Chip Hitware 7 B

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Unknown | 1998-08-19 | 31.5 KB
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Confidence	Program	Detection	Match Type	Support
`66%`	dexvert	CD Disc Image `(archive/iso)`	ext	Supported
`100%`	file	PDP-11 separate I&D executable not stripped	default (weak)
`99%`	file	data	default
hex view
+--------+-------------------------+-------------------------+--------+--------+
|00000000| 09 01 ff ff 01 00 05 00 | 43 41 78 65 73 cd cc cc |........|CAxes...|
|00000010| cc cc cc 1e c0 00 00 00 | 00 00 80 4b 40 cd cc cc |........|...K@...|
|00000020| cc cc cc 1e 40 00 00 00 | 00 00 80 4b c0 00 00 00 |....@...|...K....|
|00000030| 00 00 00 00 00 f0 3f 81 | 01 00 00 be 0a 00 00 32 |......?.|.......2|
|00000040| 00 00 00 32 00 00 00 02 | 03 00 00 7c 15 00 00 00 |...2....|...|....|
|00000050| 00 00 00 00 00 00 40 00 | 00 00 00 00 00 00 40 00 |......@.|......@.|
|00000060| 00 00 00 c0 c0 c0 00 ff | ff 01 00 0b 00 43 53 65 |........|.....CSe|
|00000070| 67 6d 65 6e 74 4f 62 6a | db 17 7e a0 80 83 12 40 |gmentObj|..~....@|
|00000080| d7 a3 70 3d 0a 57 44 c0 | 90 cc 6e 4d 0f eb 13 40 |..p=.WD.|..nM...@|
|00000090| d6 62 18 46 3d 4b 45 c0 | 00 00 01 00 00 00 00 00 |.b.F=KE.|........|
|000000a0| 02 00 00 00 02 00 00 00 | 80 80 00 00 01 00 00 00 |........|........|
|000000b0| 00 00 00 ff 00 00 00 00 | 00 00 02 00 00 00 90 cc |........|........|
|000000c0| 6e 4d 0f eb 13 40 d7 a3 | 70 3d 0a 57 44 c0 db 17 |nM...@..|p=.WD...|
|000000d0| 7e a0 80 83 12 40 d6 62 | 18 46 3d 4b 45 c0 03 80 |~....@.b|.F=KE...|
|000000e0| ec de e5 5b 02 a8 14 40 | 3d 0a d7 a3 70 fd 44 c0 |...[...@|=...p.D.|
|000000f0| 12 ae 47 e1 7a 14 16 40 | ba 33 e5 f5 f9 f4 45 c0 |..G.z..@|.3....E.|
|00000100| 00 00 01 00 00 00 00 00 | 02 00 00 00 02 00 00 00 |........|........|
|00000110| 80 80 00 00 01 00 00 00 | 00 00 00 ff 00 00 00 00 |........|........|
|00000120| 00 00 02 00 00 00 12 ae | 47 e1 7a 14 16 40 3d 0a |........|G.z..@=.|
|00000130| d7 a3 70 fd 44 c0 ec de | e5 5b 02 a8 14 40 ba 33 |..p.D...|.[...@.3|
|00000140| e5 f5 f9 f4 45 c0 03 80 | 1a 85 eb 51 b8 1e 0d 40 |....E...|...Q...@|
|00000150| 27 5c 8f c2 f5 28 21 c0 | 97 99 99 99 99 99 13 40 |'\...(!.|.......@|
|00000160| f4 28 5c 8f c2 f5 23 c0 | 00 00 01 00 00 00 00 00 |.(\...#.|........|
|00000170| 02 00 00 00 02 00 00 00 | 00 00 80 00 00 00 00 00 |........|........|
|00000180| 00 00 00 ff ff 00 00 00 | 00 00 02 00 00 00 97 99 |........|........|
|00000190| 99 99 99 99 13 40 27 5c | 8f c2 f5 28 21 c0 1a 85 |.....@'\|...(!...|
|000001a0| eb 51 b8 1e 0d 40 f4 28 | 5c 8f c2 f5 23 c0 03 80 |.Q...@.(|\...#...|
|000001b0| 1a 85 eb 51 b8 1e 0d 40 | b6 1e 85 eb 51 b8 1c c0 |...Q...@|....Q...|
|000001c0| 97 99 99 99 99 99 13 40 | 27 5c 8f c2 f5 28 21 c0 |.......@|'\...(!.|
|000001d0| 00 00 01 00 00 00 00 00 | 02 00 00 00 02 00 00 00 |........|........|
|000001e0| 00 00 80 00 00 00 00 00 | 00 00 00 ff ff 00 00 00 |........|........|
|000001f0| 00 00 02 00 00 00 1a 85 | eb 51 b8 1e 0d 40 b6 1e |........|.Q...@..|
|00000200| 85 eb 51 b8 1c c0 97 99 | 99 99 99 99 13 40 27 5c |..Q.....|.....@'\|
|00000210| 8f c2 f5 28 21 c0 03 80 | 1a 85 eb 51 b8 1e 0d 40 |...(!...|...Q...@|
|00000220| b6 1e 85 eb 51 b8 1c c0 | 1a 85 eb 51 b8 1e 0d 40 |....Q...|...Q...@|
|00000230| f4 28 5c 8f c2 f5 23 c0 | 00 00 01 00 00 00 00 00 |.(\...#.|........|
|00000240| 02 00 00 00 02 00 00 00 | 00 00 80 00 00 00 00 00 |........|........|
|00000250| 00 00 00 ff ff 00 00 00 | 00 00 02 00 00 00 1a 85 |........|........|
|00000260| eb 51 b8 1e 0d 40 b6 1e | 85 eb 51 b8 1c c0 1a 85 |.Q...@..|..Q.....|
|00000270| eb 51 b8 1e 0d 40 f4 28 | 5c 8f c2 f5 23 c0 03 80 |.Q...@.(|\...#...|
|00000280| 26 06 bf 72 b8 8a 12 40 | c3 f5 28 5c 8f c2 fd bf |&..r...@|..(\....|
|00000290| 90 c2 f5 28 5c 8f 16 40 | 28 e8 83 67 8e bb 01 c0 |...(\..@|(..g....|
|000002a0| 00 00 01 00 00 00 00 00 | 02 00 00 00 02 00 00 00 |........|........|
|000002b0| 00 00 80 00 00 00 00 00 | 00 00 00 ff ff 00 00 00 |........|........|
|000002c0| 00 00 02 00 00 00 90 c2 | f5 28 5c 8f 16 40 c3 f5 |........|.(\..@..|
|000002d0| 28 5c 8f c2 fd bf 26 06 | bf 72 b8 8a 12 40 28 e8 |(\....&.|.r...@(.|
|000002e0| 83 67 8e bb 01 c0 03 80 | 91 99 f7 0f fe be 08 40 |.g......|.......@|
|000002f0| db ae 29 e6 22 09 fd bf | 26 06 bf 72 b8 8a 12 40 |..)."...|&..r...@|
|00000300| 28 e8 83 67 8e bb 01 c0 | 00 00 01 00 00 00 00 00 |(..g....|........|
|00000310| 02 00 00 00 02 00 00 00 | 00 00 80 00 00 00 00 00 |........|........|
|00000320| 00 00 00 ff ff 00 00 00 | 00 00 02 00 00 00 91 99 |........|........|
|00000330| f7 0f fe be 08 40 db ae | 29 e6 22 09 fd bf 26 06 |.....@..|)."...&.|
|00000340| bf 72 b8 8a 12 40 28 e8 | 83 67 8e bb 01 c0 03 80 |.r...@(.|.g......|
|00000350| 9a 99 99 99 99 99 11 40 | 50 14 ae 47 e1 7a a4 3f |.......@|P..G.z.?|
|00000360| 90 c2 f5 28 5c 8f 16 40 | c3 f5 28 5c 8f c2 fd bf |...(\..@|..(\....|
|00000370| 00 00 01 00 00 00 00 00 | 02 00 00 00 02 00 00 00 |........|........|
|00000380| 00 00 80 00 00 00 00 00 | 00 00 00 ff ff 00 00 00 |........|........|
|00000390| 00 00 02 00 00 00 9a 99 | 99 99 99 99 11 40 50 14 |........|.....@P.|
|000003a0| ae 47 e1 7a a4 3f 90 c2 | f5 28 5c 8f 16 40 c3 f5 |.G.z.?..|.(\..@..|
|000003b0| 28 5c 8f c2 fd bf 03 80 | 9a 99 99 99 99 99 11 40 |(\......|.......@|
|000003c0| 50 14 ae 47 e1 7a a4 3f | 26 06 bf 72 b8 8a 12 40 |P..G.z.?|&..r...@|
|000003d0| 28 e8 83 67 8e bb 01 c0 | 00 00 01 00 00 00 00 00 |(..g....|........|
|000003e0| 02 00 00 00 02 00 00 00 | 00 00 80 00 00 00 00 00 |........|........|
|000003f0| 00 00 00 ff ff 00 00 00 | 00 00 02 00 00 00 9a 99 |........|........|
|00000400| 99 99 99 99 11 40 50 14 | ae 47 e1 7a a4 3f 26 06 |.....@P.|.G.z.?&.|
|00000410| bf 72 b8 8a 12 40 28 e8 | 83 67 8e bb 01 c0 03 80 |.r...@(.|.g......|
|00000420| 91 99 f7 0f fe be 08 40 | 50 14 ae 47 e1 7a a4 3f |.......@|P..G.z.?|
