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]

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EPISTOLAE.
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            <div xml:id="echoid-div737" type="section" level="3" n="42">
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                <p>
                  <s xml:id="echoid-s4506" xml:space="preserve">
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                  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/>
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                  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>
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                <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/>
                    <anchor type="handwritten" xlink:label="hd-0393-02a" xlink:href="hd-0393-02"/>
                  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>
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                <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>
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                  <image file="0393-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0393-01"/>
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