...this proposition is known as the Pythagorean : the square described upon the hypothenuse is equivalent to the sum of the squares described on the other two sides. As the unit of measure for the determination of the superficial relations of figures, we use a square...

...this proposition is known as the Pythagorean : the square described upon the hypothenuse is equivalent to the sum of the squares described on the other two sides. As the unit of measure for the determination of the superficial relations of figures, we use a square...

...completion of the proof, is of no further use. It is only in reality an involved mode of stating, that the square on the side subtending the right angle is equal to the sum of the squares on the two other sides of a right angled triangle.] OF EUCLID. PEOP. XIV. PEOB. To describe...

...worthy of particular notice. 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 tria,ngle, right angled at C, then will the square D described on AB...

...equal bases, and between the same parallels, are equal. 8. In any right-angled triangle, the square of the side subtending the right angle is equal to the sum of those described on the two other sides. 9. If a line be bisected, and produced to any point, the squares...

...right-angled triangle, right-angled at A : then will the square described on the hypothenuse BC be equivalent to the sum of the squares described on the other two sides, BA, AC. FGI H D Haying described a square on each of the three sides, let fall from A, on the hypothenuse,...

...triangle, but shall contain a greater angle. 2. In any right angled triangle, the square which is described on the side subtending the right angle is equal to the sum of the squares described upon the sides which contain the right angle. 3. If a straight line be divided into...

...sides the base and perpendicular. 293. The square described on the hypothenuse, or longest side, is equal to the sum of the squares described on the other two sides. Thus, suppose the longest side is 10 ft., the base 6 ft., and the perpendicular 8 ft. 10a=100. 6a=36....

...first book of Euclid's elements, or that which proves that in any right-angled triangle, the square of the side subtending the right angle is equal to the sum of the squares of the sides containing the right angle. I presume every reader to be familiar with the proposition,...

...first book of Euclid's elements, or that which proves that in any right-angled triangle, the square of the side subtending the right angle is equal to the sum of the squares of the sides containing the right angle. I presume every reader to be familiar with the proposition,...