|00000430| 9a 99 99 99 99 99 11 40 | db ae 29 e6 22 09 fd bf |.......@|..)."...|
|00000440| 00 00 01 00 00 00 00 00 | 02 00 00 00 02 00 00 00 |........|........|
|00000450| 00 00 80 00 00 00 00 00 | 00 00 00 ff ff 00 00 00 |........|........|
|00000460| 00 00 02 00 00 00 9a 99 | 99 99 99 99 11 40 50 14 |........|.....@P.|
|00000470| ae 47 e1 7a a4 3f 91 99 | f7 0f fe be 08 40 db ae |.G.z.?..|.....@..|
|00000480| 29 e6 22 09 fd bf 03 80 | 1c 85 eb 51 b8 1e 17 40 |).".....|...Q...@|
|00000490| 0e 49 3b 1d 9d f2 16 40 | 2a 78 2b 11 cc 1f 19 40 |.I;....@|*x+....@|
|000004a0| 6d 3d 0a d7 a3 70 09 40 | 00 00 01 00 00 00 00 00 |m=...p.@|........|
|000004b0| 02 00 00 00 02 00 00 00 | 00 00 80 00 00 00 00 00 |........|........|
|000004c0| 00 00 00 ff ff 00 00 00 | 00 00 02 00 00 00 1c 85 |........|........|
|000004d0| eb 51 b8 1e 17 40 6d 3d | 0a d7 a3 70 09 40 2a 78 |.Q...@m=|...p.@*x|
|000004e0| 2b 11 cc 1f 19 40 0e 49 | 3b 1d 9d f2 16 40 03 80 |+....@.I|;....@..|
|000004f0| 98 99 99 99 99 99 13 40 | 0e 49 3b 1d 9d f2 16 40 |.......@|.I;....@|
|00000500| 2a 78 2b 11 cc 1f 19 40 | b6 1e 85 eb 51 b8 12 40 |*x+....@|....Q..@|
|00000510| 00 00 01 00 00 00 00 00 | 02 00 00 00 02 00 00 00 |........|........|
|00000520| 00 00 80 00 00 00 00 00 | 00 00 00 ff ff 00 00 00 |........|........|
|00000530| 00 00 02 00 00 00 2a 78 | 2b 11 cc 1f 19 40 0e 49 |......*x|+....@.I|
|00000540| 3b 1d 9d f2 16 40 98 99 | 99 99 99 99 13 40 b6 1e |;....@..|.....@..|
|00000550| 85 eb 51 b8 12 40 03 80 | 85 eb 51 b8 1e 85 15 40 |..Q..@..|..Q....@|
|00000560| 8f c2 f5 28 5c 8f 32 40 | 0a d7 a3 70 3d 0a 19 40 |...(\.2@|...p=..@|
|00000570| 8f c2 f5 28 5c 8f 32 40 | 00 00 01 00 00 00 00 00 |...(\.2@|........|
|00000580| 02 00 00 00 02 00 00 00 | 00 00 80 00 01 00 00 00 |........|........|
|00000590| 00 00 ff ff 00 00 00 00 | 00 00 02 00 00 00 85 eb |........|........|
|000005a0| 51 b8 1e 85 15 40 8f c2 | f5 28 5c 8f 32 40 0a d7 |Q....@..|.(\.2@..|
|000005b0| a3 70 3d 0a 19 40 8f c2 | f5 28 5c 8f 32 40 ff ff |.p=..@..|.(\.2@..|
|000005c0| 01 00 09 00 43 54 72 69 | 61 6e 67 6c 65 b9 1e 85 |....CTri|angle...|
|000005d0| eb 51 b8 06 40 7b 14 ae | 47 e1 fa 39 40 e1 7a 14 |.Q..@{..|G..9@.z.|
|000005e0| ae 47 e1 11 40 1f 85 eb | 51 b8 1e 36 40 00 00 01 |.G..@...|Q..6@...|
|000005f0| 00 00 00 00 00 02 00 00 | 00 02 00 00 00 00 00 80 |........|........|
|00000600| 00 01 00 00 00 00 00 ff | ff 00 00 00 00 00 00 03 |........|........|
|00000610| 00 00 00 b9 1e 85 eb 51 | b8 06 40 1f 85 eb 51 b8 |.......Q|..@...Q.|
|00000620| 1e 36 40 71 3d 0a d7 a3 | 70 09 40 7b 14 ae 47 e1 |.6@q=...|p.@{..G.|
|00000630| fa 39 40 e1 7a 14 ae 47 | e1 11 40 cd cc cc cc cc |.9@.z..G|..@.....|
|00000640| 8c 37 40 ff ff 01 00 08 | 00 43 54 65 78 74 4f 62 |.7@.....|.CTextOb|
|00000650| 6a 66 66 66 66 66 66 10 | 40 b8 1e 85 eb 51 38 4b |jffffff.|@....Q8K|
|00000660| c0 33 33 33 33 33 33 1d | 40 e1 7a 14 ae 47 61 4b |.333333.|@.z..GaK|
|00000670| c0 00 00 00 00 0a 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000680| 00 00 00 00 00 0f 54 69 | 6d 65 73 20 4e 65 77 20 |......Ti|mes New |
|00000690| 52 6f 6d 61 6e 10 49 73 | 6f 70 74 69 6b 6f 6e 20 |Roman.Is|optikon |
|000006a0| a9 20 31 39 39 38 13 80 | 33 33 33 33 33 33 1b c0 |. 1998..|333333..|
|000006b0| b8 1e 85 eb 51 38 4b c0 | cd cc cc cc cc cc 0c c0 |....Q8K.|........|
|000006c0| e1 7a 14 ae 47 61 4b c0 | 00 00 00 00 0a 00 00 00 |.z..GaK.|........|
|000006d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 0f 54 69 6d |........|.....Tim|
|000006e0| 65 73 20 4e 65 77 20 52 | 6f 6d 61 6e 10 45 6c 65 |es New R|oman.Ele|
|000006f0| 6d 65 6e 74 61 72 79 5f | 66 61 63 74 73 03 80 33 |mentary_|facts..3|
|00000700| 33 33 33 33 33 1b c0 33 | 33 33 33 33 33 4b c0 66 |33333..3|33333K.f|
|00000710| 66 66 66 66 66 1c 40 33 | 33 33 33 33 33 4b c0 00 |fffff.@3|33333K..|
|00000720| 00 01 00 00 00 00 00 02 | 00 00 00 02 00 00 00 00 |........|........|
|00000730| 00 80 00 00 00 00 00 00 | 00 ff 00 00 00 00 00 00 |........|........|
|00000740| 00 02 00 00 00 66 66 66 | 66 66 66 1c 40 33 33 33 |.....fff|fff.@333|
|00000750| 33 33 33 4b c0 33 33 33 | 33 33 33 1b c0 33 33 33 |333K.333|333..333|
|00000760| 33 33 33 4b c0 13 80 33 | 33 33 33 33 33 1b c0 cd |333K...3|33333...|
|00000770| cc cc cc cc 0c 4b 40 85 | eb 51 b8 1e 85 fb 3f ec |.....K@.|.Q....?.|
|00000780| 51 b8 1e 85 eb 47 40 00 | 00 00 00 0e 00 00 00 00 |Q....G@.|........|
|00000790| 00 00 00 00 00 00 00 00 | 00 00 00 0f 54 69 6d 65 |........|....Time|
|000007a0| 73 20 4e 65 77 20 52 6f | 6d 61 6e ff 6f 02 54 68 |s New Ro|man.o.Th|
|000007b0| 65 6f 72 65 6d 2d 31 3a | 20 28 53 41 53 29 20 49 |eorem-1:| (SAS) I|
|000007c0| 66 20 74 68 65 20 73 69 | 64 65 73 20 62 2c 20 63 |f the si|des b, c|
|000007d0| 20 6f 66 20 74 68 65 20 | 74 72 69 61 6e 67 6c 65 | of the |triangle|
|000007e0| 20 41 42 43 20 61 72 65 | 20 63 6f 72 72 65 73 70 | ABC are| corresp|
|000007f0| 6f 6e 64 69 6e 67 6c 79 | 20 63 6f 6e 67 72 75 65 |ondingly| congrue|
|00000800| 6e 74 20 74 6f 20 74 68 | 65 20 73 69 64 65 73 20 |nt to th|e sides |
|00000810| 62 92 2c 20 63 92 20 6f | 66 20 41 92 42 92 43 92 |b., c. o|f A.B.C.|
|00000820| 20 61 6e 64 20 74 68 65 | 20 63 6f 6e 74 61 69 6e | and the| contain|
|00000830| 65 64 20 61 6e 67 6c 65 | 20 41 20 69 73 20 63 6f |ed angle| A is co|
|00000840| 6e 67 72 75 65 6e 74 20 | 74 6f 20 74 68 65 20 63 |ngruent |to the c|
|00000850| 6f 72 72 65 73 70 6f 6e | 64 69 6e 67 20 63 6f 6e |orrespon|ding con|
|00000860| 74 61 69 6e 65 64 20 61 | 6e 67 6c 65 20 41 92 2c |tained a|ngle A.,|
|00000870| 20 74 68 65 6e 20 74 68 | 65 20 74 77 6f 20 74 72 | then th|e two tr|
|00000880| 69 61 6e 67 6c 65 73 20 | 61 72 65 20 63 6f 6e 67 |iangles |are cong|
|00000890| 72 75 65 6e 74 2e 20 0d | 0a 0d 0a 50 72 6f 6f 66 |ruent. .|...Proof|
|000008a0| 3a 20 46 72 6f 6d 20 61 | 78 69 6f 6d 2d 33 2e 36 |: From a|xiom-3.6|
