var>
                  ſed
                    <var>.o.u.</var>
                  maior eſt ipſa
                    <var>.a.u.</var>
                  vt diximus, igitur multo magis
                    <var>.
                      <lb/>
                    o.u.</var>
                  maior eſt ipſa
                    <var>.a.u.</var>
                  vt
                    <reg norm="diximus" type="simple">diximꝰ</reg>
                  &
                    <reg norm="conſequenter" type="context context">cõſequẽter</reg>
                  multo magis
                    <var>.o.u.</var>
                  maior erit ipſa
                    <var>.n.e</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4470" xml:space="preserve">Quotieſcunque enim cognoſcimus proportionem anguli
                    <var>.o.</var>
                  ad angulum
                    <var>.a.</var>
                  quod
                    <lb/>
                  quidem facillimum eſt, nec non proportionem
                    <var>.t.n.</var>
                  ad
                    <var>.a.u.</var>
                  quod, etiam illico cogno-
                    <lb/>
                  ſcitur, </s>
                  <s xml:id="echoid-s4471" xml:space="preserve">tunc exſcientia cordarum & arcuum omnia etiam facillimè innueniuntur.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4472" xml:space="preserve">Verum circa
                    <reg norm="triangulum" type="context">triangulũ</reg>
                  æquilaterum, & pentagonum, alium
                    <reg norm="modum" type="context">modũ</reg>
                  inueni, ſed aliquan
                    <lb/>
                  tulum prolixiorem.</s>
                </p>
                <figure position="here" number="430">
                  <image file="0389-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0389-01"/>
                </figure>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>