 | Charles Hutton - Mathematics - 1816 - 610 pages
...Is any Right-angled Triangle, the square of the Hypothcnuse, is equal to the Sum of the Squares of the other two Sides Let ABC be a right-angled triangle, having the right angle c ; then will the square of the hypoihenu^e AB,be equal to the sum of the squares of the... | |
 | Daniel Cresswell - Euclid's Elements - 1825 - 616 pages
...is cut harmonically by that side, and the straight line so drawn, which is •within the triangle. Let ABC be a right-angled triangle, having the angle BAC a right angle; and let AD and AE, cutting CB in D, and CB produced in E, make equal angles with AB: CE is rut harmonically... | |
 | John Playfair - Geometry - 1829 - 210 pages
...Prop. 47. 1. In any right angled triangle the square described on the hypothenuse is equal to both the squares described on the other two sides. Let ABC be a right angled triangle, having the right angle ACB, and let the squares AE, FC, Cl be described on the... | |
 | Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...demonstrated. PROPOSITION XLVIII. THEOREM. — If the square described on one of the sides of a triangle, be equal to the sum of the squares described on the other two sides of it; the angle made by those two sides is a right angle. Let ABC be a triangle, which is such that... | |
 | Adrien Marie Legendre - Geometry - 1838 - 372 pages
...PROPOSITION XI. THEOREM. 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 the triangle ABC be right angled at A. Having described squares on the three sides, let fall from A,... | |
 | Charles Davies - Geometrical drawing - 1840 - 262 pages
...degrees, and 4=90 degrees. 10. In every right angled triangle, the square described on the hypothenuse, is equal to the sum of the squares described on the other two sides. Thus, if ABC be a right angled triangle, right angled at C, then will the square D described on AB... | |
 | Scotland free church, gen. assembly - 1847 - 554 pages
...it makes the alternate angles equal. 2. If the square described on one of the sides of a triangle be equal to the sum of the squares described on the other two sides, these sides contain a right angle. 3. Divide a given line into two parts, so that the rectangle contained... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 110 pages
...PROP. VII. THEOREM. 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. Let the triangle be Fig. 64. KDI, right angled at I. Describe squares on KD, KI, DI ; then we have to prove... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...BC^AB'-f-AC". Therefore, The square described on the hypolhcnuse of a right-angled triangle, is equivalent to the sum of the squares described on the other two sides. Cor. 1. Hence, by transposition, the square of one of the sides of a right-angled triangle is equivalent... | |
 | James Bates Thomson - Arithmetic - 1846 - 354 pages
...principle in geometry, that the square described on the hypothenuse of a right-angled triangle, is equal to the sum of the squares described on the other two sides. (Leg. IV. 11. Euc. I. 47.) Thus if the base of the triangle ABC is 4 feet, and the perpendicular 3... | |
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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. 