|000008b0| 2c 20 63 6f 72 72 65 73 | 70 6f 6e 64 69 6e 67 20 |, corres|ponding |
|000008c0| 61 6e 67 6c 65 73 20 61 | 72 65 20 65 71 75 61 6c |angles a|re equal|
|000008d0| 2e 20 53 68 6f 77 20 74 | 68 61 74 20 72 65 6d 61 |. Show t|hat rema|
|000008e0| 69 6e 69 6e 67 20 73 69 | 64 65 20 61 20 69 73 20 |ining si|de a is |
|000008f0| 65 71 75 61 6c 20 74 6f | 20 61 27 2e 20 49 6e 64 |equal to| a'. Ind|
|00000900| 65 65 64 2c 20 69 66 20 | 61 27 3e 61 2c 20 74 61 |eed, if |a'>a, ta|
|00000910| 6b 65 20 44 20 6f 6e 20 | 42 27 43 27 20 73 75 63 |ke D on |B'C' suc|
|00000920| 68 20 74 68 61 74 20 42 | 27 44 20 69 73 20 65 71 |h that B|'D is eq|
|00000930| 75 61 6c 20 74 6f 20 61 | 3d 42 43 2e 20 41 70 70 |ual to a|=BC. App|
|00000940| 6c 79 20 61 67 61 69 6e | 20 61 78 69 6f 6d 2d 33 |ly again| axiom-3|
|00000950| 2e 36 20 74 6f 20 74 68 | 65 20 74 72 69 61 6e 67 |.6 to th|e triang|
|00000960| 6c 65 73 20 41 42 43 20 | 61 6e 64 20 41 27 42 27 |les ABC |and A'B'|
|00000970| 44 20 61 6e 64 20 63 6f | 6e 63 6c 75 64 65 20 74 |D and co|nclude t|
|00000980| 68 61 74 20 74 68 65 79 | 20 68 61 76 65 20 65 71 |hat they| have eq|
|00000990| 75 61 6c 20 61 6e 67 6c | 65 73 2e 20 54 68 75 73 |ual angl|es. Thus|
|000009a0| 2c 20 61 6e 67 28 42 27 | 41 27 44 29 3d 61 6e 67 |, ang(B'|A'D)=ang|
|000009b0| 28 42 27 41 27 43 27 29 | 61 6e 64 20 74 68 69 73 |(B'A'C')|and this|
|000009c0| 20 63 6f 6e 74 72 61 64 | 69 63 74 73 20 61 78 69 | contrad|icts axi|
|000009d0| 6f 6d 20 33 2e 34 2e 20 | 53 69 6d 69 6c 61 72 6c |om 3.4. |Similarl|
|000009e0| 79 20 61 3e 61 27 20 72 | 65 73 75 6c 74 73 20 74 |y a>a' r|esults t|
|000009f0| 6f 20 63 6f 6e 74 72 61 | 64 69 63 74 69 6f 6e 2e |o contra|diction.|
|00000a00| 20 48 65 6e 63 65 20 6f | 6e 6c 79 20 61 3d 61 27 | Hence o|nly a=a'|
|00000a10| 20 69 73 20 70 6f 73 73 | 69 62 6c 65 2e 13 80 1a | is poss|ible....|
|00000a20| 85 eb 51 b8 1e 1b c0 a4 | 70 3d 0a d7 a3 2b 40 85 |..Q.....|p=...+@.|
|00000a30| eb 51 b8 1e 85 fb 3f 5c | 8f c2 f5 28 5c 21 40 00 |.Q....?\|...(\!@.|
|00000a40| 00 00 00 0e 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000a50| 00 00 00 0f 54 69 6d 65 | 73 20 4e 65 77 20 52 6f |....Time|s New Ro|
|00000a60| 6d 61 6e ff fa 01 54 68 | 65 6f 72 65 6d 2d 39 3a |man...Th|eorem-9:|
|00000a70| 20 49 6e 20 65 76 65 72 | 79 20 74 72 69 61 6e 67 | In ever|y triang|
|00000a80| 6c 65 20 74 68 65 20 67 | 72 65 61 74 65 72 20 61 |le the g|reater a|
|00000a90| 6e 67 6c 65 20 69 73 20 | 6f 70 70 6f 73 69 74 65 |ngle is |opposite|
|00000aa0| 20 74 6f 20 74 68 65 20 | 67 72 65 61 74 65 72 20 | to the |greater |
|00000ab0| 73 69 64 65 20 61 6e 64 | 20 69 6e 76 65 72 73 65 |side and| inverse|
|00000ac0| 6c 79 2c 20 74 68 65 20 | 67 72 65 61 74 65 72 20 |ly, the |greater |
|00000ad0| 73 69 64 65 20 69 73 20 | 6f 70 70 6f 73 69 74 65 |side is |opposite|
|00000ae0| 20 74 6f 20 74 68 65 20 | 67 72 65 61 74 65 72 20 | to the |greater |
|00000af0| 61 6e 67 6c 65 2e 0d 0a | 0d 0a 50 72 6f 6f 66 3a |angle...|..Proof:|
|00000b00| 20 41 73 73 75 6d 65 20 | 74 68 61 74 20 61 3d 42 | Assume |that a=B|
|00000b10| 43 3e 62 3d 41 43 2e 20 | 54 61 6b 65 20 44 20 6f |C>b=AC. |Take D o|
|00000b20| 6e 20 42 43 2c 20 73 2e | 74 2e 20 44 43 3d 62 2e |n BC, s.|t. DC=b.|
|00000b30| 20 54 68 65 6e 20 41 43 | 44 20 69 73 20 69 73 6f | Then AC|D is iso|
|00000b40| 73 63 65 6c 65 73 20 61 | 6e 64 20 66 72 6f 6d 20 |sceles a|nd from |
|00000b50| 70 72 65 63 65 64 69 6e | 67 20 74 68 65 6f 72 65 |precedin|g theore|
|00000b60| 6d 20 61 6e 67 28 42 29 | 3d 75 3c 77 3d 61 6e 67 |m ang(B)|=u<w=ang|
|00000b70| 28 44 41 43 29 3c 61 6e | 67 28 41 29 2e 0d 0a 46 |(DAC)<an|g(A)...F|
|00000b80| 6f 72 20 74 68 65 20 69 | 6e 76 65 72 73 65 2c 20 |or the i|nverse, |
|00000b90| 61 73 73 75 6d 65 20 74 | 68 61 74 20 61 6e 67 28 |assume t|hat ang(|
|00000ba0| 41 29 3e 61 6e 67 28 42 | 29 2e 20 54 68 65 6e 2c |A)>ang(B|). Then,|
|00000bb0| 20 62 3c 61 2e 20 49 6e | 20 66 61 63 74 2c 20 69 | b<a. In| fact, i|
|00000bc0| 66 20 62 3e 61 2c 20 74 | 68 65 6e 20 66 72 6f 6d |f b>a, t|hen from|
|00000bd0| 20 74 68 65 20 66 69 72 | 73 74 20 70 61 72 74 2c | the fir|st part,|
|00000be0| 20 77 65 20 77 6f 75 6c | 64 20 68 61 76 65 20 61 | we woul|d have a|
|00000bf0| 6e 67 28 42 29 3e 61 6e | 67 28 41 29 2e 20 4f 6e |ng(B)>an|g(A). On|
|00000c00| 20 74 68 65 20 6f 74 68 | 65 72 20 73 69 64 65 20 | the oth|er side |
|00000c10| 69 66 20 62 3d 61 2c 20 | 66 72 6f 6d 20 74 68 65 |if b=a, |from the|
|00000c20| 6f 72 65 6d 2d 33 2c 20 | 77 65 20 77 6f 75 6c 64 |orem-3, |we would|
|00000c30| 20 68 61 76 65 20 61 6e | 67 28 41 29 3d 61 6e 67 | have an|g(A)=ang|
|00000c40| 28 42 29 2e 20 54 68 75 | 73 2c 20 6f 6e 6c 79 20 |(B). Thu|s, only |
|00000c50| 61 3e 62 20 69 73 20 70 | 6f 73 73 69 62 6c 65 2e |a>b is p|ossible.|
|00000c60| 13 80 20 85 eb 51 b8 1e | 1b c0 d7 a3 70 3d 0a d7 |.. ..Q..|....p=..|
|00000c70| 31 c0 a4 70 3d 0a d7 a3 | 1c 40 66 66 66 66 66 66 |1..p=...|.@ffffff|
|00000c80| 35 c0 00 00 00 00 0e 00 | 00 00 00 00 00 00 00 00 |5.......|........|
|00000c90| 00 00 00 00 00 00 0f 54 | 69 6d 65 73 20 4e 65 77 |.......T|imes New|
|00000ca0| 20 52 6f 6d 61 6e ff 64 | 02 50 72 6f 6f 66 3a 20 | Roman.d|.Proof: |
|00000cb0| 54 68 69 73 20 69 73 20 | 74 68 65 20 6f 72 69 67 |This is |the orig|
|00000cc0| 69 6e 61 6c 20 66 6f 72 | 6d 75 6c 61 74 69 6f 6e |inal for|mulation|
|00000cd0| 20 6f 66 20 74 68 65 20 | 45 75 63 6c 69 64 65 61 | of the |Euclidea|
|00000ce0| 6e 20 70 61 72 61 6c 6c | 65 6c 2d 61 78 69 6f 6d |n parall|el-axiom|
|00000cf0| 2e 20 49 74 20 69 73 20 | 6e 6f 77 20 70 72 6f 76 |. It is |now prov|
|00000d00| 65 64 20 61 73 20 61 20 | 74 68 65 6f 72 65 6d 2c |ed as a |theorem,|
|00000d10| 20 73 69 6e 63 65 20 77 | 65 20 61 73 73 75 6d 65 | since w|e assume|
|00000d20| 20 61 6e 6f 74 68 65 72 | 20 66 6f 72 6d 75 6c 61 | another| formula|
