欧几里得语境下的列奥纳多·达·芬奇勾股定理证明

GeoGebra 命令及参数

1. Segment(A, B) → a
2. Segment(B, C) → b
3. Segment(C, D) → c
4. Segment(D, E) → d
5. Segment(E, A) → e
6. Segment(A, C) → f
7. Segment(D, F) → g
8. Segment(F, E) → h
9. Segment(B, G) → i
10. Segment(G, H) → j
11. Segment(H, C) → k
12. Segment(A, I) → l
13. Segment(I, J) → m
14. Segment(J, B) → n
15. Segment(J, G) → p
16. Segment(I, H) → q
17. Segment(F, B) → r
18. Point(r) → K
19. Segment(A, K) → s
20. Segment(K, E) → t
21. Point(r) → L
22. Segment(C, L) → a_1
23. Segment(D, L) → b_1
24. Point(c) → M
25. Segment(L, M) → c_1
26. Segment(N, O) → d_1
27. Segment(O, P) → e_1
28. Segment(P, Q) → f_1
29. Segment(Q, N) → g_1
30. Segment(N, R) → h_1
31. Segment(R, Q) → i_1
32. Segment(N, S) → j_1
33. Segment(S, T) → k_1
34. Segment(T, R) → l_1
35. Segment(R, U) → m_1
36. Segment(U, V) → n_1
37. Segment(V, Q) → p_1
38. Segment(T, U) → q_1
39. Segment(P, W) → r_1
40. Segment(W, O) → s_1
41. Segment(S, V) → t_1
42. Segment(R, W) → a_2
43. Point(a_2) → Z
44. Segment(O, Z) → b_2
45. Point(a_2) → A_1
46. Segment(A_1, Q) → c_2
47. Segment(A_1, P) → d_2
48. Point(f_1) → B_1
49. Segment(A_1, B_1) → e_2
50. Segment(K, A) → f_2
51. Polygon(G, B, I, J) → poly1, g_2, b_3, i_2, j_2
52. Polygon(E, K, B, A) → poly2, e_3, k_2, b_4, a_3
53. Polygon(B, G, H) → poly3, h_2, b_5, g_3
54. Polygon(K, E, F) → poly4, f_3, k_3, e_4
55. Polygon(B, C, H) → poly5, h_3, b_6, c_3
56. Polygon(B, C, L) → poly6, l_2, b_7, c_4
57. Polygon(C, M, L) → poly7, l_3, c_5, m_2
58. Polygon(L, M, D) → poly8, d_3, l_4, m_3
59. Polygon(B, A, I) → poly9, i_3, b_8, a_4
60. Polygon(L, D, F) → poly10, f_4, l_5, d_4
61. Polygon(U, R, S, T) → poly11, u, r_2, s_2, t_2
62. Polygon(R, Z, O, N) → poly12, r_3, z, o, n_2
63. Segment(N, Z) → p_2
64. Polygon(R, N, O, Z) → poly13, r_4, n_3, o_1, z_1
65. Polygon(R, U, V) → poly14, v, r_5, u_1
66. Polygon(Z, O, W) → poly15, w, z_2, o_2
67. Polygon(V, Q, R) → poly16, r_6, v_1, q_2
68. Polygon(R, Q, A_1) → poly17, a_5, r_7, q_3
69. Polygon(Q, B_1, A_1) → poly18, a_6, q_4, b_9
70. Polygon(B_1, A_1, P) → poly19, p_3, b_{10}, a_7
71. Polygon(R, N, S) → poly20, s_3, r_8, n_4
72. Polygon(A_1, P, W) → poly21, w_1, a_8, p_4
73. Vector(D_1, E_1) → u_2
74. Vector(F_1, G_1) → v_2
75. Vector(H_1, I_1) → w_2
76. Vector(J_1, K_1) → u_3
77. Vector(L_1, M_1) → v_3
78. Vector(N_1, O_1) → w_3
79. Vector(P_1, Q_1) → z_3
80. Vector(R_1, S_1) → j_3
81. Intersect(f_1, g_1) → T_1
82. Intersect(a_2, d_2) → U_1
83. Segment(T_1, U_1) → t_3
84. Intersect(h_1, i_1) → V_1
85. Intersect(k_1, q_1) → W_1
86. Segment(V_1, W_1) → g_4
87. Intersect(f_1, g_1) → E_2
88. Segment(E_2, D_2) → j_4
89. Intersect(f_1, e_2) → G_2
90. Point(s_1) → L_2
