DERIVE for Windows version 5.00 DfW file saved on 26 Aug 2000
C   ALTURAATRIANGULO(m, n, p, q, r, s):=n·(q - s) + m·(p - r) + y·(s - q) + x·(r - p) = 0
ALTURABTRIANGULO(m, n, p, q, r, s):=ALTURAATRIANGULO(p, q, r, s, m, n)
ALTURACTRIANGULO(m, n, p, q, r, s):=ALTURAATRIANGULO(r, s, m, n, p, q)
AREATRIANGULOV(a, b, c):=1/2·ABS(DET([a™1, a™2, 1; b™1, b™2, 1; c™1, c™2, 1]))
BARICENTROTRIANGULO(m, n, p, q, r, s):=[(r + p + m)/3, (s + q + n)/3]
CIRCUNCENTROTRIANGULO(m, n, p, q, r, s):=[1/2·(q·(- s^2 - r^2 + q·s) + p^2·s - n·(- s^2 - r^2 + q^2 + p^2) + n^2·(q - s) + m^2·(q - s))/(- q·r + p·s + n·(r - p) + m·(q - s)), - 1/2·(q^2·r - p·(r^2 + s^2) + p^2·r + n^2·(p - r) - m·(- s^2 - r^2 + q^2 + p^2) + m^2·(p - r))/(- q·r + p·s + n·(r - p) + m·(q - s))]
DISTANCIA(a, b, m, n, p):=ABS(p + n·b + m·a)·(m^2 + n^2)^(- 1/2)
DISTANCIAV(v, m, n, p):=ABS(p + n·v™2 + m·v™1)·(m^2 + n^2)^(- 1/2)
HOMOTETICODEVRESPECTOPRAZONK(u, v, p, q, k):=[p, q] + k·[u - p, v - q]
HOMOTETICODEVRESPECTOPRAZONKV(v, p, k):=p + k·(v - p)
INTERSECCIONRECTAS(©, ß, ¼, ´, ¿, µ):=[(ß·µ - ¼·¿)/(©·¿ - ß·´), (¼·´ - ©·µ)/(©·¿ - ß·´)]
INTERSECDIAGCUADR(m, n, p, q, r, s, t, u):=[(m·(p·(s - u) + t·(q - s)) - r·(q·t - p·u + n·(p - t)))/(- s·t + r·u - q·r + p·s + n·(t - p) + m·(q - u)), (s·(p·u - q·t) - n·(- r·u + q·(r - t) + p·u) + m·s·(q - u))/(- s·t + r·u - q·r + p·s + n·(t - p) + m·(q - u))]
INVERSODEVRESPECTOPPOTENCIAK(u, v, p, q, k):=[p, q] + (k·ABS([u - p, v - q])^(-2))·[u - p, v - q]
INVERSODEVRESPECTOPPOTENCIAKV(v, p, k):=p + (k·ABS(v - p)^(-2))·(v - p)
MACROALTURASTRIANGULO(m, n, p, q, r, s):=[[m, n; p, q; r, s; m, n], [ALTURAATRIANGULO(m, n, p, q, r, s), ALTURABTRIANGULO(m, n, p, q, r, s), ALTURACTRIANGULO(m, n, p, q, r, s)]]
MACRODESARGUES(m, n, p, q, r, s):=[y = x, [m, 0], [0, n], [p, p], [q, 0], [0, r], [s, s], - n·x - m·y + m·n = 0, - r·x - q·y + q·r = 0, [m·q·(r - n)/(m·r - n·q), n·r·(m - q)/(m·r - n·q)], x·(p - n) - p·y + n·p = 0, x·(r - s) + s·y + - r·s = 0, [p·s·(n - r)/(n·s - p·r), (n·(p·(r - s) - r·s) + p·r·s)/(p·r - n·s)], p·x + y·(m - p) + - m·p = 0, s·x + y·(q - s) + - q·s = 0, [(m·(p·(q - s) - q·s) + p·q·s)/(p·q - m·s), p·s·(m - q)/(m·s - p·q)], x·(n·q·(n - r)/(m·r - n·q) + p·r·(p - s)·(r - s)/(s·(n·s - p·r)) + n + (p·(r - s) - r·s)/s) + y·(n·q^2·(n - r)/(r·(m·r - n·q)) + p·r·(p - s)/(n·s - p·r) + (n·q + p·r + - q·r)/r) + (n - r)·(m·(n·(p·(q·(r - s) - r·s) - q·r·s) + p·q·r·s) + n·p·q·r·s)/((m·r - n·q)·(n·s - p·r)) = 0]