|00000d30| 74 69 6f 6e 20 66 6f 72 | 20 74 68 61 74 20 61 78 |tion for| that ax|
|00000d40| 69 6f 6d 20 28 61 78 69 | 6f 6d 2d 34 2e 31 29 2e |iom (axi|om-4.1).|
|00000d50| 0d 0a 49 6e 64 65 65 64 | 2c 20 69 66 20 74 68 65 |..Indeed|, if the|
|00000d60| 72 65 20 77 65 72 65 20 | 6e 6f 20 69 6e 74 65 72 |re were |no inter|
|00000d70| 73 65 63 74 69 6f 6e 20 | 70 6f 69 6e 74 20 6c 69 |section |point li|
|00000d80| 6b 65 20 43 2c 20 74 68 | 65 6e 20 4d 2c 20 4e 20 |ke C, th|en M, N |
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|00000db0| 6f 66 20 4d 2c 20 4e 20 | 6f 6e 20 74 68 65 20 6f |of M, N |on the o|
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|00000dd0| 73 20 69 6d 70 6f 73 73 | 69 62 6c 65 2c 20 73 69 |s imposs|ible, si|
|00000de0| 6e 63 65 20 74 68 69 73 | 20 77 6f 75 6c 64 20 63 |nce this| would c|
|00000df0| 6f 6e 74 72 61 64 69 63 | 74 20 74 68 65 6f 72 65 |ontradic|t theore|
|00000e00| 6d 2d 37 2e 20 42 75 74 | 20 4d 2c 20 4e 20 62 65 |m-7. But| M, N be|
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|00000e20| 68 20 61 2b 62 3c 70 69 | 20 6c 65 61 64 73 20 74 |h a+b<pi| leads t|
|00000e30| 6f 20 63 6f 6e 74 72 61 | 64 69 63 74 69 6f 6e 2e |o contra|diction.|
|00000e40| 20 49 6e 64 65 65 64 2c | 20 6d 61 6b 65 20 61 74 | Indeed,| make at|
|00000e50| 20 41 20 61 6e 20 61 6e | 67 6c 65 20 65 71 75 61 | A an an|gle equa|
|00000e60| 6c 20 74 6f 20 62 20 62 | 79 20 61 20 6c 69 6e 65 |l to b b|y a line|
|00000e70| 20 50 20 74 68 72 6f 75 | 67 68 20 74 68 61 74 20 | P throu|gh that |
|00000e80| 70 6f 69 6e 74 2e 20 50 | 20 69 73 20 70 61 72 61 |point. P| is para|
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|00000ee0| 74 68 65 20 6e 65 77 20 | 50 29 2c 20 61 20 63 6f |the new |P), a co|
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|00000f00| 68 65 20 61 78 69 6f 6d | 20 34 2e 31 2e 13 80 20 |he axiom| 4.1... |
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|00000f30| 00 00 00 0e 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000f40| 00 00 00 0f 54 69 6d 65 | 73 20 4e 65 77 20 52 6f |....Time|s New Ro|
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|00001fa0| 00 0f 54 69 6d 65 73 20 | 4e 65 77 20 52 6f 6d 61 |..Times |New Roma|
|00001fb0| 6e 01 41 13 80 15 ae 47 | e1 7a 14 06 40 cd cc cc |n.A....G|.z..@...|
|00001fc0| cc cc 0c 42 40 b9 1e 85 | eb 51 b8 0a 40 b8 1e 85 |...B@...|.Q..@...|
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|00001fe0| 00 00 00 00 00 00 00 00 | 00 0f 54 69 6d 65 73 20 |........|..Times |
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|00002010| a3 70 3d 0a 40 0b d7 a3 | 70 3d 8a 41 40 00 00 00 |.p=.@...|p=.A@...|
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|00002040| 6e 02 42 27 13 80 d7 a3 | 70 3d 0a d7 19 40 0b d7 |n.B'....|p=...@..|
|00002050| a3 70 3d ca 41 40 ae 47 | e1 7a 14 ae 1b 40 34 33 |.p=.A@.G|.z...@43|
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|00002070| 00 00 00 00 00 00 00 00 | 00 00 0f 54 69 6d 65 73 |........|...Times|
|00002080| 20 4e 65 77 20 52 6f 6d | 61 6e 02 43 27 13 80 00 | New Rom|an.C'...|
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|000020a0| 51 b8 1e 85 eb 1b 40 b8 | 1e 85 eb 51 b8 41 40 00 |Q.....@.|...Q.A@.|
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|000020c0| 00 00 00 0f 54 69 6d 65 | 73 20 4e 65 77 20 52 6f |....Time|s New Ro|
|000020d0| 6d 61 6e 01 43 13 80 66 | 66 66 66 66 66 14 40 49 |man.C..f|fffff.@I|
|000020e0| e1 7a 14 ae 87 42 40 66 | 66 66 66 66 66 16 40 f7 |.z...B@f|fffff.@.|
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|00002100| 00 00 00 00 00 00 00 00 | 00 00 00 0f 54 69 6d 65 |........|....Time|
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|00002190| 00 00 00 00 00 00 00 00 | 00 00 00 0f 54 69 6d 65 |........|....Time|
|000021a0| 73 20 4e 65 77 20 52 6f | 6d 61 6e 02 61 27 13 80 |s New Ro|man.a'..|
|000021b0| 99 99 99 99 99 99 09 40 | 47 e1 7a 14 ae 87 41 40 |.......@|G.z...A@|
|000021c0| 8f c2 f5 28 5c 8f 0e 40 | 33 33 33 33 33 33 41 40 |...(\..@|333333A@|
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|000021e0| 00 00 00 00 0f 54 69 6d | 65 73 20 4e 65 77 20 52 |.....Tim|es New R|
|000021f0| 6f 6d 61 6e 02 63 27 13 | 80 b9 1e 85 eb 51 b8 0e |oman.c'.|.....Q..|
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|00002220| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 0f 54 69 |........|......Ti|
|00002230| 6d 65 73 20 4e 65 77 20 | 52 6f 6d 61 6e 02 41 27 |mes New |Roman.A'|
|00002240| 13 80 e1 7a 14 ae 47 e1 | 0a 40 85 eb 51 b8 1e 85 |...z..G.|.@..Q...|
|00002250| 42 40 b8 1e 85 eb 51 b8 | 0e 40 b8 1e 85 eb 51 38 |B@....Q.|.@....Q8|
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|00002270| 00 00 00 00 00 00 0f 54 | 69 6d 65 73 20 4e 65 77 |.......T|imes New|
|00002280| 20 52 6f 6d 61 6e 01 63 | 13 80 8f c2 f5 28 5c 8f | Roman.c|.....(\.|
|00002290| 14 40 52 b8 1e 85 eb 51 | 41 40 3d 0a d7 a3 70 3d |.@R....Q|A@=...p=|
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|000022b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 0f 54 |........|.......T|
|000022c0| 69 6d 65 73 20 4e 65 77 | 20 52 6f 6d 61 6e 02 62 |imes New| Roman.b|
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|000022e0| 5c 41 40 a2 70 3d 0a d7 | a3 10 40 52 b8 1e 85 eb |\A@.p=..|..@R....|
|000022f0| 11 41 40 00 00 00 00 0e | 00 00 00 00 00 00 00 00 |.A@.....|........|
|00002300| 00 00 00 00 00 00 00 0f | 54 69 6d 65 73 20 4e 65 |........|Times Ne|
|00002310| 77 20 52 6f 6d 61 6e 01 | 75 13 80 66 66 66 66 66 |w Roman.|u..fffff|
|00002320| 66 10 40 71 3d 0a d7 a3 | b0 42 40 14 ae 47 e1 7a |f.@q=...|.B@..G.z|
|00002330| 14 12 40 b8 1e 85 eb 51 | 78 42 40 00 00 00 00 0e |..@....Q|xB@.....|
|00002340| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 0f |........|........|
|00002350| 54 69 6d 65 73 20 4e 65 | 77 20 52 6f 6d 61 6e 01 |Times Ne|w Roman.|
