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 top:20.5%;left:8.42%;width:83.14%;height:12.75%'><span style=3D'font-size:=
136%;
 color:white;mso-color-index:0'>Origini, storia e </span></span><span
 style=3D'position:absolute;top:33.75%;left:8.23%;width:83.52%;height:12.75=
%'><span
 style=3D'font-size:136%;color:white;mso-color-index:0'>sviluppi del calcol=
o </span></span><span
 style=3D'position:absolute;top:47.25%;left:8.42%;width:83.14%;height:12.75=
%'><span
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n></span></div>
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13.29%;
 width:68.16%;height:4.5%'><span style=3D'font-size:63%;color:white;mso-col=
or-index:
 0'>Storia del pensiero scientifico I e II&#13;</span></div>
 <div style=3D'mso-line-spacing:"80 20 0";position:absolute;top:71.5%;left:=
13.29%;
 width:68.16%;height:4.5%'><span style=3D'font-size:63%;color:white;mso-col=
or-index:
 0'>a.a. 2007/2008&#13;</span></div>
 <div style=3D'mso-line-spacing:"80 20 0";position:absolute;top:76.0%;left:=
13.29%;
 width:68.16%;height:4.5%'><span style=3D'font-size:63%;color:white;mso-col=
or-index:
 0;display:none'>&#13;</span></div>
 <div style=3D'mso-line-spacing:"80 20 0";position:absolute;top:80.25%;
 left:13.29%;width:68.16%;height:4.0%'><span style=3D'font-size:56%;color:w=
hite;
 mso-color-index:0'>Docente </span><span style=3D'font-size:56%;color:white;
 mso-color-index:0'><i>Flavia Marcacci</i></span></div>
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 seguito illustrato &egrave; ad uso strettamente didattico e non utilizzabi=
le
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 <div class=3DB style=3D'position:absolute;top:18.5%;left:4.49%;width:88.2%;
 height:6.75%'><span style=3D'mso-special-format:nobullet;display:none'>&#8=
226;</span>Bibliografia&#13;</div>
 <div class=3DB1><span style=3D'position:absolute;top:26.24%;left:12.73%;
 width:84.64%;height:4.0%'><span style=3D'font-size:64%'><span class=3DB1B
 style=3D'position:absolute;left:-3.76%'>&#8211;</span></span><span
 style=3D'font-size:64%'>E. Giusti, </span><span style=3D'font-size:64%'><i=
>Piccola
 storia del calcolo infinitesimale dall&#8217;antichit&agrave; al </i></spa=
n></span><span
 style=3D'position:absolute;top:30.25%;left:12.73%;width:87.82%;height:4.0%=
'><span
 style=3D'font-size:64%'><i>Novecento</i></span><span style=3D'font-size:64=
%'>,
 Istituti Editoriali e Poligrafici Internazionali, Pisa-Roma </span></span>=
<span
 style=3D'position:absolute;top:34.25%;left:12.73%;width:79.96%;height:4.0%=
'><span
 style=3D'font-size:64%'>2007.&#13;</span></span></div>
 <div class=3DB1><span style=3D'position:absolute;top:39.0%;left:12.73%;wid=
th:87.64%;
 height:4.0%'><span style=3D'font-size:64%'><span class=3DB1B style=3D'posi=
tion:absolute;
 left:-3.63%'>&#8211;</span></span><span style=3D'font-size:64%'>F. Giusti
 &#8211; E. Bartoli, </span><span style=3D'font-size:64%'><i>Analisi. Fonda=
menti
 teorici</i></span><span style=3D'font-size:64%'>, Ed. Tramontana, </span><=
/span><span
 style=3D'position:absolute;top:43.0%;left:12.73%;width:79.96%;height:4.0%'=
><span
 style=3D'font-size:64%'>Milano 1990.&#13;</span></span></div>
 <div class=3DB1 style=3D'position:absolute;top:48.0%;left:9.55%;width:84.6=
4%;
 height:4.0%'><span style=3D'position:absolute;top:0%;left:3.76%;width:96.2=
3%;
 height:100.0%'><span style=3D'font-size:64%'><span class=3DB1B style=3D'po=
sition:
 absolute;left:-3.9%'>&#8211;</span></span><span style=3D'font-size:64%'>G.