MACROMEDIANASTRIANGULO(m, n, p, q, r, s):=[[m, n; p, q; r, s; m, n], [MEDIANAATRIANGULO(m, n, p, q, r, s), MEDIANABTRIANGULO(m, n, p, q, r, s), MEDIANACTRIANGULO(m, n, p, q, r, s)]]
MACROMEDIATRICESTRIANGULO(m, n, p, q, r, s):=[[m, n; p, q; r, s; m, n], [MEDIATRIZATRIANGULO(m, n, p, q, r, s), MEDIATRIZBTRIANGULO(m, n, p, q, r, s), MEDIATRIZCTRIANGULO(m, n, p, q, r, s)]]
MACRORECTAEULERTRIANGULO(m, n, p, q, r, s):=[[m, n; p, q; r, s; m, n], RECTAEULERTRIANGULO(m, n, p, q, r, s)]
MEDIANAATRIANGULO(m, n, p, q, r, s):=RECTAPORDOSPUNTOS(m, n, (p + r)/2, (q + s)/2)
MEDIANABTRIANGULO(m, n, p, q, r, s):=MEDIANAATRIANGULO(p, q, r, s, m, n)
MEDIANACTRIANGULO(m, n, p, q, r, s):=MEDIANAATRIANGULO(r, s, m, n, p, q)
MEDIATRIZ(a, b, c, d):=d^2 + c^2 - b^2 - a^2 + 2·y·(b - d) + 2·x·(a - c) = 0
MEDIATRIZATRIANGULO(m, n, p, q, r, s):=MEDIATRIZ(p, q, r, s)
MEDIATRIZBTRIANGULO(m, n, p, q, r, s):=MEDIATRIZATRIANGULO(p, q, m, n, r, s)
MEDIATRIZCTRIANGULO(m, n, p, q, r, s):=MEDIATRIZATRIANGULO(r, s, m, n, p, q)
MEDIATRIZV(a, b):=(b - a)™1·(x - ((a + b)/2)™1) + (b - a)™2·(y - ((a + b)/2)™2) = 0
NORMALUNITARIA(a, b, m, n, p):=IF(p + n·b + m·a > 0, - (1·(m^2 + n^2)^(- 1/2))·[m, n], (1·(m^2 + n^2)^(- 1/2))·[m, n])
NORMALUNITARIAV(v, m, n, p):=IF(p + n·v™2 + m·v™1 > 0, - (1·(m^2 + n^2)^(- 1/2))·[m, n], (1·(m^2 + n^2)^(- 1/2))·[m, n])
ORTOCENTROTRIANGULO(m, n, p, q, r, s):=[- (m·(r·s - p·q + n·(p - r)) + (q·s + p·r - n·(q + s) + n^2)·(q - s))/(- q·r + p·s + n·(r - p) + m·(q - s)), (- q·r·s + p·(q·s - r^2) + p^2·r + n·(r·s - p·q) + m·(r^2 - p^2 + n·(q - s)) + m^2·(p - r))/(- q·r + p·s + n·(r - p) + m·(q - s))]
PMEDIO(a, b, c, d):=[(a + c)/2, (b + d)/2]
PUNTOMEDIOV(a, b):=(a + b)/2
RECTACARTAPUNTOPENDIENTE(m, n, p):=IF(n ” 0, SOLVE(p + n·y + m·x = 0, y), SOLVE(p + n·y + m·x = 0, x))
RECTAEULERTRIANGULO(m, n, p, q, r, s):=[BARICENTROTRIANGULO(m, n, p, q, r, s), ORTOCENTROTRIANGULO(m, n, p, q, r, s), CIRCUNCENTROTRIANGULO(m, n, p, q, r, s)]
RECTAPARALELA(m, n, p, a, b):=m·(x - a) + n·(y - b) = 0
RECTAPARALELAV(m, n, p, v):=m·(x - v™1) + n·(y - v™2) = 0
RECTAPENDIENTEARECTACART(a, b, m):=IF(m = –, x = a, b - m·a - y + m·x = 0)
RECTAPENDIENTEARECTACARTV(a, m):=IF(m = –, x = a™1, a™2 - m·a™1 - y + m·x = 0)
RECTAPERPENDICULAR(m, n, p, a, b):=n·(x - a) - m·(y - b) = 0
RECTAPERPENDICULARV(m, n, p, v):=n·(x - v™1) - m·(y - v™2) = 0
RECTAPORDOSPUNTOS(a, b, c, d):=- b·c + a·d + y·(c - a) + x·(b - d) = 0
RECTAPORDOSPUNTOSV(u, v):=- u™2·v™1 + u™1·v™2 + y·(v™1 - u™1) + x·(u™2 - v™2) = 0
