...sum and difference of two lines is equal to the difference of the squares of the lines. PROP. XXIV. The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the two other sides. PROP. XXV. The square of any side of an oblique-angled...

...BC is equal to three times the square on AC. 6. Three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of its three medians. 1. In any quadrilateral figure the squares on the diagonals are together equal to...

...principles, which are demonstrated in geometry, afford applications of square root. PRINCIPLES. — I. The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides; therefore, II. The hypotenuse is equal to the square...

...principles, which are demonstrated in geometry, afford applications of square root. PRINCIPLES. — I. The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides; therefore, II. The hypotenuse is equal to the square...

...adapted to arouse feeling. No one but its discoverer was ever moved to enthusiasm by the truth that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the remaining sides. A coldly logical and unanswerable argument dealing with...

...Demonstrative geometry will show the truth in all cases of the following principle : PRINCIPLE 54. — The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. 57. Measure off 6 inches on one side of a square surface...

...that is pure \ t , conviction is the proof of some theorem of Geometry, as, .;' for instance, that the square of the hypotenuse of a rightangled triangle is equal to the sum of the squares of the other two sides. All the proof adduced appeals solely to the intellect,...

...principles, which are demonstrated in geometry, afford applications of square root: PRINCIPLES. — I. The square of the hypotenuse of a rightangled triangle is equal to the sum of the squares of the other two sides ; therefore, II. T7'e hypotenuse is equal to the square...

...diameter ; divide the circumference by the diameter; the quotient will be 3.1416 approximately. II. The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. For proof, the pupil is referred to geometry. We may...

...c + d. Whence a + b + cjrd= 2 right angles. .-. B + A + C=2 right angles. CHAPTER II. THEOREM. 10. The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. Pythagoras, who was born at Samos about 569 BC, was...