 Prodi, </span><span style=3D'font-size:64%'><i>Analisi matematica</i></spa=
n><span
 style=3D'font-size:64%'>, Bollati Boringhieri, Torino 1992.&#13;</span></s=
pan></div>
 <div class=3DB1 style=3D'position:absolute;top:52.74%;left:9.55%;width:83.=
33%;
 height:4.0%'><span style=3D'position:absolute;top:0%;left:3.82%;width:96.1=
7%;
 height:100.0%'><span style=3D'font-size:64%'><span class=3DB1B style=3D'po=
sition:
 absolute;left:-3.97%'>&#8211;</span></span><span style=3D'font-size:64%'>A=
rchimede,
 </span><span style=3D'font-size:64%'><i>Opere</i></span><span style=3D'fon=
t-size:
 64%'>, a cura di A. Frajese, UTET, Torino 1988.&#13;</span></span></div>
 <div class=3DB style=3D'position:absolute;top:58.49%;left:4.49%;width:88.2=
%;
 height:7.75%'><span style=3D'mso-special-format:nobullet;display:none'>&#8=
226;</span><span
 style=3D'font-size:113%'>Sitografia&#13;</span></div>
 <div class=3DB style=3D'position:absolute;top:67.25%;left:4.49%;width:88.2=
%;
 height:4.0%'><span style=3D'mso-special-format:nobullet;display:none'>&#82=
26;</span><span
 style=3D'font-size:56%'><span style=3D'mso-tab-count:1;width:4.25%'> </spa=
n></span><span
 style=3D'font-size:56%'><p:onmouseclick hyperlinktype=3D"url"
  href=3D"http://www.fisicamente.net/"/><a href=3D"http://www.fisicamente.n=
et/"
 target=3D"_parent" onclick=3D"window.event.cancelBubble=3Dtrue;" style=3D'=
position:
 relative'>www.fisicamente.net</a></span><span style=3D'font-size:56%;displ=
ay:
 none'>&#13;</span></div>
 <div class=3DB style=3D'position:absolute;top:72.0%;left:4.49%;width:88.2%;
 height:4.0%'><span style=3D'mso-special-format:nobullet;display:none'>&#82=
26;</span><span
 style=3D'font-size:50%'><span style=3D'mso-tab-count:1;width:4.25%'> </spa=
n></span><span
 style=3D'font-size:56%'><p:onmouseclick hyperlinktype=3D"url"
  href=3D"http://www.matematicamente.it/cultura/storia_della_matematica"/><a
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 target=3D"_parent" onclick=3D"window.event.cancelBubble=3Dtrue;" style=3D'=
position:
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><span
 style=3D'font-size:56%;display:none'>&#13;</span></div>
 <div class=3DB style=3D'position:absolute;top:76.75%;left:4.49%;width:94.3=
8%;
 height:4.0%'><span style=3D'mso-special-format:nobullet;display:none'>&#82=
26;</span><span
 style=3D'font-size:56%'><span style=3D'mso-tab-count:1;width:3.97%'> </spa=
n></span><span
 style=3D'font-size:56%'><p:onmouseclick hyperlinktype=3D"url" location=3D"=
2"
  href=3D"http://www.dm.unipi.it/pages/maurolic/edizioni/archimed/intro.htm=
"/><a
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2"
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position:
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m#2</a></span><span
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%'>Parte
 I<br>
  </span></span><span style=3D'position:absolute;top:31.25%;left:0%;width:1=
00.37%;
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ily:
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 infinitesimale: <br>
  </i></span></span><span style=3D'position:absolute;top:44.0%;left:6.17%;
 width:88.2%;height:12.25%'><span style=3D'font-family:"AvantGarde Md BT";
 font-size:123%;text-shadow:auto'><i>gli antefatti<br>
  </i></span></span><span style=3D'position:absolute;top:56.0%;left:6.17%;
 width:88.2%;height:12.25%'><span style=3D'font-family:"AvantGarde Md BT";
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  strokecolor=3D"black [1]">
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 </v:line><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s4100"
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1.87%;
 width:3.55%;height:1.75%'><![endif]>
