 | George Shoobridge Carr - 1880
...(p—q). [П. 12, 13, The following cases are important : — (i.) When p = q, 62+c2 = 2q*+2d2; ie, the sum of the squares of two sides of a triangle is equal to twice the square of half the base, together with twice the square of the bisecting line drawn from the vertex. (ii.) When p = 2q,... | |
 | Charles Scott Venable - 1881 - 380 σελίδες
...square of the opposite side ; and if it is obtuse, the sum will be less. PROPOSITION XIV. THEOREM. The sum of the squares of two sides of a triangle is equivalent to twice the square of the median to the third side together with twice the square of half... | |
 | Charles Davies, Adrien Marie Legendre - 1885 - 538 σελίδες
...third side. PROPOSITION XIV. THEOREM. In any triangle, the sum of the squares described on two sides is equal to twice the square of half the third side, increased by twice the square of the line drawn from the middle point of that side to the vertex of the opposite angle. AB~" + AC2 = 2BE2... | |
 | George Shoobridge Carr - 1886 - 1036 σελίδες
...(pq). [II. 12, 13. The following cases are important : — (i.) When p = q} Ъ*+с* = 2ç2+2tf ; ie, the sum of the squares of two sides of a triangle is equal to twice the square of half the base, together with twice the square of the bisecting line drawn from the vertex. (ii.) When p = 2q,... | |
 | Dalhousie University - 1887 - 206 σελίδες
...a limit to the magnitude of the square : but if divided externally there is no limit. Shew why. 2. The sum of the squares of two sides of a triangle is equal to twice the sum of the squares of half the other side and of the corresponding median. Prove. 3. One circle cannot... | |
 | George Albert Wentworth - 1888 - 272 σελίδες
...lutlf the third side increased by twice the square of the median upon that side. II. The difference of the squares of two sides of a triangle is equal to twice the product of the third side by the projection of the median upon that side, A MD In the triangle ABC... | |
 | Edward Albert Bowser - 1890 - 420 σελίδες
...AE'. QED 334. COR. Subtracting (2) from (1) in (333), we have AB'-AC'=:2BCxED. Hence, the difference of the squares of two sides of a triangle is equal to twice the product of the third side by the projection of the median upon that side. Let the student prove the... | |
 | Edward Albert Bowser - 1891 - 424 σελίδες
...be taken in AC so that BD = BC, prove that the square on BC = AC X CD. Proposition 28. Theorem. 333. The sum of the squares of two sides of a triangle...side increased by twice the square of the median upon that side. A Hyp. Let ABC be a A, AE the median bisecting BC. To prove AlT + AC' = 2 BE' + 2 AE\ Proof.... | |
 | Seth Thayer Stewart - 1891 - 426 σελίδες
...Conclusion : Since ABC is any oblique-angled triangle, etc. Corollary I. The sum of the squares of any two sides of a triangle is equal to twice the square...side, increased by twice the square of the median to that side. Corollary II. The difference of the squares of any two sides of a triangle is equal to... | |
 | George Albert Wentworth - 1895 - 468 σελίδες
...equals in the above equality, AW = BC* + AC* + 2 BC x DC. QE iO. PROPOSITION XIX. THEOREM. 344. I. The sum of the squares of two sides of a triangle...the square of half the third side increased by twice tJte square of the median upon that side. II. The difference of the squares of two sides of a triangle... | |
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The sum of the squares of two sides of a triangle is equal to twice the square of half the third side increased by twice the square of the median upon that side. 