ROTACION(v, p, ang):=p + [(v™1 - p™1)·COS(ang) - (v™2 - p™2)·SIN(ang), (v™1 - p™1)·SIN(ang) + (v™2 - p™2)·COS(ang)]
SIMETRICO(a, b, m, n, p):=[a, b] + 2·DISTANCIA(a, b, m, n, p)·NORMALUNITARIA(a, b, m, n, p)
SIMETRICODEPUNTORESPECTOPUNTO(a, b, p, q):=2·[p, q] - [a, b]
SIMETRICODEPUNTORESPECTOPUNTOV(v, p):=2·p - v
SIMETRICOPUNTORESPECTORECTA(a, b, m, n, p):=[(- 2·p·m - 2·b·m·n + a·(n^2 - m^2))/(m^2 + n^2), (- 2·p·n - 2·a·m·n + b·(m^2 - n^2))/(m^2 + n^2)]
SIMETRICOPUNTORESPECTORECTAV(v, m, n, p):=[(- 2·p·m - 2·v™2·m·n + v™1·(n^2 - m^2))/(m^2 + n^2), (- 2·p·n - 2·v™1·m·n + v™2·(m^2 - n^2))/(m^2 + n^2)]
SIMETRICOV(v, m, n, p):=v + 2·DISTANCIAV(v, m, n, p)·NORMALUNITARIAV(v, m, n, p)
macrodesargues(m, n, p, q, r, s):=[y - x = 0, [m, 0], [0, n], [p, p], [q, 0], [0, r], [s, s], m·n - m·y + - n·x = 0, q·r - q·y + - r·x = 0, [m·q·(r - n)/(m·r - n·q), n·r·(m - q)/(m·r - n·q)], n·p - p·y + x·(p - n) = 0, - r·s + s·y + x·(r - s) = 0, [p·s·(n - r)/(n·s - p·r), (n·(p·(r - s) - r·s) + p·r·s)/(p·r - n·s)], - m·p + y·(m - p) + p·x = 0, - q·s + y·(q - s) + s·x = 0, [(m·(p·(q - s) - q·s) + p·q·s)/(p·q - m·s), p·s·(m - q)/(m·s - p·q)], (q - m)·(m·(n·(p·(q·(r - s) - r·s) - q·r·s) + p·q·r·s) + n·p·q·r·s)/((m·r - n·q)·(m·s - p·q)) + y·(n·p·q^2·s - m·q·(n·s·(p + q) + p·r·(s - q)) + m^2·(n·q·s + p·r·(s - q)))/((m·r - n·q)·(p·q - m·s)) + x·(q - m)·(m·r·s·(n - p) + n·p·q·(s - r))/((m·r - n·q)·(m·s - p·q)) = 0]
A:=[m, 0]
Asub1:=[q, 0]
B:=[0, n]
C:=[p, p]
D:=[q, 0]
E:=[0, r]
F:=[s, s]
ang:=
c:=[p, p]
hCross:=APPROX(- 69/16)
vCross:=APPROX(56818181818181823/100000000000000000)
©:=
´:=
µ:=
¼:=
¿:=
ß:=
# ÿÿ   CTextObj        T    ÿ¿{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fmodern\fcharset2 DfW5 Printer;}{\f3\fmodern\fcharset2 DfW5 Printer;}{\f4\fswiss\fprq2 System;}}
{\colortbl\red0\green0\blue0;}
\deflang1034\pard\plain\f2\fs24 El teorema de Desargues con DERIVE.
\par Se carga el fichero de colineaci\'f3n.
\par Se pueden escoger los tri\'e1ngulos con los v\'e9rtices en los ejes y en la bisectriz x=y.
\par }
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{\colortbl\red0\green0\blue0;}
\deflang1034\pard\plain\f2\fs24 Formamos los lados de los tri\'e1ngulos ABC y DEF
\par }
€   &    J   ÿn{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fmodern\fcharset2 DfW5 Printer;}{\f3\fmodern\fcharset2 DfW5 Printer;}{\f4\fswiss\fprq2 System;}}
{\colortbl\red0\green0\blue0;}
\deflang1034\pard\plain\f2\fs24 y a continuaci\'f3n las intersecciones que hay que considerar en el teorema de Desargues, M,N,P.