91. Intersect(b, c) → A_2
92. Segment(A_2, M_2) → m_5
93. Segment(M_2, N_2) → n_5
94. Intersect(c, d) → O_2
95. Segment(N_2, O_2) → p_5
96. Intersect(r, a_1) → P_2
97. Point(h) → Q_2
98. Segment(P_2, Q_2) → q_5
99. Point(t) → R_2
100. Segment(P_2, R_2) → s_5
101. Intersect(d, e) → S_2
102. Segment(S_2, M_2) → t_5
103. Intersect(a, e) → T_2
104. Intersect(j, k) → V_2
105. Segment(V_2, W_2) → e_6
106. Segment(W_2, M_2) → f_6
107. Point(f_6) → Z_2
108. Segment(A_2, Z_2) → g_6
109. Segment(R_2, A_2) → j_6
110. Segment(V_2, M_2) → k_6
111. Segment(A_2, W_2) → h_4
112. Segment(Z_2, H_3) → g_7
113. Segment(H_3, I_3) → h_7
114. Segment(I_3, M_2) → i_7
115. Segment(M_2, H_3) → j_7
116. Segment(M_2, Z_2) → k_7
117. Segment(Z_2, J_3) → l_7
118. Segment(J_3, V_2) → m_7
119. Polygon(Z_2, A_2, M_2) → poly22, m_8, z_4, a_9
120. Segment(I_3, N_2) → c_6
121. Point(j) → U_2
122. Segment(A_2, U_2) → d_6
123. Segment(U_2, G_3) → e_7
124. Segment(G_3, Z_2) → f_7
125. Point(c_1) → K_3
126. Segment(M_2, K_3) → n_7
127. Segment(L_3, U_2) → p_7
128. Segment(G_3, L_3) → q_7
129. Segment(M_2, L_3) → s_7
130. Point(s_7) → M_3
131. Segment(M_3, G_3) → t_7
132. Segment(Z_2, M_3) → c_8
133. Polygon(V_2, A_2, M_2) → poly23, m_9, v_4, a_{10}
134. Polygon(M_3, G_3, L_3) → poly24, l_8, m_{10}, g_8
135. Intersect(c, c_1) → O_3
136. Polygon(A_2, M_2, O_3) → poly25, o_3, a_{11}, m_{11}
137. Polygon(M_2, N_2, P_2) → poly26, p_8, m_{12}, n_8
138. Intersect(g_6, s_7) → P_3
139. Polygon(M_2, Z_2, P_3) → poly27, p_9, m_{13}, z_5
140. Polygon(Z_2, P_3, M_3) → poly28, m_{14}, z_6, p_{10}
141. Polygon(Z_2, H_3, M_2) → poly29, m_{15}, z_7, h_8
142. Polygon(G_3, M_3, Z_2) → poly30, z_8, g_9, m_{16}
143. Intersect(i, j) → R_3
144. Polygon(L_3, U_2, V_2) → poly31, v_5, l_9, u_4
145. Polygon(H_3, M_2, N_2, I_3) → poly32, h_9, m_{17}, n_9, i_8
146. Polygon(H_3, Z_2, M_2) → poly33, m_{18}, h_{10}, z_9
147. Intersect(d, r) → A_4
148. Polygon(O_2, P_2, A_4) → poly34, a_{12}, o_4, p_{11}
149. Intersect(e_7, s_7) → B_4
150. Polygon(V_2, B_4, U_2) → poly35, u_5, v_6, b_{11}
151. Intersect(i, n) → C_4
152. Intersect(m, q) → D_4
153. Intersect(m, n) → E_4
154. Polygon(R_3, C_4, D_4, E_4) → poly36, r_9, c_{10}, d_{10}, e_9
155. Intersect(r, t) → F_4
156. Polygon(C_4, F_4, S_2, T_2) → poly37, c_{11}, f_9, s_9, t_9
157. Polygon(G_3, M_3, M_2, Z_2) → poly38, g_{10}, m_{19}, m_{20}, z_{10}
158. Polygon(H_3, M_2, N_2, I_3) → poly39, h_{11}, m_{21}, n_{10}, i_9
159. Polygon(C_4, R_3, V_2) → poly40, v_7, c_{12}, r_{10}
160. Intersect(g, h) → G_4
161. Polygon(F_4, S_2, G_4) → poly41, g_{11}, f_{10}, s_{10}
162. Polygon(V_2, A_2, C_4) → poly42, c_{13}, v_8, a_{13}
163. Polygon(C_4, A_2, P_2) → poly43, p_{12}, c_{14}, a_{14}
