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
411 399
412 400
413 401
414 402
415 403
416 404
417 405
418 406
419 407
420 408
421 409
422 410
423 411
424 412
425 413
426 414
427 415
428 416
429 417
430 418
431 419
432 420
433 421
434 422
435 423
436 424
437 425
438 426
439
440
< >
page |< < (381) 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-div737" type="section" level="3" n="42">
              <div xml:id="echoid-div737" type="letter" level="4" n="1">
                <p>
                  <s xml:id="echoid-s4506" xml:space="preserve">
                    <pb o="381" rhead="EPISTOLAE." n="393" file="0393" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0393"/>
                  tractat de centris libræ, ſeu ſtateræ: </s>
                  <s xml:id="echoid-s4507" xml:space="preserve">A ſpice igitur in .4. ſupradicta, quod cum appen-
                    <lb/>
                  ſæ fuerint omnes illæ partes ponderum, partibus longitudinis ipſius
                    <var>.l.K.</var>
                  in qua volo
                    <lb/>
                  vt à punctis
                    <var>.e.</var>
                  et
                    <var>.d.</var>
                  imagineris duas lineas
                    <var>.e.o.</var>
                  et
                    <var>.d.u.</var>
                  inuicem æquales, & ferè per-
                    <lb/>
                  pendiculares ipſi
                    <var>.l.K.</var>
                  hoc eſt reſpicientes mundi centrum; </s>
                  <s xml:id="echoid-s4508" xml:space="preserve">imagineris etiam
                    <var>.o.u.</var>
                    <lb/>
                    <handwritten xlink:label="hd-0393-01" xlink:href="hd-0393-01a" number="20"/>
                  quæ ſit paralle la ipſi
                    <var>.l.k.</var>
                  quæ diuiſa ſit in puncto
                    <var>.i.</var>
                  ſupra
                    <var>.g</var>
                  . </s>
                  <s xml:id="echoid-s4509" xml:space="preserve">Hinc nulli dubium erit,
                    <lb/>
                  cum
                    <var>.g.</var>
                  fuerit centrum totius ponderis appenſi ipſi
                    <var>.l.K.</var>
                  quod
                    <var>.i.</var>
                  ſimiliter erit centrum
                    <lb/>
                  cum directe locatum ſit ſupra
                    <var>.g.</var>
                  hoc eſt in eadem directionis linea, quod quidem
                    <lb/>
                  non indiget aliqua demonſtratione, cum per ſe ſatis pateat. </s>
                  <s xml:id="echoid-s4510" xml:space="preserve">Vnde ex communi
                    <lb/>
                  conceptu
                    <var>.o.</var>
                  erit centrum ponderis appenſi ipſi
                    <var>.l.h.</var>
                  et
                    <var>.u.</var>
                  erit centrum ponderis ap-
                    <lb/>
                  penſi. ipſi
                    <var>h.K</var>
                  . </s>
                  <s xml:id="echoid-s4511" xml:space="preserve">Scimus
                    <reg norm="igitur" type="simple">igit̃</reg>
                    <var>.i.</var>
                  eſſe
                    <reg norm="centrum" type="context">cẽtrum</reg>
                  duorum, hoc eſt ipſius
                    <var>.l.h.</var>
                  & ipſius
                    <var>.h.k.</var>
                  con
                    <lb/>
                  tinuatorum per totam
                    <var>.l.k</var>
                  . </s>
                  <s xml:id="echoid-s4512" xml:space="preserve">Nunc ergo ſi conſideremus
                    <var>.l.k.</var>
                  diuiſam eſſe, hoc eſt di-
                    <lb/>
                  ſiunctam in puncto
                    <var>.h.</var>
                  inueniemus nihilominus
                    <var>.i.</var>
                  centrum eſſe dictorum ponderum,
                    <lb/>
                  & quod tantum eſt, ipſam eſſe
                    <reg norm="continuam" type="context">continuã</reg>
                  , quantum diuiſam in dicto puncto
                    <var>.h.</var>
                  neque
                    <lb/>
                  ex hoc, punctum
                    <var>.i.</var>
                  erit magis vel minus centrum duorum ponderum
                    <var>.l.h.</var>
                  et
                    <var>.h.k.</var>
                  quo
                    <lb/>
                  rum vnum pendet totum ab
                    <var>.o.</var>
                  aliud verò totum ab
                    <var>.u.</var>
                  & hoc modo in longitudine
                    <var>.
