title: "Pythagoras sin reegel"
text: "Pythagoras sin reegel as wel ian faan a bed\u00fc\u00fcdenst reegeln uun a geometrii. Hat sait, dat uun en rochtwinkelt triihuk a kwadrooten auer jo tau kateeten tuup j\u00fcst so grat san \u00fcs det kwadroot auer det hypotenuus. \n\nWan  an  a lengden faan a kateeten \u00fc\u00fcb eder sidj faan a rocht winkel san, an  at lengde faan det hypotenuus, diar di rocht winkel jinauer leit, do t\u00e4\u00e4lt:\n\n \n\nDet reegel as efter Pythagoras faan Samos n\u00e4\u00e4md, auer hi wel di iarst weesen as, di det reegel bewiset h\u00e4\u00e4. Det reegel salew wiar oober al loong f\u00f6\u00f6r ham bek\u00e4\u00e4nd.\n\nReegnin \nDet reegel as so wichtag, auer d\u00fc leewen m\u00e4 tau gratin det traad \u00fctjreegne k\u00f6nst:\n - det hypotenuus\n .\n - a kateeten\n\nPythagoreesk taalen \n\nDet san trii hial taalen, diar d\u00fc uun det reegel iinsaat k\u00f6nst:\n \n \n \n \n\n.. det gongt widjer saner aanj.\n\nAn do k\u00f6nst d\u00fc a Pythagoreesk taalen uk noch \u00fctjwidje:\n \n  (mool 2)\n  (mool 3)\n\n.. an so widjer.\n\nBewis \n\nDet grat kwadroot as  lung an  briad; det areal as sodenang .\n\nWan d\u00fc faan det grat kwadroot 4 triihuken wechnamst, do blaft det c-kwadroot auer.\n\nJo 4 triihuken san eder  grat, aal 4 tuup san do  grat.\n .\n\nWan d\u00fc det widjer reegenst (iarst binomisk formel), komst d\u00fc tu:\n .\n\nN\u00fc t\u00e4\u00e4lst d\u00fc \u00fc\u00fcb arke sidj  uf, an do blaft auer:\n\nLuke uk diar \n\n Euklid sin kateetenreegel\n Euklid sin h\u00f6\u00f6chdereegel\n\nGeometrii"