 <div v:shape=3D"_x0000_s4098" class=3DT style=3D'position:absolute;top:8.5=
%;
 left:-.56%;width:101.31%;height:8.5%'><span style=3D'font-size:91%;text-sh=
adow:
 auto;color:#990000'>L&#8217;Antichit&agrave;: problemi di esaustione</span=
></div>
 <div v:shape=3D"_x0000_s4099" class=3DB>
 <div style=3D'mso-line-spacing:"90 20 0"'><span style=3D'position:absolute;
 top:21.25%;left:9.92%;width:100.93%;height:4.5%'><span style=3D'font-size:=
63%'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-3.71%'>&#8226;<=
/span></span><span
 style=3D'font-size:63%'>Dei due grandi problemi che hanno portato
 all&#8217;invenzione del calcolo </span></span><span style=3D'position:abs=
olute;
 top:25.25%;left:9.92%;width:86.32%;height:4.5%'><span style=3D'font-size:6=
3%'>infinitesimale,
 il </span><span style=3D'font-size:63%'><i>problema delle tangenti</i></sp=
an><span
 style=3D'font-size:63%'> e il </span><span style=3D'font-size:63%'><i>prob=
lema
 delle </i></span></span><span style=3D'position:absolute;top:29.24%;left:9=
.92%;
 width:89.32%;height:4.5%'><span style=3D'font-size:63%'><i>quadrature</i><=
/span><span
 style=3D'font-size:63%'>, solo il secondo trov&ograve; ampio spazio
 nell&#8217;antichit&agrave;.&#13;</span></span></div>
 <div style=3D'mso-line-spacing:"90 20 0";position:absolute;top:34.0%;left:=
6.17%;
 width:88.2%;height:4.5%'><span style=3D'position:absolute;top:0%;left:4.24=
%;
 width:95.75%;height:100.0%'><span style=3D'font-size:63%;visibility:hidden=
'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-4.43%'>&#8226;<=
/span></span><span
 style=3D'font-size:63%;display:none'>&#13;</span></span></div>
 <div style=3D'mso-line-spacing:"90 20 0"'><span style=3D'position:absolute;
 top:39.0%;left:9.92%;width:90.63%;height:4.5%'><span style=3D'font-size:63=
%'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-4.13%'>&#8226;<=
/span></span><span
 style=3D'font-size:63%'>Teoria delle grandezze: esprimere una quantit&agra=
ve; in
 funzione di </span></span><span style=3D'position:absolute;top:43.0%;left:=
9.92%;
 width:94.56%;height:4.5%'><span style=3D'font-size:63%'>un&#8217;altra pre=
sa ad
 unit&agrave; di misura. La scoperta dell&#8217;irrazionale. La </span></sp=
an><span
 style=3D'position:absolute;top:47.0%;left:9.92%;width:84.45%;height:4.5%'>=
<span
 style=3D'font-size:63%'>teoria delle proporzioni di Eudosso. <span
 style=3D'mso-tab-count:1;width:2.48%'> </span>&#13;</span></span></div>
 <div style=3D'mso-line-spacing:"90 20 0";position:absolute;top:51.75%;
 left:6.17%;width:88.2%;height:4.5%'><span style=3D'mso-special-format:nobu=
llet;
 display:none'>&#8226;</span><span style=3D'font-size:63%'><span
 style=3D'mso-tab-count:1;width:4.25%'> </span>&#13;</span></div>
 <div style=3D'mso-line-spacing:"90 20 0"'><span style=3D'position:absolute;
 top:56.75%;left:9.92%;width:100.93%;height:4.5%'><span style=3D'font-size:=
63%'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-3.71%'>&#8226;<=
/span></span><span
 style=3D'font-size:63%'>sec. III-XVII: la &#8220;misura&#8221; &egrave; in
 realt&agrave; un confronto con altre grandezze. </span></span><span
 style=3D'position:absolute;top:60.75%;left:9.92%;width:93.25%;height:4.5%'=
><span
 style=3D'font-size:63%'>Es. anzich&eacute; dire &#8220;l&#8217;area di un
 cerchio di raggio </span><span style=3D'font-size:63%'><i>r</i></span><span
 style=3D'font-size:63%'> &egrave; pari a </span><span style=3D'font-family=
:Greek;
 font-size:63%'>p</span><span style=3D'font-size:63%'><i>r</i></span><span
 style=3D'font-size:38%;position:relative;top:-.54em;mso-text-raise:36%'>2<=
/span><span
 style=3D'font-size:63%'>&#8221;, un </span></span><span style=3D'position:=
absolute;
 top:64.75%;left:9.92%;width:97.75%;height:4.5%'><span style=3D'font-size:6=