\par }
€8   V  ø   b   User      ð¿      RECTAPORDOSPUNTOSV(A,B)€8   n  ø   z   User      ð¿	      RECTAPORDOSPUNTOSV(D,E)€H  †  ð  ’  Simp(#8)ü©ñÒMb`?
      -n*x-m*y+m*n=0€H  ž  ð  ª  Simp(#9)ú~j¼t“x?      -r*x-q*y+q*r=0€8   ¶  ˜  Â   User      ð¿      'INTERSECCIONRECTAS(-n,-m,m*n,-r,-q,q*r)€   Î    ò  	Simp(#12){®Gáz„?      )[m*q*(r-n)/(m*r-n*q),n*r*(m-q)/(m*r-n*q)]€8   þ  ø   
   User      ð¿      RECTAPORDOSPUNTOSV(C,B)€8     ø   "   User      ð¿      RECTAPORDOSPUNTOSV(E,F)€8  .     :  	Simp(#14){®Gázt?      x*(p-n)-p*y+n*p=0€8  F     R  	Simp(#15)ü©ñÒMbp?      x*(r-s)+s*y-r*s=0€8   ^  Ð  j   User      ð¿      )INTERSECCIONRECTAS(p-n,-p,n*p,r-s,s,-r*s)€à   v  P  š  	Simp(#18){®Gáz„?      7[p*s*(n-r)/(n*s-p*r),(n*(p*(r-s)-r*s)+p*r*s)/(p*r-n*s)]€8   ¦  ø   ²   User      ð¿      RECTAPORDOSPUNTOSV(C,A)€8   ¾  ø   Ê   User      ð¿      RECTAPORDOSPUNTOSV(F,D)€8  Ö     â  	Simp(#20){®Gázt?      p*x+y*(m-p)-m*p=0€8  î     ú  	Simp(#21)ú~j¼t“x?      s*x+y*(q-s)-q*s=0€8     Ø     User      ð¿      )INTERSECCIONRECTAS(p,m-p,-m*p,s,q-s,-q*s)€       0   ÿ@{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fmodern\fcharset2 DfW5 Printer;}{\f3\fmodern\fcharset2 DfW5 Printer;}{\f4\fswiss\fprq2 System;}}
{\colortbl\red0\green0\blue0;}
\deflang1034\pard\plain\f3\fs24 Examinamos si estos tres puntos est\'e1n alineados
\par }
€8   <        User      ð¿      ©AREATRIANGULOV([m*q*(r-n)/(m*r-n*q),n*r*(m-q)/(m*r-n*q)],[p*s*(n-r)/(n*s-p*r),(n*(p*(r-s)-r*s)+p*r*s)/(p*r-n*s)],[(m*(p*(q-s)-q*s)+p*q*s)/(p*q-m*s),p*s*(m-q)/(m*s-p*q)])€˜  œ     ¨  	Simp(#25)B`åÐ"Û¹?      0€   ´    ê   ÿ“{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fmodern\fcharset2 DfW5 Printer;}{\f3\fmodern\fcharset2 DfW5 Printer;}{\f4\fswiss\fprq2 System;}}
{\colortbl\red0\green0\blue0;}
\deflang1034\pard\plain\f2\fs24 Con esto se demuestra el teorema de Desargues.
\par 
\par Para tener una idea gr\'e1fica se puede hacer una macro como la que sigue
\par }
€8   ö     Ê   User      ð¿      ÿ MACRODESARGUES(m,n,p,q,r,s):=[y=x,[m,0],[0,n],[p,p],[q,0],[0,r],[s,s],-n*x-m*y+m*n=0,-r*x-q*y+q*r=0,[m*q*(r-n)/(m*r-n*q),n*r*(m-q)/(m*r-n*q)],x*(p-n)-p*y+n*p=0,x*(r-s)+s*y-r*s=0,[p*s*(n-r)/(n*s-p*r),(n*(p*(r-s)-r*s)+p*r*s)/(p*r-n*s)],p*x+y*(m-p)-m*p=0,s*x+y*(q-s)-q*s=0,[(m*(p*(q-s)-q*s)+p*q*s)/(p*q-m*s),p*s*(m-q)/(m*s-p*q)],x*(n*q*(n-r)/(m*r-n*q)+p*r*(p-s)*(r-s)/(s*(n*s-p*r))+n+(p*(r-s)-r*s)/s)+y*(n*q^2*(n-r)/(r*(m*r-n*q))+p*r*(p-s)/(n*s-p*r)+(n*q+p*r-q*r)/r)+(n-r)*(m*(n*(p*(q*(r-s)-r*s)-q*r*s)+p*q*r*s)+n*p*q*r*s)/((m*r-n*q)*(n*s-p*r))=0]€   Ö    ú   ÿn{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fmodern\fcharset2 DfW5 Printer;}{\f3\fmodern\fcharset2 DfW5 Printer;}{\f4\fswiss\fprq2 System;}}
{\colortbl\red0\green0\blue0;}
\deflang1034\pard\plain\f2\fs24 con la que se puede experimentar con valores num\'e9ricos que nos permitan hacer una gr\'e1fica.
