 | Eli Todd Tappan - 1873 - 288 σελίδες
...AB + AC + 2ACXAD. 413. Corollary — If the square described on one side of a triangle is equivalent to the sum of the squares described on the other two sides, then the opposite angle is a right angle. For the last two theorems show that it can be neither acute... | |
 | Edward Olney - 1872 - 472 σελίδες
...346. COR.. 3. — .The square described on the hypotenuse of a right angled triangle is equivalent to the sum of the squares described on the other two sides. DEM.— From Cor. 1, AC" = AB x AD and also CBa = AB x DB. Therefore, adding, AC4 + CB =AB (AD + DB)... | |
 | Edward Olney - 1872 - 102 σελίδες
...PYTHAGOREAN PROPOSITION. 668. The square described on the hypotenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides. Fio. 372. 1st METHOD.—Let ABC be the given triangle, and ACED the square described on the hypotenuse.... | |
 | Edward Olney - 1872 - 562 σελίδες
...compared? 346. COR. 3. — The square described on the hypotenuse of a right angled triangle is equivalent to the sum of the squares described on the other two sides. DEM.— From Oar. 1, AC* = AB x AD and also CB* = AB x DB. Therefore, adding, AC* + CB* =AB (AD + DB)... | |
 | William Chauvenet - 1872 - 382 σελίδες
...PROPOSITION X.— THEOREM. 25. The square described upon the hypotenuse of a right triangle is equivalent to the sum of the squares described on the other two sides. ia a Let the triangle ABC be right angled at C; then, the square AH, described upon the hypotenuse,... | |
 | Benjamin Greenleaf - 1873 - 202 σελίδες
...EQ THEOREM IX. 195. The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides. Let ABC be a right-angled M triangle, having the right angle at A . then the square described on the... | |
 | Bombay city, univ - 1874 - 648 σελίδες
...unlimited length, from a given point without it. 2. Show that if the square described on one of the sides 8 of a triangle be equal to the sum of the squares described on the other two sides of it, the anglo contained by these two sides is a right angle. 3. In every triangle the square on the side subtending... | |
 | Euclides - 1874 - 120 σελίδες
...that the area of the triangle on the hypotenuse is equal to the area of the other two. PROPOSITION 48. THEOREM. If the square described on one of the sides of a triangle be equal to the squares- described on the ether two sides of it, the angle contained by these two sides is a right... | |
 | Braithwaite Arnett - 1874 - 130 σελίδες
...bisectors of two consecutive angles of a quadrilateral is half the sum of the two remaining angles. 5. If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle.... | |
 | Francis Cuthbertson - 1874 - 400 σελίδες
...the square on PR. Similarly it may be proved that the O QC is = the square on RQ; PROPOSITION XXXVI. If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by those sides is a right angle.... | |
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If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle. 