3%'>antico
 diceva &#8220;il cerchio &egrave; uguale a un triangolo che ha come base <=
/span></span><span
 style=3D'position:absolute;top:68.75%;left:9.92%;width:84.45%;height:4.5%'=
><span
 style=3D'font-size:63%'>la circonferenza e come altezza il raggio&#8221;. =
&#13;</span></span></div>
 <div style=3D'mso-line-spacing:"90 20 0";position:absolute;top:73.5%;left:=
6.17%;
 width:88.2%;height:4.5%'><span style=3D'position:absolute;top:0%;left:4.24=
%;
 width:95.75%;height:100.0%'><span style=3D'font-size:63%;visibility:hidden=
'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-4.43%'>&#8226;<=
/span></span><span
 style=3D'font-size:63%;display:none'>&#13;</span></span></div>
 <div style=3D'mso-line-spacing:"90 20 0";position:absolute;top:78.5%;left:=
6.17%;
 width:88.2%;height:4.5%'><span style=3D'position:absolute;top:0%;left:4.24=
%;
 width:95.75%;height:100.0%'><span style=3D'font-size:63%'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-4.43%'>&#8226;<=
/span></span><span
 style=3D'font-size:63%'>Equivalenza =3D equiscomponibilit&agrave;.</span><=
/span></div>
 </div>
 <v:line id=3D"_x0000_s4102" style=3D'position:absolute' from=3D"14.125pt,4=
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:#990000'>L&#8217;Esaustione</span></div>
 <div v:shape=3D"_x0000_s5123" class=3DHB><span style=3D'position:absolute;
 top:12.0%;left:8.23%;width:90.63%;height:4.0%'><span style=3D'font-size:64=
%'><span
 class=3DHBB style=3D'position:absolute;left:-4.13%'>&#8226;</span></span><=
span
 style=3D'font-size:64%'>Esaustione =3D procedimento di costruzione della f=
igura
 intermedia tra </span></span><span style=3D'position:absolute;top:16.0%;
 left:8.23%;width:80.33%;height:4.0%'><span style=3D'font-size:64%'>due
 figure.&#13;</span></span>
 <div style=3D'position:absolute;top:21.0%;left:4.49%;width:84.08%;height:4=
.0%'><span
 style=3D'position:absolute;top:0%;left:4.45%;width:95.54%;height:100.0%'><=
span
 style=3D'font-size:64%'><span class=3DHBB style=3D'position:absolute;left:=
-4.66%'>&#8226;</span></span><span
 style=3D'font-size:64%'>Zenone, Democrito, Eudosso, Euclide (l. XII),
 al-Haytham.&#13;</span></span></div>
 <div style=3D'position:absolute;top:25.75%;left:4.49%;width:84.08%;height:=
4.0%'><span
 style=3D'position:absolute;top:0%;left:4.45%;width:95.54%;height:100.0%'><=
span
 style=3D'font-size:64%'><span class=3DHBB style=3D'position:absolute;left:=
-4.66%'>&#8226;</span></span><span
 style=3D'font-size:64%'>Un esempio da Archimede:</span></span></div>
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  fillcolor=3D"#bbe0e3 [4]" stroked=3D"f" strokecolor=3D"black [1]">
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e;
 top:35.25%;left:5.24%;width:102.62%;height:3.5%'><span style=3D'font-size:=
89%;
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 style=3D'font-size:89%;color:#333399;mso-color-index:5'><b>: il cerchio &e=
grave;
 uguale a un triangolo che ha come base la circonferenza e </b></span></spa=
n><span
 style=3D'position:absolute;top:38.75%;left:5.24%;width:87.07%;height:3.5%'=
><span
 style=3D'font-size:89%;color:#333399;mso-color-index:5'><b>come altezza il
 raggio.&#13;</b></span></span></div>
 <div style=3D'mso-line-spacing:"100 50 0"'><span style=3D'position:absolut=
e;
 top:44.0%;left:5.24%;width:104.3%;height:3.5%'><span style=3D'font-size:89=
%;
 color:#333399;mso-color-index:5'><b>Si dia un </b></span><span
 style=3D'font-size:89%;color:#333399;mso-color-index:5'><b><i>n </i></b></=
span><span
 style=3D'font-size:89%;color:#333399;mso-color-index:5'><b>tale che il pol=
igono
 iscritto P</b></span><span style=3D'font-size:51%;color:#333399;mso-color-=
index:
 5;position:relative;top:.37em;mso-text-raise:-25%'><b>n</b></span><span
