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 |< < (344) 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-div642" type="section" level="3" n="28">
              <div xml:id="echoid-div662" type="letter" level="4" n="7">
                <p>
                  <s xml:id="echoid-s4168" xml:space="preserve">
                    <pb o="344" rhead="IO. BAPT. BENED." n="356" file="0356" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0356"/>
                  refleyus ſecabit cathetum
                    <var>.b.o.</var>
                  in puncto
                    <var>.c.</var>
                  intra ſpeculum, nec dubitandum eſt quin
                    <lb/>
                  linea
                    <var>.e.b.</var>
                  ſectura ſit
                    <var>.b.o.</var>
                  eo quod cum angulus
                    <var>.o.e.c.</var>
                  ſit maior angulo
                    <var>.e.o.c.</var>
                  ex .19.
                    <lb/>
                  primi, & ſimiliter angulus
                    <var>.b.e.f.</var>
                  ſequitur ex .13. dicti, angulos
                    <var>.b.e.o.</var>
                  et
                    <var>.e.o.b.</var>
                  eſſe mi
                    <lb/>
                  nores duobus rectis, vnde ex penultima petitione primi, duæ lineæ
                    <var>.b.e.</var>
                  et
                    <var>.o.b.</var>
                    <reg norm="inuicem" type="context">inuicẽ</reg>
                    <lb/>
                  concurrent. </s>
                  <s xml:id="echoid-s4169" xml:space="preserve">Quare poſſumus ex hoc, quoddam corollarium extrahere, hoc eſt
                    <lb/>
                    <reg norm="neceſſarium" type="context">neceſſariũ</reg>
                    <reg norm="semper" type="context">sẽper</reg>
                  exiſtat, vt linea
                    <var>.c.e.</var>
                  minor eſſe linea
                    <var>.c.o</var>
                  . </s>
                  <s xml:id="echoid-s4170" xml:space="preserve">Sed vnde eueniat quod ip
                    <lb/>
                  ſa neceſſariò debeat ſemper maior eſſe ipſa
                    <var>.c.g.</var>
                  clarum eſt ex .7. tertij Eucli. </s>
                  <s xml:id="echoid-s4171" xml:space="preserve">Nunc
                    <lb/>
                  imaginemur ductas eſſe duas
                    <reg norm="tangentes" type="context">tãgentes</reg>
                    <var>.b.d.</var>
                  et
                    <var>.b.h.</var>
                  & ab
                    <var>.e.</var>
                    <reg norm="ipsam" type="context">ipsã</reg>
                    <var>.e.i.</var>
                  vnde certi erimus,
                    <lb/>
                  quod ab interuallo inter
                    <var>.h.</var>
                  et
                    <var>.d.</var>
                  punctum
                    <var>.b.</var>
                    <reg norm="ponſſibile" type="context">põſſibile</reg>
                  ſit vt reflectatur. </s>
                  <s xml:id="echoid-s4172" xml:space="preserve">Accipiamus
                    <lb/>
                  nunc
                    <var>.p.c.</var>
                  minorem medietate ipſius
                    <var>.b.c.</var>
                  & à puncto
                    <var>.p.</var>
                  imaginemur tangentem
                    <var>.p.q.</var>
                    <lb/>
                  in puncto
                    <var>.q.</var>
                  prorractaq́ue ſit
                    <var>.b.q.</var>
                  vt radius incidentiæ, </s>
                  <s xml:id="echoid-s4173" xml:space="preserve">tunc dico, radium reflexum
                    <lb/>
                  ipſius
                    <var>.b.q.</var>
                    <reg norm="non" type="context">nõ</reg>
                  concurrere in eodem puncto
                    <var>.c.</var>
                  ipſius catheti, ſi vero dixeris
                    <reg norm="quod" type="simple">ꝙ</reg>
                  ſic. </s>
                  <s xml:id="echoid-s4174" xml:space="preserve">Eſto
                    <lb/>
                    <reg norm="igitur" type="simple">igit̃</reg>
                  radius dictus
                    <var>.c.q.s</var>