\par }
€8     H     User      ð¿      MACRODESARGUES(1,1,0.2,2,5,4)ÿÿ   CDispOleObj     $    ÿÿ  	 CDispItem                † ÐÏà¡±á                >  þÿ	                               þÿÿÿ                       	   
                     ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿýÿÿÿÁ  þÿÿÿþÿÿÿýÿÿÿýÿÿÿýÿÿÿýÿÿÿýÿÿÿýÿÿÿýÿÿÿýÿÿÿýÿÿÿýÿÿÿýÿÿÿýÿÿÿýÿÿÿ                                              !   "   #   $   %   &   '   (   )   *   +   ,   -   .   /   0   1   2   3   4   5   6   7   8   9   :   ;   <   =   >   ?   @   A   B   C   D   E   F   G   H   I   J   K   L   M   N   O   P   Q   R   S   T   U   V   W   X   Y   Z   [   \   ]   ^   _   `   a   b   c   d   e   f   g   h   i   j   k   l   m   n   o   p   q   r   s   t   u   v   w   x   y   z   {   |   }   ~      €   R o o t   E n t r y                                               ÿÿÿÿÿÿÿÿ         À      F            @@|À   À        O l e                                                         
 ÿÿÿÿÿÿÿÿÿÿÿÿ                                               C O N T E N T S                                                  ÿÿÿÿÿÿÿÿÿÿÿÿ                                       ®_      C o m p O b j                                                        ÿÿÿÿ                                       {       þÿÿÿ   þÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ                                                               þÿ
  ÿÿÿÿ      À      F5   Imagen (Mapa de bits independiente del dispositivo ) ÿÿÿÿ   
   StaticDib ô9²q                                                                                                                                                                                                                                                                                                                                                    ‚   ƒ   „   …   †   ‡   ˆ   ‰   Š   ‹   Œ      Ž         ‘   ’   “   ”   •   –   —   ˜   ™   š   ›   œ      ž   Ÿ       ¡   ¢   £   ¤   ¥   ¦   §   ¨   ©   ª   «   ¬   ­   ®   ¯   °   ±   ²   ³   ´   µ   ¶   ·   ¸   ¹   º   »   ¼   ½   ¾   ¿   À   Á   Â   Ã   Ä   Å   Æ   Ç   È   É   Ê   Ë   Ì   Í   Î   Ï   Ð   Ñ   Ò   Ó   Ô   Õ   Ö   ×   Ø   Ù   Ú   Û   Ü   Ý   Þ   ß   à   á   â   ã   ä   å   æ   ç   è   é   ê   ë   ì   í   î   ï   ð   ñ   ò   ó   ô   õ   ö   ÷   ø   ù   ú   û   ü   ý   þ   ÿ                      	  