                      <lb/>
                    o.u.</var>
                  diuiſa vt dictum eſt, habebimus propoſitum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4513" xml:space="preserve">Reliquam propoſitionem tibi relinquo.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4514" xml:space="preserve">Illa verò propoſitio, quam tibi dixi Archimedem tacuiſſe in huiuſmodi materia
                    <lb/>
                  eſt, quod ſi duo pondera æquilibrant ab extremis alicuius ſtateræ, in certis præfixis
                    <lb/>
                  diſtantijs à centro. </s>
                  <s xml:id="echoid-s4515" xml:space="preserve">Tunc dico ſi eorum vno manente alterum moueatur remotius
                    <lb/>
                  ab ipſo centro quod illud deſcendet, & ſi vicinius ipſi centro appenſum fuerit aſcen-
                    <lb/>
                  det. </s>
                  <s xml:id="echoid-s4516" xml:space="preserve">Hæc enim propoſitio quotidie omnibus in locis videtur, ipſam verſo4; </s>
                  <s xml:id="echoid-s4517" xml:space="preserve">puto Ar
                    <lb/>
                  chimedem prætermiſiſſe ob facilitatem, cum ab antedicta ferè dependeat.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4518" xml:space="preserve">Sit exempli gratia ſtatera
                    <var>.a.u.</var>
                  cuius centr um ſit
                    <var>.i.</var>
                  & pondera
                    <var>.u.a.</var>
                  appenſa, ſein-
                    <lb/>
                    <handwritten xlink:label="hd-0393-02" xlink:href="hd-0393-02a" number="21"/>
                  uicem habeant vt
                    <var>.i.u.</var>
                  et
                    <var>.i.a.</var>
                  ſe inuicem habent. </s>
                  <s xml:id="echoid-s4519" xml:space="preserve">Nunc dico quod ſi pondus ipſius
                    <var>.u.</var>
                    <lb/>
                  poſitum fuerit vicinius centro vt puta in
                    <var>.o.</var>
                  inmoto exiſtente pondere, a. quod bra-
                    <lb/>
                  chium
                    <var>.i.o.u.</var>
                  aſcendet, & è conuerſo, ſi remotius poſitum fuerit, deſcendet.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4520" xml:space="preserve">
                    <reg norm="Ponatur" type="simple">Ponat̃</reg>
                  ergo vt
                    <reg norm="dictum" type="context">dictũ</reg>
                  eſt in
                    <var>.o.</var>
                  vicinius
                    <reg norm="centro" type="context">cẽtro</reg>
                  , quapropter brachium
                    <var>.i.o.</var>
                    <reg norm="breuius" type="simple">breuiꝰ</reg>
                  erit
                    <lb/>
                  brachio
                    <var>.i.u.</var>
                  vnde minor proportio erit ipſius
                    <var>.i.o.</var>
                  ad
                    <var>.i.a.</var>
                  quàm.i.u. ad eundem
                    <var>.a.i.</var>
                  &
                    <lb/>
                  conſequenter quam ponderis ipſius
                    <var>.a.</var>
                  (quod ſit
                    <var>.n.e.</var>
                  ) ad pondus ipſius
                    <var>.u</var>
                  . </s>
                  <s xml:id="echoid-s4521" xml:space="preserve">Quare ſi cx
                    <lb/>
                  pondere
                    <var>.n.e.</var>
                  dempta fuerit
                    <var>.e.</var>
                  pars eius, ita quod reliqua pars
                    <var>.n.</var>
                  ſe habeat ad pondus
                    <lb/>
                  o. vt ſe habet. i
                    <unsure/>
                    <var>.o.</var>
                  ad
                    <var>.i.a.</var>
                  tunc ſtatera non mouebitur; </s>
                  <s xml:id="echoid-s4522" xml:space="preserve">addita verò parte
                    <var>.e.</var>
                  ex com-
                    <lb/>
                  muni conceptu, a. deſcendet vnde
                    <var>.o.</var>
                  aſcenderet conuerſum verò ex ſimilibus ratio-
                    <lb/>
                  nibus per te concludes.</s>
                </p>
                <figure position="here" number="434">
                  <image file="0393-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0393-01"/>
                </figure>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>