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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IO. BAPT. BENED.
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            <div xml:id="echoid-div703" type="section" level="3" n="35">
              <div xml:id="echoid-div703" type="letter" level="4" n="1">
                <pb o="364" rhead="IO. BAPT. BENED." n="376" file="0376" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0376"/>
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            <div xml:id="echoid-div708" type="section" level="3" n="36">
              <div xml:id="echoid-div708" type="letter" level="4" n="1">
                <head xml:id="echoid-head536" xml:space="preserve">DE AVGMENTO PONDERIS CORPORIS
                  <lb/>
                ad ſtateram appenſi, & quadam alia demonſtratione,
                  <lb/>
                & quibuſdam erroribus Tartaleæ.</head>
                <head xml:id="echoid-head537" style="it" xml:space="preserve">Mutio Groto.</head>
                <p>
                  <s xml:id="echoid-s4350" xml:space="preserve">SI ea quæ à me audiuiſti non credis, conſidera quæſo libram ſeu ſtateram
                    <lb/>
                    <var>o.a.</var>
                  cuius centrum non longitudinis ſed ponderum ſit
                    <var>.i.</var>
                  quę ſtatera, vt ori
                    <lb/>
                  zontaliter conſiſtat, oportebit pondus extremitatis
                    <var>.o.</var>
                  ita ſe habere
                    <lb/>
                  ad pondus extremitatis
                    <var>.a.</var>
                  ut
                    <var>.a.i.</var>
                  ſe habet ad
                    <var>.o.i.</var>
                  quod te ſcire puto, ima
                    <lb/>
                  ginemur nunc d uas lineas
                    <var>.a.e.</var>
                  et
                    <var>.o.n.</var>
                  paralle las
                    <reg norm="infinitasque" type="simple">infinitasq́;</reg>
                  & à puncto
                    <var>.n.</var>
                  immobili,
                    <lb/>
                  & fixo extra ſtateram, tranſeat per
                    <var>.i.</var>
                  linea
                    <var>.n.i.e</var>
                  . </s>
                  <s xml:id="echoid-s4351" xml:space="preserve">Cogitemus etiam punctum
                    <var>.e.</var>
                  inter
                    <lb/>
                  ſectionis ipſius
                    <var>.n.i.e.</var>
                  cum
                    <var>.a.e.</var>
                  progredi vniformiter
                    <reg norm="continuòque" type="simple">continuòq́;</reg>
                  ab
                    <var>.a.</var>
                  per lineam
                    <var>.a.e.</var>
                    <lb/>
                  vnde punctum
                    <var>.i.</var>
                  interſectionis ipſius
                    <var>.n.i.e.</var>
                  cum
                    <var>.a.i.o.</var>
                  ſemper vicinius fiet puncto
                    <var>.o.</var>
                    <lb/>
                  nec unquam cum illo vnum erit, quamuis moueatur tempore infinito. </s>
                  <s xml:id="echoid-s4352" xml:space="preserve">Nunc autem
                    <lb/>
                  dico, quod cum ſtateram
                    <var>.o.i.a.</var>
                  oporteat ſemper orizontalem eſſe virtute ponderis,
                    <lb/>
                  o. oportebit pundus
                    <var>.o.</var>
                  in infinitum etiam augeri,
                    <reg norm="quotieſcunque" type="simple">quotieſcunq;</reg>
                  pondus
                    <var>.a.</var>
                  nunquam
                    <lb/>
                  diminui voluerimus vel econtra hoc in infinitum diminui, ſi illud nunquam augeri
                    <lb/>
                  voluerimus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4353" xml:space="preserve">Sedre vera non putabam te indigere aliqua demonſtratione, quod linea
                    <var>.b.h.</var>
                  di-
                    <lb/>
                  uiſa ſit per æqualia à
                    <unsure/>
                  linea
                    <var>.c.a.</var>
                  cum hæc perpendicularis ſit ab
                    <var>.a.</var>
                  ad baſim
                    <var>.g.d.</var>
                  in
                    <reg norm="triam" type="context">triã</reg>
                    <lb/>
                  gulo orthogonio
                    <var>.g.a.d.</var>
                  & cum ſit
                    <var>.b.h.</var>
                  perpendicularis ad
                    <var>.a.o.</var>
                  ex ſuppoſito quæ
                    <var>.a.