                  . </s>
                  <s xml:id="echoid-s4175" xml:space="preserve">Imaginemur
                    <reg norm="tangentem" type="context context">tãgentẽ</reg>
                    <var>.e.i.</var>
                  in puncto
                    <var>.e.</var>
                  vnde ex .18. quinti Alha
                    <lb/>
                  zem, vel .12. ſexti Vitellionis proportio
                    <var>.b.i.</var>
                  ad
                    <var>.i.c.</var>
                  erit, vt
                    <var>.b.o.</var>
                  ad
                    <var>.o.c.</var>
                  & ſimiliter erit
                    <lb/>
                  ipſius
                    <var>.b.p.</var>
                  ad
                    <var>.p.c.</var>
                  vt
                    <var>.b.o.</var>
                  ad
                    <var>.o.c.</var>
                  ex eadem. </s>
                  <s xml:id="echoid-s4176" xml:space="preserve">Quare ex .11. quinti Eucli. proportio ip
                    <lb/>
                  ſius
                    <var>.b.p.</var>
                  ad
                    <var>.p.c.</var>
                  erit vt ipſius
                    <var>.b.i.</var>
                  ad
                    <var>.i.c.</var>
                  ſed quia
                    <var>.p.b.</var>
                  vt pars ipſius
                    <var>.b.i.</var>
                  minor eſt ip-
                    <lb/>
                  ſa, ergo ex .14. dicti
                    <var>.p.c.</var>
                  minor erit ipſa
                    <var>.c.i.</var>
                  hoc eſt totum minus ſua parte, quod eſt
                    <lb/>
                  impoſſibile, </s>
                  <s xml:id="echoid-s4177" xml:space="preserve">quare non in ipſo catheto videbitur imago ipſius obiecti.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4178" xml:space="preserve">Aliud notandum etiam cernere potes ex ipſis ſpeculis ſphæricis conuexis, hoc eſt
                    <lb/>
                  quod poſſibile ſit aliquoties, radium reflexum concurrere cum catheto incidentiæ
                    <lb/>
                  extra ſpeculum inter puncta
                    <var>.g.</var>
                  et
                    <var>.p.</var>
                  vt exempli gratia .ſi punctus
                    <var>.p.</var>
                  eſſet exactè
                    <lb/>
                  in medio inter
                    <var>.b.</var>
                  et g. </s>
                  <s xml:id="echoid-s4179" xml:space="preserve">tunc punctum
                    <var>.c.</var>
                  ipſius concurſus cum catheto incidentiæ eſſet
                    <lb/>
                  inter
                    <var>.g.</var>
                  et
                    <var>.p.</var>
                  eo quod
                    <reg norm="cum" type="context">cũ</reg>
                  linea
                    <var>.p.q.</var>
                  debeat @iui lere
                    <reg norm="angulum" type="context">angulũ</reg>
                    <var>.b.</var>
                  q, c.
                    <reg norm="per" type="simple">ꝑ</reg>
                  ęqualia, oportebit
                    <lb/>
                  c. poſitum eſſe inter
                    <var>.g.</var>
                  et
                    <var>.p.</var>
                  quia angulus
                    <var>.g.q.p.</var>
                  maior eſt angulo
                    <var>.p.q.b.</var>
                  vt per te faci
                    <lb/>
                  le potes ratiotinari, imaginando cir
                    <lb/>
                    <figure xlink:label="fig-0356-01" xlink:href="fig-0356-01a" number="388">
                      <image file="0356-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0356-01"/>
                    </figure>
                  culum circa
                    <reg norm="triangulum" type="context">triãgulum</reg>
                    <var>.g.q.b.</var>
                  & dia
                    <lb/>
                  merrum perpendicularem .ad
                    <var>.g.b.</var>
                    <lb/>
                  in puncto
                    <var>.p.</var>
                  producendo poſtea
                    <var>.q.
