Desargues’ sætning.
Hvis de linjer, der forbinder samhørende punkter i de to trekanter ABC og A'B'C', går gennem samme punkt, P, så vil skæringspunkterne, R, S og T, mellem samhørende sider i de to trekanter ligge på samme linje. På figuren kan du flytte punkterne P, A, B, C, A', B' og C'.
Girard Desargues, fransk matematiker (1591-1661).
Figure figure = Position [0,0] Size[x,y] Origin[x*3/20,y] Unit x/20 Color "white" Dynamic;
//Axes axes = Color "black";
//Grid grid = Color "blue";
//Units units = Color "black";
Point P = [5,13] Free Size 2.5 Color "red";
Point A = [1,2] Free Size 2.5 Color "red";
Point B = [7,4] Free Size 2.5 Color "red";
Point C = [5,5] Free Size 2.5 Color "red";
Line lPA = Start P Dir A-P Infinite Size 1.5 Color "black";
Line lPB = Start P Dir B-P Infinite Size 1.5 Color "black";
Line lPC = Start P Dir C-P Infinite Size 1.5 Color "black";
Line lAB1 = Start A Dir B-A Infinite Size 1.5 Color "lightgray";
Line lBC1 = Start B Dir C-B Infinite Size 1.5 Color "lightgray";
Line lCA1 = Start C Dir A-C Infinite Size 1.5 Color "lightgray";
Line lAB = Start A Dir B-A Size 1.5 Color "red";
Line lBC = Start B Dir C-B Size 1.5 Color "red";
Line lCA = Start C Dir A-C Size 1.5 Color "red";
Point Am = [3,7.5] Slider lPA Size 2.5 Color "red";
Point Bm = [6.6,6] Slider lPB Size 2.5 Color "red";
Point Cm = [5,8] Slider lPC Size 2.5 Color "red";
Line lABm1 = Start Am Dir Bm-Am Infinite Size 1.5 Color "lightgray";
Line lBCm1 = Start Bm Dir Cm-Bm Infinite Size 1.5 Color "lightgray";
Line lCAm1 = Start Cm Dir Am-Cm Infinite Size 1.5 Color "lightgray";
Line lABm = Start Am Dir Bm-Am Size 1.5 Color "red";
Line lBCm = Start Bm Dir Cm-Bm Size 1.5 Color "red";
Line lCAm = Start Cm Dir Am-Cm Size 1.5 Color "red";
Point R = intersect( A, B, Am, Bm ) Size 2.5 Color "blue";
Point S = intersect( B, C, Bm, Cm ) Size 2.5 Color "blue";
Point T = intersect( C, A, Cm, Am ) Size 2.5 Color "blue";
Line l = Start R Dir S-R Infinite Size 1.5 Color "blue";
Label labA = "A" At A Offset [10,0] Color "black";
Label labB = "B" At B Offset [10,0] Color "black";
Label labC = "C" At C Offset [10,0] Color "black";
Label labAm = "A'" At Am Offset [10,0] Color "black";
Label labBm = "B'" At Bm Offset [10,0] Color "black";
Label labCm = "C'" At Cm Offset [10,0] Color "black";
Label labP = "P" At P Offset [10,0] Color "black";
Label labR = "R" At R Offset [10,0] Color "black";
Label labS = "S" At S Offset [10,0] Color "black";
Label labT = "T" At T Offset [10,0] Color "black";