Proposition 13 Euclide Book II (Law of Cosines)

 dans Euclide Geometry Principles par Harvey Littleman

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Define h=HB

Case 1) H in AC

a^2=h^2+(b-m)^2

c^2=h^2+m^2

a^2-c^2=b^2-2mb

Therefore a^2=b^2+c^2-2mb

 

Case 2) A in HC

• a^2=h^2+(b+m)^2
• c^2=h^2+m^2
• a^2-c^2=b^2+2mb
• Therefore a^2=b^2+c^2+2mb

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