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 |< < (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>