 | Euclides - 1845 - 546 pages
...of the squares be joined ; the sum of the squares of the sides of the hexagonal figure thus formed is equal to four times the sum of the squares of the sides of the triangle. GEOMETRICAL EXERCISES ON BOOK III. THEOREM I. If AB, CD be chords of a circle... | |
 | Samuel Earnshaw - Statics - 1845 - 290 pages
...+ BC* + BD* + CD1 - *(AG* + BGF + CG2 + Hence the sum of the squares of the six edges of a pyramid is equal to four times the sum of the squares of the distances of its angular points from its centre of gravity. 168. When a system of bodies is in equilibrium... | |
 | Alexander Jamieson - Mechanics - 1845 - 572 pages
...(a* + J'+c'+^ + S' + S'2), that 18 In any triangular pyramid, the sum of the squares of its six edges is equal to four times the sum of the squares of the distances of the centre of gravity from each angle of the figure. This property of the triangular pyramid... | |
 | Dionysius Lardner - Science - 1846 - 664 pages
...very extensive, is evident from the ecstasy into which Pythagoras was thrown when he discovered that the square of the hypotenuse of a right-angled triangle is equal to the square of the two sides : for ignorance of this very elementary, but important proposition, necessarily... | |
 | John Narrien - Conic sections - 1846 - 252 pages
...proposition it may be proved, that the sum of the squares of the four diagonals of the parallelepiped BN is equal to four times the sum of the squares of the three edges about one of the solid angles ; that is, We have already, as above, the value of OP2. Now... | |
 | 1847 - 364 pages
...with much regret. LXXXVI. By Amicus. In every tetrahedron, the sum of the squares of the six edges is equal to four times the sum of the squares of the lines which join the middles of the opposite edges. [FntST SOLUTION. Mr. JW Elliott, Greatham.~\ Let... | |
 | Thomas Rainey - Arithmetic - 1849 - 320 pages
...fall outside of the triangle, the line of the base must be produced until it meets the vertical line. The square* of the hypotenuse of a right-angled triangle, is equal to the sum of the squares of the base and side. For example ; the base of a right-angled triangle is 8,... | |
 | Thomas Dick - Astronomy - 1850 - 964 pages
...as extremely trivial, and almost unworthy of regard. The properties of a triangle, such as, " that the square of the hypotenuse of a right-angled triangle, is equal to the squares of the other two sides"—" that the three angles of a triangle are equal to two right... | |
 | Thomas Dick - Cosmology - 1850 - 684 pages
...as extremely trivial, and almost unworthy of regard. The properties of a triangle, such as, " that the square of the hypotenuse of a right-angled triangle, is equal to the squares of the other two sides"—" that the three angles of a triangle are equal to two right... | |
 | John Radford Young - Measurement - 1850 - 294 pages
...triangle, from knowing the third side. It is proved in the 47th Prop, of Enclid's first book, that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the base and perpendicular; and consequently that the square of one of these... | |
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The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. 