 style=3D'font-size:89%;color:#333399;mso-color-index:5'><b>&lt;C. Sia T</b=
></span><span
 style=3D'font-size:51%;color:#333399;mso-color-index:5;position:relative;
 top:.37em;mso-text-raise:-25%'><b>n</b></span><span style=3D'font-size:89%;
 color:#333399;mso-color-index:5'><b><span
 style=3D'mso-spacerun:yes'>&nbsp;</span>il triangolo avente come base il <=
/b></span></span><span
 style=3D'position:absolute;top:47.5%;left:5.24%;width:95.31%;height:3.5%'>=
<span
 style=3D'font-size:89%;color:#333399;mso-color-index:5'><b>perimetro di P<=
/b></span><span
 style=3D'font-size:51%;color:#333399;mso-color-index:5;position:relative;
 top:.37em;mso-text-raise:-25%'><b>n</b></span><span style=3D'font-size:89%;
 color:#333399;mso-color-index:5'><b>. Allora T</b></span><span
 style=3D'font-size:51%;color:#333399;mso-color-index:5;position:relative;
 top:.37em;mso-text-raise:-25%'><b>n</b></span><span style=3D'font-size:89%;
 color:#333399;mso-color-index:5'><b>&lt;T. Crescendo </b></span><span
 style=3D'font-size:89%;color:#333399;mso-color-index:5'><b><i>n</i></b></s=
pan><span
 style=3D'font-size:89%;color:#333399;mso-color-index:5'><b>, P</b></span><=
span
 style=3D'font-size:59%;color:#333399;mso-color-index:5;position:relative;
 top:.37em;mso-text-raise:-25%'><b>n</b></span><span style=3D'font-size:89%;
 color:#333399;mso-color-index:5'><b><span
 style=3D'mso-spacerun:yes'>&nbsp;</span>approssima sempre meglio C. </b></=
span></span><span
 style=3D'position:absolute;top:51.25%;left:5.24%;width:87.07%;height:3.5%'=
><span
 style=3D'font-size:89%;color:#333399;mso-color-index:5'><b>Ovvero, &#13;</=
b></span></span></div>
 <div style=3D'mso-line-spacing:"100 50 0";position:absolute;top:56.5%;
 left:5.24%;width:87.07%;height:3.5%'><span style=3D'font-size:89%;color:#3=
33399;
 mso-color-index:5;display:none'><b>&#13;</b></span></div>
 <div style=3D'mso-line-spacing:"100 50 0"'><span style=3D'position:absolut=
e;
 top:62.0%;left:5.24%;width:100.56%;height:3.5%'><span style=3D'font-size:8=
9%;
 color:#333399;mso-color-index:5'><b>Per assurdo, sia prima C&gt;T. Si pren=
da
 Q=3DC-T. Si pu&ograve; allora trovare un poligono </b></span></span><span
 style=3D'position:absolute;top:65.5%;left:5.24%;width:87.07%;height:3.5%'>=
<span
 style=3D'font-size:89%;color:#333399;mso-color-index:5'><b>iscritto P</b><=
/span><span
 style=3D'font-size:59%;color:#333399;mso-color-index:5;position:relative;
 top:.37em;mso-text-raise:-25%'><b>n</b></span><span style=3D'font-size:89%;
 color:#333399;mso-color-index:5'><b><span
 style=3D'mso-spacerun:yes'>&nbsp;</span>t.c. <span style=3D'mso-tab-count:=
3;
 width:28.76%'> </span>da cui&#13;</b></span></span></div>
 <div style=3D'mso-line-spacing:"100 50 0"'><span style=3D'position:absolut=
e;
 top:70.75%;left:5.24%;width:96.44%;height:3.5%'><span style=3D'font-size:8=
9%;
 color:#333399;mso-color-index:5'><b>Ma ci&ograve; &egrave; impossibile
 perch&eacute; P</b></span><span style=3D'font-size:59%;color:#333399;mso-c=
olor-index:
 5;position:relative;top:.37em;mso-text-raise:-25%'><b>n</b></span><span
 style=3D'font-size:89%;color:#333399;mso-color-index:5'><b>=3D T</b></span=
><span
 style=3D'font-size:59%;color:#333399;mso-color-index:5;position:relative;
 top:.37em;mso-text-raise:-25%'><b>n</b></span><span style=3D'font-size:89%;
 color:#333399;mso-color-index:5'><b>&lt;T. Analogamente si ragiona sui
 poligoni </b></span></span><span style=3D'position:absolute;top:74.25%;
 left:5.24%;width:87.07%;height:3.5%'><span style=3D'font-size:89%;color:#3=
33399;
 mso-color-index:5'><b>circoscritti</b></span><span style=3D'font-size:89%;
 color:#333399;mso-color-index:5'>. </span></span></div>
 </div>
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