|00002360| 76 13 80 66 66 66 66 66 | 66 10 40 01 00 00 00 00 |v..fffff|f.@.....|
|00002370| 40 41 40 14 ae 47 e1 7a | 14 12 40 48 e1 7a 14 ae |@A@..G.z|..@H.z..|
|00002380| 07 41 40 00 00 00 00 0e | 00 00 00 00 00 00 00 00 |.A@.....|........|
|00002390| 00 00 00 00 00 00 00 0f | 54 69 6d 65 73 20 4e 65 |........|Times Ne|
|000023a0| 77 20 52 6f 6d 61 6e 01 | 76 13 80 3e 0a d7 a3 70 |w Roman.|v..>...p|
|000023b0| 3d 0e 40 d7 a3 70 3d 0a | 97 42 40 b8 1e 85 eb 51 |=.@..p=.|.B@....Q|
|000023c0| b8 10 40 cd cc cc cc cc | 4c 42 40 00 00 00 00 0e |..@.....|LB@.....|
|000023d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 0f |........|........|
|000023e0| 54 69 6d 65 73 20 4e 65 | 77 20 52 6f 6d 61 6e 01 |Times Ne|w Roman.|
|000023f0| 75 03 80 7b 14 ae 47 e1 | 7a 10 40 ec 51 b8 1e 85 |u..{..G.|z.@.Q...|
|00002400| 6b 40 40 66 66 66 66 66 | 66 16 40 ae 47 e1 7a 14 |k@@fffff|f.@.G.z.|
|00002410| 2e 3b 40 00 00 01 00 00 | 00 00 00 02 00 00 00 02 |.;@.....|........|
|00002420| 00 00 00 00 00 80 00 01 | 00 00 00 00 00 00 ff ff |........|........|
|00002430| 00 00 00 00 00 02 00 00 | 00 7b 14 ae 47 e1 7a 10 |........|.{..G.z.|
|00002440| 40 ae 47 e1 7a 14 2e 3b | 40 66 66 66 66 66 66 16 |@.G.z..;|@ffffff.|
|00002450| 40 ec 51 b8 1e 85 6b 40 | 40 03 80 00 00 00 00 00 |@.Q...k@|@.......|
|00002460| 00 10 40 d7 a3 70 3d 0a | d7 3f 40 52 b8 1e 85 eb |..@..p=.|.?@R....|
|00002470| 51 16 40 33 33 33 33 33 | b3 3d 40 00 00 01 00 00 |Q.@33333|.=@.....|
|00002480| 00 00 00 02 00 00 00 02 | 00 00 00 00 00 ff 00 01 |........|........|
|00002490| 00 00 00 00 00 00 00 ff | 00 00 00 00 00 02 00 00 |........|........|
|000024a0| 00 00 00 00 00 00 00 10 | 40 d7 a3 70 3d 0a d7 3f |........|@..p=..?|
|000024b0| 40 52 b8 1e 85 eb 51 16 | 40 33 33 33 33 33 b3 3d |@R....Q.|@33333.=|
|000024c0| 40 13 80 c3 f5 28 5c 8f | c2 0d 40 a4 70 3d 0a d7 |@....(\.|..@.p=..|
|000024d0| 23 40 40 00 00 00 00 00 | 00 10 40 d7 a3 70 3d 0a |#@@.....|..@..p=.|
|000024e0| d7 3f 40 00 00 00 00 0e | 00 00 00 00 00 00 00 00 |.?@.....|........|
|000024f0| 00 00 00 00 00 00 00 0f | 54 69 6d 65 73 20 4e 65 |........|Times Ne|
|00002500| 77 20 52 6f 6d 61 6e 01 | 41 13 80 b8 1e 85 eb 51 |w Roman.|A......Q|
|00002510| b8 16 40 33 33 33 33 33 | b3 3d 40 d7 a3 70 3d 0a |..@33333|.=@..p=.|
|00002520| d7 17 40 c3 f5 28 5c 8f | 42 3d 40 00 00 00 00 0e |..@..(\.|B=@.....|
|00002530| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 0f |........|........|
|00002540| 54 69 6d 65 73 20 4e 65 | 77 20 52 6f 6d 61 6e 01 |Times Ne|w Roman.|
|00002550| 42 11 80 e1 7a 14 ae 47 | e1 11 40 7b 14 ae 47 e1 |B...z..G|..@{..G.|
|00002560| fa 38 40 66 66 66 66 66 | 66 18 40 1f 85 eb 51 b8 |.8@fffff|f.@...Q.|
|00002570| 1e 35 40 00 00 01 00 00 | 00 00 00 02 00 00 00 02 |.5@.....|........|
|00002580| 00 00 00 00 00 80 00 01 | 00 00 00 00 00 ff ff 00 |........|........|
|00002590| 00 00 00 00 00 03 00 00 | 00 66 66 66 66 66 66 18 |........|.ffffff.|
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|000025b0| 40 1f 85 eb 51 b8 1e 35 | 40 e1 7a 14 ae 47 e1 11 |@...Q..5|@.z..G..|
|000025c0| 40 cd cc cc cc cc 8c 37 | 40 03 80 71 3d 0a d7 a3 |@......7|@..q=...|
|000025d0| 70 09 40 7b 14 ae 47 e1 | fa 39 40 66 66 66 66 66 |p.@{..G.|.9@fffff|
|000025e0| 66 18 40 7b 14 ae 47 e1 | fa 38 40 00 00 01 00 00 |f.@{..G.|.8@.....|
|000025f0| 00 00 00 02 00 00 00 02 | 00 00 00 00 00 80 00 01 |........|........|
|00002600| 00 00 00 00 00 ff ff 00 | 00 00 00 00 00 02 00 00 |........|........|
|00002610| 00 71 3d 0a d7 a3 70 09 | 40 7b 14 ae 47 e1 fa 39 |.q=...p.|@{..G..9|
|00002620| 40 66 66 66 66 66 66 18 | 40 7b 14 ae 47 e1 fa 38 |@ffffff.|@{..G..8|
|00002630| 40 03 80 b9 1e 85 eb 51 | b8 06 40 1f 85 eb 51 b8 |@......Q|..@...Q.|
|00002640| 1e 36 40 0a d7 a3 70 3d | 0a 17 40 1f 85 eb 51 b8 |.6@...p=|..@...Q.|
|00002650| 1e 35 40 00 00 01 00 00 | 00 00 00 02 00 00 00 02 |.5@.....|........|
|00002660| 00 00 00 00 00 80 00 01 | 00 00 00 00 00 ff ff 00 |........|........|
|00002670| 00 00 00 00 00 02 00 00 | 00 b9 1e 85 eb 51 b8 06 |........|.....Q..|
|00002680| 40 1f 85 eb 51 b8 1e 36 | 40 0a d7 a3 70 3d 0a 17 |@...Q..6|@...p=..|
|00002690| 40 1f 85 eb 51 b8 1e 35 | 40 13 80 ae 47 e1 7a 14 |@...Q..5|@...G.z.|
|000026a0| ae 07 40 7b 14 ae 47 e1 | 7a 3a 40 ec 51 b8 1e 85 |..@{..G.|z:@.Q...|
|000026b0| eb 09 40 0a d7 a3 70 3d | 0a 3a 40 00 00 00 00 0e |..@...p=|.:@.....|
|000026c0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 0f |........|........|
|000026d0| 54 69 6d 65 73 20 4e 65 | 77 20 52 6f 6d 61 6e 01 |Times Ne|w Roman.|
|000026e0| 44 13 80 66 66 66 66 66 | 66 18 40 f6 28 5c 8f c2 |D..fffff|f.@.(\..|
|000026f0| 75 39 40 85 eb 51 b8 1e | 85 19 40 85 eb 51 b8 1e |u9@..Q..|..@..Q..|
|00002700| 05 39 40 00 00 00 00 0e | 00 00 00 00 00 00 00 00 |.9@.....|........|
|00002710| 00 00 00 00 00 00 00 0f | 54 69 6d 65 73 20 4e 65 |........|Times Ne|
|00002720| 77 20 52 6f 6d 61 6e 01 | 42 13 80 0a d7 a3 70 3d |w Roman.|B.....p=|
|00002730| 0a 17 40 8f c2 f5 28 5c | 0f 35 40 29 5c 8f c2 f5 |..@...(\|.5@)\...|
|00002740| 28 18 40 1f 85 eb 51 b8 | 9e 34 40 00 00 00 00 0e |(.@...Q.|.4@.....|
|00002750| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 0f |........|........|
|00002760| 54 69 6d 65 73 20 4e 65 | 77 20 52 6f 6d 61 6e 01 |Times Ne|w Roman.|
|00002770| 43 13 80 52 b8 1e 85 eb | 51 04 40 33 33 33 33 33 |C..R....|Q.@33333|
|00002780| 33 36 40 8f c2 f5 28 5c | 8f 06 40 c3 f5 28 5c 8f |36@...(\|..@..(\.|
|00002790| c2 35 40 00 00 00 00 0e | 00 00 00 00 00 00 00 00 |.5@.....|........|
|000027a0| 00 00 00 00 00 00 00 0f | 54 69 6d 65 73 20 4e 65 |........|Times Ne|
|000027b0| 77 20 52 6f 6d 61 6e 01 | 41 13 80 71 3d 0a d7 a3 |w Roman.|A..q=...|
|000027c0| 70 11 40 8f c2 f5 28 5c | 0f 38 40 48 e1 7a 14 ae |p.@...(\|.8@H.z..|
|000027d0| 47 13 40 f6 28 5c 8f c2 | 75 37 40 00 00 00 00 0e |G.@.(\..|u7@.....|
