 | Euclid - 1835 - 540 pages
...parallelogram that has one right angle has all its angles right angles. PROP. XLVII. THEOR. In any right angled triangle, the square which is described upon the side...sides which contain the right angle. Let ABC be a right angled triangle having the right angle BAG ; the square described upon the side BC is equal to... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...remaining complement BK is equal to the remaining complement KD. PROP. XXXVII. THEOR. In any right angled triangle, the square which is described upon the side subtending the right angle, is equivalent to the squares described upon the sides which contain the right angle. Let ABC be a right... | |
 | Mathematics - 1835 - 684 pages
...to the sum of the squares of the other two sides, the angle contained by those two sides shall be a right angle. Let ABC be a right-angled triangle, having the right angle, В AC : the square of В С shall be equal to the sum of the squares of В A, AC. Upon В С, В A,... | |
 | Mathematics - 1836 - 488 pages
...which are about the diameter of any parallelogram, are equal to one another. XLVII. In any right angled triangle, the square which is described upon the side...described upon the sides which contain the right angle. XLVIII. If the square described upon one of the sides of a triangle, be equal to the squares described... | |
 | John Playfair - Geometry - 1836 - 148 pages
...square upon the side BC,. is equal to the squares upon the sides AB, AC. Therefore, in any right angled triangle, the square which is described upon the side...described upon the sides which contain the right angle. Which was to be proved. PROP. XVIIL THEOR. If the square described upon one of the sides of a triangle... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...that has one right angle has all its angles right angles. ', PROP. XLVII. THEOR. In any right angled triangle, the square which is described upon the side...sides which contain the right angle. . ( Let ABC be a right angled triangle having the right angle BAG ; the square described upon the side BC is equal to... | |
 | Edward Tagart - Logic - 1837 - 156 pages
...of the term straight, the less likely they were to enclose a space. If I were asked how I know that in any rightangled triangle the square which is described...described upon the sides which contain the right angle, my first answer might be, that I knew it by studying the 47th of the first book of Euclid. But the... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...I. THEOR. IN any right-angled triangle, the square which is described upon the hypotenuse, that is, the side subtending the right angle, is equal to the...be a right-angled triangle, having the right angle BAC; the square described upon the hypotenuse BC is equal to the squares described upon ISA, AC. On... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...ADE = 2 right Zs, 5. that the fig. is rectangular (and :. a square.) PROPOSITION XLVII. ii Theorem. In any right-angled triangle, the square which is...described upon the sides which contain the right angle. In the construction of the figure it is necessary to show that GA is on the same right line with AC... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...the right angle, is equal to the similar and similarly described figures upon the sides containing the right angle. Let ABC be a right-angled triangle, having the right angle BAG ; the rectilineal figure described upon BC is equal to the similar and similarly described figures upon BA,... | |
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In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle. 