                      <lb/>
                    o.</var>
                  in ſe habet punctum medium baſis
                    <var>.g.d.</var>
                  nec
                    <reg norm="non" type="context">nõ</reg>
                  illud anguli recti
                    <var>.a.</var>
                  quod per ſe cla
                    <lb/>
                  riſſimum eſt, cum iam ſcis
                    <var>.o.</var>
                  eſſe centrum circuli circundantis triangulum
                    <var>.g.a.d.</var>
                  or-
                    <lb/>
                  thogonium, et
                    <var>.g.d.</var>
                  eius diameter, vnde
                    <var>.o.a.</var>
                  æquabitur ipſi
                    <var>.o.g.</var>
                  quapropter angulus
                    <lb/>
                  o.
                    <reg norm="am" type="context">ã</reg>
                  . g. æquabitur angulo
                    <var>.g.</var>
                  ex quinta primi, </s>
                  <s xml:id="echoid-s4354" xml:space="preserve">deinde ex .32. eiuſdem, angulus
                    <var>.h.</var>
                  æqua
                    <lb/>
                  bitur angulo
                    <var>.d.</var>
                  eo quod an gulus
                    <var>.e.</var>
                  rectus eſt, quemadmodum et
                    <var>.a.</var>
                  ſed angulus
                    <var>.d.</var>
                    <lb/>
                  æqualis eſt angulo
                    <var>.g.a.c</var>
                  . </s>
                  <s xml:id="echoid-s4355" xml:space="preserve">& propterea angulus
                    <var>.h.</var>
                  erit etiam æqualis angulo
                    <var>.h.a.u.</var>
                    <lb/>
                  vnde
                    <var>.h.u.</var>
                  æqualis erit ipſi
                    <var>.u.
                      <lb/>
                    a.</var>
                  ex .6. primi, cum poſtea angulus
                    <var>.
                      <lb/>
                      <anchor type="figure" xlink:label="fig-0376-01a" xlink:href="fig-0376-01"/>
                    o.a.d.</var>
                  æqualis ſitangulo
                    <var>.d.</var>
                  ex quin­
                    <lb/>
                  ta primi erit angulus
                    <var>.a.b.e.</var>
                  æqua-
                    <lb/>
                  lis angulo
                    <var>.g.</var>
                  ex .32. dicta, eo quod
                    <lb/>
                  e. rectus eſt, & ex eadem æqualis
                    <lb/>
                  erit angulo
                    <var>.d.a.c.</var>
                  vnde
                    <var>.u.b.</var>
                  erit
                    <lb/>
                  æqualis ipſi
                    <var>.u.a.</var>
                  ex .6. dicti, & ideo
                    <lb/>
                  æqualis eric ipſi
                    <var>.u.h</var>
                  . </s>
                  <s xml:id="echoid-s4356" xml:space="preserve">Reliqua ve-
                    <lb/>
                  rò illius propoſitionis credo ex te
                    <lb/>
                  omnia poſſe
                    <reg norm="intelligere" type="context">ĩtelligere</reg>
                  , excepto,
                    <reg norm="quod" type="simple">ꝙ</reg>
                    <lb/>
                  vt tibi ſignificaui ſi à
                    <reg norm="puncto" type="context">pũcto</reg>
                    <var>.i.</var>
                  com-
                    <lb/>
                  muni ipſi
                    <var>.a.c.u.</var>
                  & circunferentiæ,
                    <lb/>
                  ducta fuerit
                    <var>.i.x.</var>
                  ad
                    <reg norm="punctum" type="context">pũctum</reg>
                    <var>.x.</var>
                  com
                    <lb/>
                  mune vni parallelæ à
                    <reg norm="puncto" type="context">pũcto</reg>
                    <var>.g.</var>
                  ipſi
                    <lb/>
                    <var>h.b.</var>
                  & circunferentiæ, quod di-
                    <lb/>
                  cta
                    <var>.i.x.</var>
                  ad rectos erit ipſi
                    <var>.a.b.d.</var>
                  eo
                    <lb/>
                  quod cum angulus
                    <var>.a.g.x.</var>
                  æqualis </s>
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