|000027e0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 0f |........|........|
|000027f0| 54 69 6d 65 73 20 4e 65 | 77 20 52 6f 6d 61 6e 01 |Times Ne|w Roman.|
|00002800| 4d 13 80 48 e1 7a 14 ae | 47 09 40 c2 f5 28 5c 8f |M..H.z..|G.@..(\.|
|00002810| c2 39 40 1f 85 eb 51 b8 | 1e 0d 40 e1 7a 14 ae 47 |.9@...Q.|..@.z..G|
|00002820| 61 39 40 00 00 00 00 0e | 00 00 00 00 00 00 00 00 |a9@.....|........|
|00002830| 00 00 00 00 00 00 00 0f | 54 69 6d 65 73 20 4e 65 |........|Times Ne|
|00002840| 77 20 52 6f 6d 61 6e 01 | 75 13 80 1f 85 eb 51 b8 |w Roman.|u.....Q.|
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|00002c40| 6d 61 6e 01 45 13 80 29 | 5c 8f c2 f5 28 18 40 00 |man.E..)|\...(.@.|
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|00002d10| 73 20 4e 65 77 20 52 6f | 6d 61 6e 01 75 11 80 08 |s New Ro|man.u...|
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|00002e50| 00 00 00 00 00 00 00 00 | 00 00 00 0f 54 69 6d 65 |........|....Time|
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|00002f40| 6d 61 6e 01 75 13 80 31 | 33 33 33 33 33 0f 40 3f |man.u..1|33333.@?|
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|000031d0| 77 20 52 6f 6d 61 6e 01 | 42 13 80 5f 8f c2 f5 28 |w Roman.|B.._...(|
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|000032f0| 40 86 eb 51 b8 1e 85 07 | 40 6d 3d 0a d7 a3 70 09 |@..Q....|@m=...p.|
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|000033a0| 00 00 00 00 00 00 00 00 | 00 00 00 0f 54 69 6d 65 |........|....Time|
|000033b0| 73 20 4e 65 77 20 52 6f | 6d 61 6e 01 41 13 80 9a |s New Ro|man.A...|
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|000033f0| 00 00 00 0f 54 69 6d 65 | 73 20 4e 65 77 20 52 6f |....Time|s New Ro|
|00003400| 6d 61 6e 01 42 13 80 30 | 33 33 33 33 33 17 40 15 |man.B..0|33333.@.|
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|000034c0| 00 00 00 00 00 00 00 00 | 00 00 00 0f 54 69 6d 65 |........|....Time|
|000034d0| 73 20 4e 65 77 20 52 6f | 6d 61 6e 01 61 13 80 8e |s New Ro|man.a...|
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|00003520| 6d 61 6e 01 62 13 80 29 | 5c 8f c2 f5 28 10 40 78 |man.b..)|\...(.@x|
|00003530| 14 ae 47 e1 7a 10 40 46 | e1 7a 14 ae 47 11 40 70 |..G.z.@F|.z..G.@p|
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|00003560| 73 20 4e 65 77 20 52 6f | 6d 61 6e 01 63 13 80 64 |s New Ro|man.c..d|
|00003570| 66 66 66 66 66 16 40 64 | 66 66 66 66 66 0e 40 82 |fffff.@d|fffff.@.|
|00003580| eb 51 b8 1e 85 17 40 dd | 7a 14 ae 47 e1 0a 40 00 |.Q....@.|z..G..@.|
|00003590| 00 00 00 0e 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000035a0| 00 00 00 0f 54 69 6d 65 | 73 20 4e 65 77 20 52 6f |....Time|s New Ro|
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|000035c0| 0a d7 a3 70 3d 16 40 f4 | 28 5c 8f c2 f5 18 40 7a |...p=.@.|(\....@z|
|000035d0| 14 ae 47 e1 7a 14 40 00 | 00 00 00 0e 00 00 00 00 |..G.z.@.|........|
|000035e0| 00 00 00 00 00 00 00 00 | 00 00 00 0f 54 69 6d 65 |........|....Time|
|000035f0| 73 20 4e 65 77 20 52 6f | 6d 61 6e 01 75 ff ff 01 |s New Ro|man.u...|
|00003600| 00 0a 00 43 43 69 72 63 | 6c 65 4f 62 6a c3 27 d8 |...CCirc|leObj.'.|
|00003610| a6 a1 0c 01 40 c0 c3 79 | 11 7d 78 02 40 52 1f c7 |....@..y|.}x.@R..|
|00003620| 5f e2 ac 1a 40 20 53 3c | 07 a6 d4 01 c0 00 00 01 |_...@ S<|........|
|00003630| 00 00 00 00 00 02 00 00 | 00 02 00 00 00 00 00 80 |........|........|
|00003640| 00 00 00 00 00 00 00 00 | ff ff 00 00 00 00 00 02 |........|........|
|00003650| 00 00 00 9a 99 99 99 99 | 99 11 40 50 14 ae 47 e1 |........|..@P..G.|
|00003660| 7a a4 3f 90 c2 f5 28 5c | 8f 16 40 c3 f5 28 5c 8f |z.?...(\|..@..(\.|
|00003670| c2 fd bf 70 0b 5b 8c 91 | 26 02 40 28 80 c4 cc 2a |...p.[..|&.@(...*|
|00003680| 43 31 f2 07 40 3f 15 90 | 4c 89 6f fb bf 5e 66 c4 |C1..@?..|L.o..^f.|
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|000036a0| 00 00 00 00 00 01 00 00 | 00 02 00 00 00 00 00 80 |........|........|
|000036b0| 00 01 00 00 00 00 00 ff | 00 00 00 00 00 00 00 02 |........|........|
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|000036e0| 09 fd bf a0 99 99 99 99 | 99 b9 3f 02 00 00 00 28 |........|..?....(|
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|00003710| c0 00 00 01 00 00 00 00 | 00 01 00 00 00 02 00 00 |........|........|
|00003720| 00 00 00 80 00 01 00 00 | 00 00 00 ff 00 00 00 00 |........|........|
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|00003740| e8 83 67 8e bb 01 c0 8c | 6c 25 d9 1e f1 12 40 28 |..g.....|l%....@(|
|00003750| e8 83 67 8e bb 01 c0 80 | 99 99 99 99 99 b9 3f 02 |..g.....|......?.|
|00003760| 00 00 00 28 80 2a 5c 8f | c2 f5 28 16 40 27 5c 8f |...(.*\.|..(.@'\.|
|00003770| c2 f5 28 fc bf f6 28 5c | 8f c2 f5 16 40 5c 8f c2 |..(...(\|....@\..|
|00003780| f5 28 5c ff bf 00 00 01 | 00 00 00 00 00 01 00 00 |.(\.....|........|
|00003790| 00 02 00 00 00 00 00 80 | 00 01 00 00 00 00 00 ff |........|........|
|000037a0| 00 00 00 00 00 00 00 02 | 00 00 00 90 c2 f5 28 5c |........|......(\|
|000037b0| 8f 16 40 c3 f5 28 5c 8f | c2 fd bf f6 28 5c 8f c2 |..@..(\.|....(\..|
|000037c0| f5 16 40 c3 f5 28 5c 8f | c2 fd bf 80 99 99 99 99 |..@..(\.|........|
|000037d0| 99 b9 3f 02 00 00 00 13 | 80 14 ae 47 e1 7a 14 0a |..?.....|...G.z..|
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|000037f0| 40 bc 1e 85 eb 51 b8 fe | bf 00 00 00 00 0e 00 00 |@....Q..|........|
|00003800| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 0f 54 69 |........|......Ti|
|00003810| 6d 65 73 20 4e 65 77 20 | 52 6f 6d 61 6e 01 75 13 |mes New |Roman.u.|
|00003820| 80 72 3d 0a d7 a3 70 11 | 40 d7 a3 70 3d 0a d7 fb |.r=...p.|@..p=...|
|00003830| bf 90 c2 f5 28 5c 8f 12 | 40 70 3d 0a d7 a3 70 01 |....(\..|@p=...p.|
|00003840| c0 00 00 00 00 0e 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003850| 00 00 00 00 00 0f 54 69 | 6d 65 73 20 4e 65 77 20 |......Ti|mes New |