                      <lb/>
                    p.</var>
                    <reg norm="vſque" type="simple">vſq;</reg>
                  ad
                    <reg norm="alteram" type="context">alterã</reg>
                    <reg norm="partem" type="context">partẽ</reg>
                  circunferen-
                    <lb/>
                  tiæ ipſius circuli. </s>
                  <s xml:id="echoid-s4180" xml:space="preserve">
                    <reg norm="argumentando" type="context context">argumẽtãdo</reg>
                  dein-
                    <lb/>
                  de mediante vltima ſexti, illud
                    <reg norm="idem" type="context">idẽ</reg>
                    <lb/>
                  po@es etiam ſcire ex .22. quinti Alha
                    <lb/>
                  zeni. & ex .26. ſexti Vitellionis. </s>
                  <s xml:id="echoid-s4181" xml:space="preserve">vn-
                    <lb/>
                  de ſi ad ambas pupillas venerint ra
                    <lb/>
                  dij reflexi ipſius obiecti
                    <var>.b.a.</var>
                  duobus
                    <lb/>
                  punctis huiuſmodi ſpeculi, ita di-
                    <lb/>
                  ſtantibus à puncto
                    <var>.g.</var>
                  vt
                    <var>.q</var>
                  . </s>
                  <s xml:id="echoid-s4182" xml:space="preserve">tunc com
                    <lb/>
                  mune punctum concurſus axium vi
                    <lb/>
                  ſualium erit in catheto inter
                    <var>.g.p.</var>
                    <lb/>
                  vbi apparebit imago ex ſuperius di
                    <lb/>
                  ctis rationibus, ita vt
                    <reg norm="non" type="context">nõ</reg>
                  ſolum con
                    <lb/>
                  cauis, ſed etiam conuexis hoc accidere poſſit.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4183" xml:space="preserve">In planis autem
                    <reg norm="nunquam" type="context">nunquã</reg>
                  hoc poteſt euenire, vt tibi alias dixi, eo quod ſi
                    <reg norm="acceperi- mus" type="conjecture">accéperi-
                      <lb/>
                    mus</reg>
                    <reg norm="rectam" type="context">rectã</reg>
                    <var>.m.r.</var>
                  pro
                    <reg norm="coni" type="context">cõi</reg>
                  ſectione
                    <reg norm="ſuperficiei" type="simple">ſuꝑficiei</reg>
                    <var>.l.t.x.</var>
                  reflexionis &
                    <reg norm="ſuperficiei" type="simple">ſuꝑficiei</reg>
                  ſpeculi,
                    <reg norm="punctumque" type="context context simple">pũctũq́;</reg>
                    <lb/>
                  lucidum
                    <var>.l.</var>
                    <reg norm="protractoque" type="simple">protractoq́;</reg>
                  catheto
                    <var>.l.r.t.</var>
                    <reg norm="lineisque" type="simple">lineisq́;</reg>
                  incidentiæ
                    <var>.l.x.</var>
                  et
                    <var>.l.m.</var>
                  reflexionis etiam
                    <lb/>
                    <var>x.y.</var>
                  et
                    <var>.m.z.</var>
                  cum anguli
                    <var>.l.x.r.</var>
                  et
                    <var>.y.x.h.</var>
                  et
                    <var>.r.x.t.</var>
                  æquales inuicem ſint, & ſic anguli
                    <var>.l.m.
                      <lb/>
                    r.</var>
                  et
                    <var>.z.m.h.</var>
                  et
                    <var>.r.m.t.</var>
                  erit
                    <var>.r.t.</var>
                  tam pro triangulo
                    <var>.r.x.t.</var>
                  quam pro triangulo
                    <var>.r.m.t.</var>
                  æqua
                    <lb/>
                  lis
                    <var>.r.l.</var>
                  ex .26. primi, ita quod ſemper in puncto
                    <var>.t.</var>
                    <reg norm="conuenient" type="context">conueniẽt</reg>
                  omnes radij reflexi ipſius </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum