...equivalent to the algebraical formula, (a + b) X (a — 6) = a2 — b\ PROPOSITION XI. — THEOREM. 237. The square described on the hypothenuse of a right-angled...the squares described on the other two sides. Let ABC be a right-angled triangle, having the right angle at A ; then the square described on the hypothenuse...

...sustained by the common practice of mankind. The mechanic does not think it necessary, to prove that the square described on the hypothenuse of a right-angled...sum of the squares described on the other two sides, every time that he attempts to square a building. It is enough for him to know that this truth has...

...equivalent to the quadrilateral AFD E, and then a rectangle equivalent to the triangle. The square on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares on the other sides. 148. Describe the squares on the sides (fig. 126), and through D, the right-angle,...

...(« + &) (a THEOREM VI. 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. Let ABC be a triangle, right-angled at B; then will For, construct squares on each of the sides, draw BD...

...demonstration from Euclid. 408. Theorem — The square described on the hypotenuse of a right angled triangle is equivalent to the sum of the squares described on the two legs. Let ABC be a right angled triangle, having the right angle BAC. The square described on the...

...described on the lines, together with twice the rectangle contained by the lines." P. VIII. B. IV. "The square described on the hypothenuse of a right-angled...of the squares described on the other two sides." P. XI. B. IV. " In every quadrilateral inseribed in a circle, the rectangle of the two diagonals, is...

...described on the lines, together with twice the rectangle contained by the lines." P. VIII. B. IV. "The- square described on the hypothenuse of a right-angled...of the squares described on the other two sides." P. XI. B. IV. "In every quadrilateral inscribed in a circle, the rectangle of the two diagonals, is...

...and (a + b) x (a — b) = a * — b\ THEOREM XXXIX. TJte square described on the hypotenuse of any right-angled triangle is equivalent to the sum of the squares described on the other two sides. Let ABC represent any right-angled triangle, the right angle at B; we are to prove that the square on AC...

...— b\ PROPOSITION XI. — THEOREM. 237. The square described on the hypothenuse of a fight-angled triangle is equivalent to the sum of the squares described on the other two sides. Let ABC be a right-angled triangle, having the right angle at A ; then the square described H on the hypothenuse...

...a given rectilinear figure. 3rd. A square equivalent to a given rectangle. 3. Prove that the square on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares on the sides. 4. Find a square equivalent to — 1st. The sum of two given squares. 2nd. The difference...