|00003860| 52 6f 6d 61 6e 01 75 13 | 80 90 c2 f5 28 5c 8f 12 |Roman.u.|....(\..|
|00003870| 40 27 5c 8f c2 f5 28 fc | bf ae 47 e1 7a 14 ae 13 |@'\...(.|..G.z...|
|00003880| 40 9c 99 99 99 99 99 01 | c0 00 00 00 00 0e 00 00 |@.......|........|
|00003890| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 0f 54 69 |........|......Ti|
|000038a0| 6d 65 73 20 4e 65 77 20 | 52 6f 6d 61 6e 01 76 13 |mes New |Roman.v.|
|000038b0| 80 34 33 33 33 33 33 15 | 40 9f 70 3d 0a d7 a3 f8 |.433333.|@.p=....|
|000038c0| bf 52 b8 1e 85 eb 51 16 | 40 b4 47 e1 7a 14 ae ff |.R....Q.|@.G.z...|
|000038d0| bf 00 00 00 00 0e 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000038e0| 00 00 00 00 00 0f 54 69 | 6d 65 73 20 4e 65 77 20 |......Ti|mes New |
|000038f0| 52 6f 6d 61 6e 01 76 13 | 80 eb 51 b8 1e 85 eb 05 |Roman.v.|..Q.....|
|00003900| 40 df 7a 14 ae 47 e1 fa | bf 28 5c 8f c2 f5 28 08 |@.z..G..|.(\...(.|
|00003910| 40 fa 28 5c 8f c2 f5 00 | c0 00 00 00 00 0e 00 00 |@.(\....|........|
|00003920| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 0f 54 69 |........|......Ti|
|00003930| 6d 65 73 20 4e 65 77 20 | 52 6f 6d 61 6e 01 41 13 |mes New |Roman.A.|
|00003940| 80 14 ae 47 e1 7a 14 12 | 40 ec 51 b8 1e 85 eb 01 |...G.z..|@.Q.....|
|00003950| c0 32 33 33 33 33 33 13 | 40 70 3d 0a d7 a3 70 05 |.233333.|@p=...p.|
|00003960| c0 00 00 00 00 0e 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003970| 00 00 00 00 00 0f 54 69 | 6d 65 73 20 4e 65 77 20 |......Ti|mes New |
|00003980| 52 6f 6d 61 6e 01 42 13 | 80 e2 7a 14 ae 47 e1 16 |Roman.B.|..z..G..|
|00003990| 40 1b ae 47 e1 7a 14 fe | bf 00 00 00 00 00 00 18 |@..G.z..|........|
|000039a0| 40 90 c2 f5 28 5c 8f 02 | c0 00 00 00 00 0e 00 00 |@...(\..|........|
|000039b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 0f 54 69 |........|......Ti|
|000039c0| 6d 65 73 20 4e 65 77 20 | 52 6f 6d 61 6e 01 43 13 |mes New |Roman.C.|
|000039d0| 80 1e 85 eb 51 b8 1e 11 | 40 6a 3d 0a d7 a3 70 dd |....Q...|@j=...p.|
|000039e0| 3f 3e 0a d7 a3 70 3d 12 | 40 a0 13 ae 47 e1 7a 94 |?>...p=.|@...G.z.|
|000039f0| 3f 00 00 00 00 0e 00 00 | 00 00 00 00 00 00 00 00 |?.......|........|
|00003a00| 00 00 00 00 00 0f 54 69 | 6d 65 73 20 4e 65 77 20 |......Ti|mes New |
|00003a10| 52 6f 6d 61 6e 01 4f 03 | 80 e1 7a 14 ae 47 e1 06 |Roman.O.|..z..G..|
|00003a20| 40 cc cc cc cc cc cc 14 | c0 ae 47 e1 7a 14 ae 1b |@.......|..G.z...|
|00003a30| 40 cc cc cc cc cc cc 14 | c0 00 00 01 00 00 00 00 |@.......|........|
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|00003a60| 7a 14 ae 47 e1 06 40 cc | cc cc cc cc cc 14 c0 ae |z..G..@.|........|
|00003a70| 47 e1 7a 14 ae 1b 40 cc | cc cc cc cc cc 14 c0 89 |G.z...@.|........|
|00003a80| 80 c2 f5 28 5c 8f c2 09 | 40 69 66 66 66 66 66 06 |...(\...|@ifffff.|
|00003a90| c0 7c 14 ae 47 e1 7a 16 | 40 cc cc cc cc cc cc 14 |.|..G.z.|@.......|
|00003aa0| c0 00 00 01 00 00 00 00 | 00 02 00 00 00 02 00 00 |........|........|
|00003ab0| 00 00 00 80 00 00 00 00 | 00 00 00 00 ff ff 00 00 |........|........|
|00003ac0| 00 00 00 02 00 00 00 ae | 47 e1 7a 14 ae 11 40 ff |........|G.z...@.|
|00003ad0| ff ff ff ff ff 0f c0 ae | 47 e1 7a 14 ae 11 40 cc |........|G.z...@.|
|00003ae0| cc cc cc cc cc 14 c0 32 | 33 33 33 33 33 f3 3f 03 |.......2|33333.?.|
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|00003b00| c0 ba 1e 85 eb 51 b8 18 | 40 cc cc cc cc cc cc 14 |.....Q..|@.......|
|00003b10| c0 00 00 01 00 00 00 00 | 00 02 00 00 00 02 00 00 |........|........|
|00003b20| 00 00 00 80 00 00 00 00 | 00 00 00 00 ff ff 00 00 |........|........|
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|00003b40| ff ff ff ff ff 0f c0 ba | 1e 85 eb 51 b8 18 40 cc |........|...Q..@.|
|00003b50| cc cc cc cc cc 14 c0 03 | 80 ae 47 e1 7a 14 ae 11 |........|..G.z...|
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|00003ba0| 17 f0 20 59 a5 15 40 32 | a5 38 71 3a b4 12 c0 ae |.. Y..@2|.8q:....|
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|00003bd0| c0 ae 47 e1 7a 14 ae 11 | 40 cc cc cc cc cc cc 14 |..G.z...|@.......|
|00003be0| c0 00 00 01 00 00 00 00 | 00 02 00 00 00 02 00 00 |........|........|
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|00003d00| b4 12 c0 80 99 99 99 99 | 99 b9 3f 02 00 00 00 28 |........|..?....(|
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|00003d90| 66 66 66 14 c0 20 85 eb | 51 b8 1e 19 40 32 33 33 |fff.. ..|Q...@233|
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|00003dd0| b8 18 40 cc cc cc cc cc | cc 14 c0 20 85 eb 51 b8 |..@.....|... ..Q.|
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|00003e10| 40 ff ff ff ff ff ff 0f | c0 00 00 00 00 0e 00 00 |@.......|........|
|00003e20| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 0f 54 69 |........|......Ti|
|00003e30| 6d 65 73 20 4e 65 77 20 | 52 6f 6d 61 6e 01 4f 13 |mes New |Roman.O.|
|00003e40| 80 f6 28 5c 8f c2 f5 10 | 40 1e 85 eb 51 b8 1e 15 |..(\....|@...Q...|
|00003e50| c0 16 ae 47 e1 7a 14 12 | 40 e2 7a 14 ae 47 e1 16 |...G.z..|@.z..G..|
|00003e60| c0 00 00 00 00 0e 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003e70| 00 00 00 00 00 0f 54 69 | 6d 65 73 20 4e 65 77 20 |......Ti|mes New |
|00003e80| 52 6f 6d 61 6e 01 41 13 | 80 3e 0a d7 a3 70 3d 18 |Roman.A.|.>...p=.|
|00003e90| 40 cc cc cc cc cc cc 14 | c0 5c 8f c2 f5 28 5c 19 |@.......|.\...(\.|
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|00003eb0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 0f 54 69 |........|......Ti|
|00003ec0| 6d 65 73 20 4e 65 77 20 | 52 6f 6d 61 6e 01 42 13 |mes New |Roman.B.|
|00003ed0| 80 2a 5c 8f c2 f5 28 16 | 40 5c 8f c2 f5 28 5c 11 |.*\...(.|@\...(\.|
|00003ee0| c0 48 e1 7a 14 ae 47 17 | 40 1e 85 eb 51 b8 1e 13 |.H.z..G.|@...Q...|
|00003ef0| c0 00 00 00 00 0e 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003f00| 00 00 00 00 00 0f 54 69 | 6d 65 73 20 4e 65 77 20 |......Ti|mes New |