                                               !  "  #  $  %  &  '  (  )  *  +  ,  -  .  /  0  1  2  3  4  5  6  7  8  9  :  ;  <  =  >  ?  @  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  [  \  ]  ^  _  `  a  b  c  d  e  f  g  h  i  j  k  l  m  n  o  p  q  r  s  t  u  v  w  x  y  z  {  |  }  ~    €    ‚  ƒ  „  …  †  ‡  ˆ  ‰  Š  ‹  Œ    Ž      ‘  ’  “  ”  •  –  —  ˜  ™  š  ›  œ    ž  Ÿ     ¡  ¢  £  ¤  ¥  ¦  §  ¨  ©  ª  «  ¬  ­  ®  ¯  °  ±  ²  ³  ´  µ  ¶  ·  ¸  ¹  º  »  ¼  ½  ¾  ¿  À  Á  Â  Ã  Ä  Å  Æ  Ç  È  É  Ê  Ë  Ì  Í  Î  Ï  Ð  Ñ  Ò  Ó  Ô  Õ  Ö  ×  Ø  Ù  Ú  Û  Ü  Ý  Þ  ß  à  á  â  ã  ä  å  æ  ç  è  é  ê  ë  ì  í  î  ï  ð  ñ  ò  ó  ô  õ  ö  ÷  ø  ù  ú  û  ü  ý  þ  ÿ                     	  
                                               !  "  #  $  %  &  '  (  )  *  +  ,  -  .  /  0  1  2  3  4  5  6  7  8  9  :  ;  <  =  >  ?  @  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  [  \  ]  ^  _  `  a  b  c  d  e  f  g  h  i  j  k  l  m  n  o  p  q  r  s  t  u  v  w  x  y  z  {  |  }  ~    €    ‚  ƒ  „  …  †  ‡  ˆ  ‰  Š  ‹  Œ    Ž      ‘  ’  “  ”  •  –  —  ˜  ™  š  ›  œ    ž  Ÿ     ¡  ¢  £  ¤  ¥  ¦  §  ¨  ©  ª  «  ¬  ­  ®  ¯  °  ±  ²  ³  ´  µ  ¶  ·  ¸  ¹  º  »  ¼  ½  ¾  ¿  À  Á  Â  Ã  Ä  Å  Æ  Ç  È  É  Ê  Ë  Ì  Í  Î  Ï  Ð  Ñ  Ò  Ó  Ô  Õ  Ö  ×  Ø  Ù  Ú  Û  Ü  Ý  Þ  ß  à  á  â  ã  ä  å  æ  ç  è  é  ê  ë  ì  í  î  ï  ð  ñ  ò  ó  ô  õ  ö  ÷  ø  ù  ú  û  ü  ý  þ  ÿ                     	  
                                               !  "  #  $  %  &  '  (  )  *  +  ,  -  .  /  0  1  2  3  4  5  6  7  8  9  :  ;  <  =  >  ?  @  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  [  \  ]  ^  _  `  a  b  c  d  e  f  g  h  i  j  k  l  m  n  o  p  q  r  s  t  u  v  w  x  y  z  {  |  }  ~    €    ‚  ƒ  „  …  †  ‡  ˆ  ‰  Š  ‹  Œ    Ž      ‘  ’  “  ”  •  –  —  ˜  ™  š  ›  œ    ž  Ÿ     ¡  ¢  £  ¤  ¥  ¦  §  ¨  ©  ª  «  ¬  ­  ®  ¯  °  ±  ²  ³  ´  µ  ¶  ·  ¸  ¹  º  »  ¼  ½  ¾  ¿  À  Á  Â  Ã  Ä  Å  Æ  Ç  È  É  Ê  Ë  Ì  Í  Î  Ï  Ð  Ñ  Ò  Ó  Ô  Õ  Ö  ×  Ø  Ù  Ú  Û  Ü  Ý  Þ  ß  à  á  â  ã  ä  å  æ  ç  è  é  ê  ë  ì  í  î  ï  ð  ñ  ò  ó  ô  õ  ö  ÷  ø  ù  ú  û  ü  ý  þ  ÿ                     	  
                                               !  "  #  $  %  &  '  (  )  *  +  ,  -  .  /  0  1  2  3  4  5  6  7  8  9  :  ;  <  =  >  ?  @  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  [  \  ]  ^  _  `  a  b  c  d  e  f  g  h  i  j  k  l  m  n  o  p  q  r  s  t  u  v  w  x  y  z  {  |  }  ~    €    ‚  ƒ  „  …  †  ‡  ˆ  ‰  Š  ‹  Œ    Ž      ‘  ’  “  ”  •  –  —  ˜  ™  š  ›  œ    ž  Ÿ     ¡  ¢  £  ¤  ¥  ¦  §  ¨  ©  ª  «  ¬  ­  ®  ¯  °  ±  ²  ³  ´  µ  ¶  ·  ¸  ¹  º  »  ¼  ½  ¾  ¿  À  Á  Â  Ã  Ä  Å  Æ  Ç  È  É  Ê  Ë  Ì  Í  Î  Ï  Ð  Ñ  Ò  Ó  Ô  Õ  Ö  ×  Ø  Ù  Ú  Û  Ü  Ý  Þ  ß  à  á  â  ã  ä  å  æ  ç  è  é  ê  ë  ì  í  î  ï  ð  ñ  ò  ó  ô  õ  ö  ÷  ø  ù  ú  û  ü  ý  þ  ÿ                     	  
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