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In right-angled triangles the square on the side opposite the right angle equals the sum of the squares on the sides containing the right angle.
Let ABC be a right-angled triangle having the angle BAC right.

I say that the square on BC equals the sum of the squares on BA and AC.
Describe the square BDEC on BC, and the squares GB and HC on BA and AC. Draw AL through A parallel to either BD or CE, and join AD and FC.

Since each of the angles BAC and BAG is right, it follows that with a straight line BA, and at the point A on it, the two straight lines AC and AG not lying on the same side make the adjacent angles equal to two right angles, therefore CA is in a straight line with AG.

For the same reason BA is also in a straight line with AH.
Since the angle DBC equals the angle FBA, for each is right, add the angle ABC to each, therefore the whole angle DBA equals the whole angle FBC.

Since DB equals BC, and FB equals BA, the two sides AB and BD equal the two sides FB and BC respectively, and the angle ABD equals the angle FBC, therefore the base AD equals the base FC, and the triangle ABD equals the triangle FBC.

Now the parallelogram BL is double the triangle ABD, for they have the same base BD and are in the same parallels BD and AL. And the square GB is double the triangle FBC, for they again have the same base FB and are in the same parallels FB and GC.

Therefore the parallelogram BL also equals the square GB.

Similarly, if AE and BK are joined, the parallelogram CL can also be proved equal to the square HC. Therefore the whole square BDEC equals the sum of the two squares GB and HC.

And the square BDEC is described on BC, and the squares GB and HC on BA and AC.

Therefore the square on BC equals the sum of the squares on BA and AC.
Therefore in right-angled triangles the square on the side opposite the right angle equals the sum of the squares on the sides containing the right angle.
New Team Page Beta
Player Ma St Ag Pa Av Skills Inj G Cp Td It Cs Mvp SPP Cost  
1
Rotspawn
4 5 1+ - 9+
Disturbing Presence, Foul Appearance, Loner, Mighty Blow, Nurgle's Rot, Really Stupid, Regeneration, Tentacles
Piling On, Guard, Block, Break Tackle
  37 0 0 0 32 2 74/ 230k
(140+90)k
 
2
Bloater
4 4 2+ - 9+
Disturbing Presence, Foul Appearance, Nurgle's Rot, Regeneration
Block, Jump Up
  14 0 0 0 2 3 19/ 160k
(110+50)k
 
3
Bloater
4 4 2+ - 9+
Disturbing Presence, Foul Appearance, Nurgle's Rot, Regeneration
Mighty Blow, Block, Dodge, Claw
  37 0 1 0 17 3 52/ 200k
(110+90)k
 
4
Bloater
4 4 2+ - 9+
Disturbing Presence, Foul Appearance, Nurgle's Rot, Regeneration
Piling On, Block, Claw
  22 0 0 0 13 2 36/ 170k
(110+60)k
 
5
Pestigor
6 3 3+ - 8+
Horns, Nurgle's Rot, Regeneration
  3 0 0 0 1 0 2/ 80k
(80+0)k
 
6
Pestigor
6 3 3+ - 8+
Horns, Nurgle's Rot, Regeneration
  7 0 0 0 0 0 0/ 80k
(80+0)k
 
7
Pestigor
7 3 3+ - 8+
Horns, Nurgle's Rot, Regeneration
Sure Hands, +MA, Dodge, Block
  37 5 9 0 2 4 56/ 180k
(80+100)k
 
9
Pestigor
6 4 3+ - 8+
Horns, Nurgle's Rot, Regeneration
Block, +ST, Mighty Blow
  19 2 4 0 3 3 35/ 170k
(80+90)k
 
10
Rotter
5 3 3+ - 8+
Decay, Nurgle's Rot
  4 0 0 0 0 0 0/ 40k
(40+0)k
 
11
Rotter
5 3 2+ - 8+
Decay, Nurgle's Rot
-ag 2 0 0 0 0 0 0/ 40k
(40+0)k
 
17
Journeyman Rotter
5 3 3+ - 8+
Decay, Nurgle's Rot
Loner
  0 0 0 0 0 0 0/ 40k
(40+0)k
 
10 players
Coach: TaoJones Re-Rolls (140k): 5  
Race: Nurgle Dedicated Fans: 6  
Current Team Value: 1740k Assistant Coaches: 0  
Treasury: 50k Cheerleaders: 0  
Team Value: 1740k Apothecary: No  
Games this Season: 38 / 15 Current Re-draft Budget: 1350k

