...in form from themselves, though not in magnitude, such as Book I. 47, in which it is asserted that the sum of the squares on the sides of a right-angled triangle, is equal to the square on the hypothenuse. The first class of these, the problems, should be carefully...

...in form from themselves, though not in magnitude, such as Book I. 47, in which it is asserted that the sum of the squares on the sides of a right-angled triangle, is equal to the square on the hypothenuse. The first class of 1,2 these, the problems, should be carefully...

...in form from themselves, though not in magnitude, such as Book I. 47, in which it is asserted that the sum of the squares on the sides of a right-angled triangle, is equal to the square on the hypothenuse. The first class of these, Ihe problems, should be carefully...

...the theorem which forms the forty-seventh proposition of Euclid's first book, and according to whii'h the sum of the, squares on the .sides of a right-angled triangle is equal to the square on the hypotbenuse. Pythagoreans. The followers of Pytfia-' gor:is, a native...

...the theorem which forms the forty-seventh proposition of Euclid's first book, and according to which the sum of the squares on the sides of a right-angled triangle is equal to the square on the hypotheuuse. Pythagorean*. The followers of Pythagoras, a native of Samoa,...

...representing to ourselves on paper the figure of Euclid's thirty-second proposition we can conclude that the sum of the interior angles of a triangle is two right angles. In neither case does Kant mean that the material image is necessary : it is only an empirical means...

...right angles. The result would be the same if any other polygon were taken. c\ Cor. 1.— Hence, the sum of the interior angles of a triangle is two right angles ; of a quadrilateral, four; of a pentagon, six ; and so on. Cor. 2. — By motion, the sum of the interior...

...square of the ordinate, plus the square of the abscissa, is equal to the square of the radius, since the sum of the squares on the sides of a right-angled triangle is equal to th« square of its hypothenuse. This relation is expressed by the equation and as this...

...angles of one are equal respectively to the angles of the other. PROPOSITION XXIII. THEOREM 138. The sum of the interior angles of a triangle is two right angles. Let ABC be any A. To Prove Z1+Z2+Z3=2 EA's. Proof. Draw DE through the vertex R, parallel to AC. Z...

...elementary geometry. The steps by which he demonstrated the equality of the square on the hypotenuse to the sum of the squares on the sides of a right-angled triangle, are not known. We know that in Euclid's Elements almost every one of the preceding forty -six propositions...