164. Polygon(O_3, P_2, O_2) → poly44, o_5, o_6, p_{13}
165. Polygon(A_2, P_2, G_4, O_2) → poly45, a_{15}, p_{14}, g_{12}, o_7
166. Polygon(A_2, P_2, O_3) → poly46, o_8, a_{16}, p_{15}
167. Polygon(O_3, P_2, O_2) → poly47, o_9, o_{10}, p_{16}
168. Polygon(O_2, A_4, P_2) → poly48, p_{17}, o_{11}, a_{17}
169. Polygon(C_4, T_2, D_4) → poly49, d_{11}, c_{15}, t_{10}
170. Polygon(O_2, G_4, P_2) → poly50, p_{18}, o_{12}, g_{13}
171. Intersect(f, r) → H_4
172. Polygon(C_4, H_4, T_2) → poly51, t_{11}, c_{16}, h_{12}
173. Polygon(T_2, F_4, S_2) → poly52, s_{11}, t_{12}, f_{11}
174. Polygon(F_4, C_4, T_2) → poly53, t_{13}, f_{12}, c_{17}
175. Polygon(P_2, O_2, G_4) → poly54, g_{14}, p_{19}, o_{13}
176. Polygon(V_2, D_4, E_4, R_3) → poly55, v_9, d_{12}, e_{10}, r_{11}
177. Polygon(C_4, T_2, S_2, G_4) → poly56, c_{18}, t_{14}, s_{12}, g_{15}
178. Polygon(V_2, A_2, T_2, D_4) → poly57, v_{10}, a_{18}, t_{15}, d_{13}
179. Polygon(A_2, H_4, G_4, O_2) → poly58, a_{19}, h_{13}, g_{16}, o_{14}
180. Polygon(M_2, L_3, U_2, A_2) → poly59, m_{22}, l_{10}, u_6, a_{20}
181. Polygon(L_3, G_3, Z_2, M_2) → poly60, l_{11}, g_{17}, z_{11}, m_{23}
182. Polygon(H_3, P_2, N_2, I_3) → poly61, h_{14}, p_{20}, n_{11}, i_{10}
183. Polygon(H_3, Z_2, A_2, P_2) → poly62, h_{15}, z_{12}, a_{21}, p_{21}
184. Intersect(r_1, s_1) → K_4
185. Intersect(j, k) → Z_1
186. Intersect(i, j) → B_2
187. Intersect(a, b) → C_2
188. Polygon(Z_1, B_2, C_2) → poly63, c_7, z_{13}, b_{12}
189. Intersect(b, c) → F_2
190. Polygon(Z_1, C_2, F_2) → poly64, f_5, z_{14}, c_9
191. Intersect(r, a_1) → H_2
192. Polygon(F_2, C_2, H_2) → poly65, h_5, f_8, c_{19}
193. Intersect(r, t) → I_2
194. Intersect(d, e) → J_2
195. Intersect(g, h) → K_2
196. Polygon(I_2, J_2, K_2) → poly66, k_4, i_4, j_5
197. Intersect(m, n) → A_3
198. Polygon(B_2, C_2, A_3) → poly67, a_{22}, b_{13}, c_{20}
199. Intersect(a, e) → C_3
200. Polygon(C_3, I_2, J_2) → poly68, j_8, c_{21}, i_5
201. Intersect(f, r) → D_3
202. Polygon(C_2, C_3, D_3) → poly69, d_5, c_{22}, c_{23}
203. Intersect(c, c_1) → E_3
204. Intersect(c, d) → F_3
205. Polygon(E_3, H_2, F_3) → poly70, f_{13}, e_5, h_6
206. Polygon(F_2, E_3, H_2) → poly71, h_{16}, f_{14}, e_8
207. Intersect(l, m) → Q_3
208. Polygon(C_2, Q_3, A_3) → poly72, a_{23}, c_{24}, q_6
209. Polygon(D_3, C_3, I_2) → poly73, i_6, d_7, c_{25}
210. Polygon(C_2, C_3, Q_3) → poly74, q_8, c_{26}, c_{27}
211. Polygon(H_2, F_3, K_2) → poly75, k_5, h_{17}, f_{15}
212. Vector(S_3, T_3) → w_4
213. Vector(U_3, V_3) → m_4
214. Vector(W_3, J_4) → s_4
215. Vector(L_4, M_4) → t_4
216. Vector(O_4, P_4) → w_5
217. Vector(Q_4, R_4) → g_5
218. Vector(S_4, T_4) → w_6
219. Vector(U_4, V_4) → l_6
220. Vector(W_4, Z_4) → m_6