Games Played:38 (6/6/26) |TD Diff:-42 (27 - 69) |Cas Diff:39 (68/45/9 - 33/34/16)
Last Opponent: Shortmans

  For   Against  
Opponent Race TV SPP Cas Gold Score TV SPP Cas Gold Gate
100 000 MoretonesHuman1000k61/1/050k0 - 41230k160/0/190k2k
Skin and Bones(Mostly Bones)Shambling Undead1000k72/2/030k1 - 21160k100/1/170k1k
TG UnitedOrc1030k83/0/060k0 - 21310k161/2/090k2k
True HeartsHuman950k103/1/070k0 - 11000k70/0/060k2k
Skin and Bones(Mostly Bones)Shambling Undead1180k102/2/020k0 - 11180k90/1/080k1k
Matchsticks BCShambling Undead1090k173/2/060k1 - 01210k61/0/030k1k
Skull Collection AgencyOrc1250k60/1/040k0 - 21140k151/1/070k1k
Government MotorsChaos Chosen1300k63/0/010k0 - 31330k180/2/080k2k
Nurgle WhatNurgle1280k120/3/150k0 - 11300k132/1/060k1k
100 000 MoretonesHuman1430k174/0/050k2 - 11370k100/1/060k1k
TG UnitedOrc1420k141/1/070k2 - 11470k80/0/030k1k
Internet ArgumentsOgre1560k152/2/130k1 - 11600k131/2/030k1k
Rainbow of SerenityChaos Renegade1410k21/1/130k0 - 21530k191/3/080k1k
USS EnterpriseOrc1360k61/0/010k0 - 21310k150/3/070k2k
Unbreakable SnowflakesWood Elf1360k123/3/070k0 - 51280k230/0/160k1k
Worst of the WorstChaos Renegade1460k123/0/120k0 - 11480k90/1/060k1k
Poach CatsChaos Renegade1580k100/1/050k1 - 21460k121/1/050k1k
RanopplĂ  IISlann1640k92/1/070k1 - 21910k162/1/00k1k
Se HordeOrc1640k81/0/030k1 - 11670k150/3/080k2k
Rainbow of SerenityChaos Renegade1550k103/1/050k1 - 11670k91/0/060k1k
Unbreakable SnowflakesWood Elf1600k120/3/0120k1 - 01340k00/0/00k1k
Worst of the WorstChaos Renegade1700k133/2/050k1 - 11740k111/1/070k1k
Rumat NörtitNurgle1730k92/0/040k0 - 31770k262/2/250k1k
Pofesionals BBCDark Elf1560k82/0/050k0 - 31550k182/0/160k0k
DistrozNecromantic Horror1540k143/0/030k1 - 31390k182/1/020k0k
ChromaticChaos Chosen1580k110/1/180k2 - 01650k70/0/130k1k
Tribal TerminatorsSlann1610k141/1/140k1 - 31680k246/0/150k1k
Hoppa!Slann1590k92/1/060k1 - 21300k140/0/070k1k
Be Green my friend BBCOrc1660k102/1/050k0 - 21610k100/0/080k1k
Goon PuddingHigh Elf1680k112/0/120k0 - 41800k190/1/050k1k
Sewer SacrificesSkaven1500k211/4/070k3 - 11510k110/1/160k1k
Get SlimedSlann1720k183/1/130k1 - 21750k130/1/040k1k
WarpStoned ShadowsUnderworld Denizens1730k161/4/060k1 - 11710k183/1/140k1k
Abomination DissertationsNecromantic Horror1760k90/1/150k0 - 11750k111/0/180k1k
Underworld UnderlingsUnderworld Denizens1800k225/2/050k1 - 21860k161/1/070k1k
Worst of the WorstChaos Renegade1900k111/2/050k1 - 21950k192/0/260k1k
Forbidden SirensShambling Undead1760k71/0/020k1 - 31680k171/1/170k1k
ShortmansChaos Dwarf1810k91/0/040k1 - 11860k151/1/260k0k