|00003f10| 52 6f 6d 61 6e 01 43 13 | 80 ba 1e 85 eb 51 b8 18 |Roman.C.|.....Q..|
|00003f20| 40 0a d7 a3 70 3d 0a 13 | c0 d8 a3 70 3d 0a d7 19 |@...p=..|...p=...|
|00003f30| 40 cc cc cc cc cc cc 14 | c0 00 00 00 00 0e 00 00 |@.......|........|
|00003f40| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 0f 54 69 |........|......Ti|
|00003f50| 6d 65 73 20 4e 65 77 20 | 52 6f 6d 61 6e 01 75 13 |mes New |Roman.u.|
|00003f60| 80 86 eb 51 b8 1e 85 15 | 40 cc cc cc cc cc cc 12 |...Q....|@.......|
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|00003f80| c0 00 00 00 00 0e 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003f90| 00 00 00 00 00 0f 54 69 | 6d 65 73 20 4e 65 77 20 |......Ti|mes New |
|00003fa0| 52 6f 6d 61 6e 01 76 03 | 80 c3 f5 28 5c 8f c2 01 |Roman.v.|...(\...|
|00003fb0| 40 27 5c 8f c2 f5 28 21 | c0 65 66 66 66 66 66 1a |@'\...(!|.efffff.|
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|00004070| 1e 85 eb 51 b8 1c c0 80 | 99 99 99 99 99 b9 3f 02 |...Q....|......?.|
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|00004090| 5c 8f c2 23 c0 e6 51 b8 | 1e 85 eb 0d 40 28 5c 8f |\..#..Q.|....@(\.|
|000040a0| c2 f5 28 24 c0 00 00 01 | 00 00 00 00 00 01 00 00 |..($....|........|
|000040b0| 00 02 00 00 00 00 00 80 | 00 01 00 00 00 00 00 ff |........|........|
|000040c0| 00 00 00 00 00 00 00 02 | 00 00 00 1a 85 eb 51 b8 |........|......Q.|
|000040d0| 1e 0d 40 f4 28 5c 8f c2 | f5 23 c0 e6 51 b8 1e 85 |..@.(\..|.#..Q...|
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|00004170| eb 51 b8 0a 40 e2 7a 14 | ae 47 e1 1a c0 ee 28 5c |.Q..@.z.|.G....(\|
|00004180| 8f c2 f5 0c 40 a2 70 3d | 0a d7 a3 1c c0 00 00 00 |....@.p=|........|
|00004190| 00 0e 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000041a0| 00 0f 54 69 6d 65 73 20 | 4e 65 77 20 52 6f 6d 61 |..Times |New Roma|
|000041b0| 6e 01 41 13 80 15 ae 47 | e1 7a 14 0a 40 ac 47 e1 |n.A....G|.z..@.G.|
|000041c0| 7a 14 ae 23 c0 4e b8 1e | 85 eb 51 0c 40 8c c2 f5 |z..#.N..|..Q.@...|
|000041d0| 28 5c 8f 24 c0 00 00 00 | 00 0e 00 00 00 00 00 00 |(\.$....|........|
|000041e0| 00 00 00 00 00 00 00 00 | 00 0f 54 69 6d 65 73 20 |........|..Times |
|000041f0| 4e 65 77 20 52 6f 6d 61 | 6e 01 43 13 80 ff ff ff |New Roma|n.C.....|
|00004200| ff ff ff 13 40 65 66 66 | 66 66 66 20 c0 1d 85 eb |....@eff|fff ....|
|00004210| 51 b8 1e 15 40 45 e1 7a | 14 ae 47 21 c0 00 00 00 |Q...@E.z|..G!....|
|00004220| 00 0e 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00004230| 00 0f 54 69 6d 65 73 20 | 4e 65 77 20 52 6f 6d 61 |..Times |New Roma|
|00004240| 6e 01 42 13 80 8f c2 f5 | 28 5c 8f 0a 40 27 5c 8f |n.B.....|(\..@'\.|
|00004250| c2 f5 28 21 c0 1a 85 eb | 51 b8 1e 0d 40 f2 28 5c |..(!....|Q...@.(\|
|00004260| 8f c2 f5 21 c0 00 00 00 | 00 0e 00 00 00 00 00 00 |...!....|........|
|00004270| 00 00 00 00 00 00 00 00 | 00 0f 54 69 6d 65 73 20 |........|..Times |
|00004280| 4e 65 77 20 52 6f 6d 61 | 6e 01 44 13 80 a4 70 3d |New Roma|n.D...p=|
|00004290| 0a d7 a3 04 40 59 8f c2 | f5 28 5c 20 c0 29 5c 8f |....@Y..|.(\ .)\.|
|000042a0| c2 f5 28 08 40 31 33 33 | 33 33 33 21 c0 00 00 00 |..(.@133|333!....|
|000042b0| 00 0e 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000042c0| 00 0f 54 69 6d 65 73 20 | 4e 65 77 20 52 6f 6d 61 |..Times |New Roma|
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|00005a60| 6d 20 41 2c 20 63 61 6e | 20 6e 65 76 65 72 20 62 |m A, can| never b|
|00005a70| 65 20 6f 72 74 6f 67 6f | 6e 61 6c 20 74 6f 20 74 |e ortogo|nal to t|
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|00005b00| 00 00 0e 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
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|00005b30| 20 54 68 72 6f 75 67 68 | 20 61 20 70 6f 69 6e 74 | Through| a point|
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|00005ba0| 20 4c 2c 20 61 6e 64 20 | 66 6f 72 6d 20 6f 6e 20 | L, and |form on |
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|00005c10| 20 61 78 69 6f 6d 2d 33 | 2e 31 29 2e 20 54 68 65 | axiom-3|.1). The|
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|00005c30| 43 42 44 20 61 72 65 20 | 65 71 75 61 6c 20 28 74 |CBD are |equal (t|
|00005c40| 68 65 6f 72 65 6d 2d 31 | 29 2e 20 48 65 6e 63 65 |heorem-1|). Hence|
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|00005c60| 44 42 29 20 69 73 20 61 | 20 72 69 67 68 74 20 61 |DB) is a| right a|
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|00005ca0| 74 77 6f 20 6f 72 74 68 | 6f 67 6f 6e 61 6c 73 20 |two orth|ogonals |
|00005cb0| 41 44 2c 20 41 44 27 20 | 66 72 6f 6d 20 41 20 74 |AD, AD' |from A t|
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|00005cd0| 68 65 20 74 72 69 61 6e | 67 6c 65 20 41 44 44 27 |he trian|gle ADD'|
|00005ce0| 20 63 6f 6e 74 72 61 64 | 69 63 74 73 20 74 68 65 | contrad|icts the|
|00005cf0| 6f 72 65 6d 2d 37 2e 13 | 80 1a 85 eb 51 b8 1e 1b |orem-7..|....Q...|
|00005d00| c0 33 33 33 33 33 33 26 | c0 14 ae 47 e1 7a 14 f6 |.333333&|...G.z..|
|00005d10| 3f a4 70 3d 0a d7 a3 2c | c0 00 00 00 00 0e 00 00 |?.p=...,|........|
|00005d20| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 0f 54 69 |........|......Ti|
|00005d30| 6d 65 73 20 4e 65 77 20 | 52 6f 6d 61 6e e6 54 68 |mes New |Roman.Th|
|00005d40| 65 6f 72 65 6d 2d 31 34 | 3a 20 54 68 72 6f 75 67 |eorem-14|: Throug|
|00005d50| 68 20 61 20 70 6f 69 6e | 74 20 41 20 6f 6e 20 74 |h a poin|t A on t|
|00005d60| 68 65 20 6c 69 6e 65 20 | 4c 20 74 68 65 72 65 20 |he line |L there |
|00005d70| 69 73 20 65 78 61 63 74 | 6c 79 20 6f 6e 65 20 6f |is exact|ly one o|
|00005d80| 72 74 68 6f 67 6f 6e 61 | 6c 20 74 6f 20 4c 2e 0d |rthogona|l to L..|
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|00005db0| 20 64 69 72 65 63 74 6c | 79 20 72 69 73 65 20 41 | directl|y rise A|
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