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Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
Elements of Euclid [selections from book 1-6] adapted to modern methods in ... - Page 98
by Euclides - 1874

## Elementary Mathematics: Embracing Arithmetic Geometry, and Algebra

Lewis Sergeant - 1873
...one angle of a parallelogram is a right angle, so is each of the others. Proposition 47. — Theorem. The square on the hypotenuse of a right-angled triangle is equal to the squares on the sides. If C is the right angle in ABC, the square on AB = the squares on AC, CB....

## The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...points, is equal to the sum of the squares on the other two sides and on the diagonals. 27. Prove that the square on the hypotenuse of a right-angled triangle...together with the square on the difference of the sides. 28. In any triangle, if a line be drawn from the vertex bisecting the base, the sum of the squares...

## Philosophical Works of the Late James Frederick Ferrier, Volume 1

James Frederick Ferrier - Philosophy - 1875 - 532 pages
...This, therefore, is not a truth valid at all times for all intelligence. Take another case. I say, The square on the hypotenuse of a right-angled triangle is equal to the squares on the other two sides ; or, to take a simpler case, I say that two straight lines cannot...

## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...triangle, the area, and the line bisecting the base, construct the triangle.. '* IV. 30. Shew that the square on the hypotenuse of a right-angled triangle,...together with the square on the difference of the sides. 31. In the triangle ABC, if AD be the perpendicular let fall upon the side BC; then the square...

## The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884 - 434 pages
...opposite an obtuse angle of a triangle is greater than the squares on the other two sides. 15. Five times the square on the hypotenuse of a right.angled triangle is equal to four times the sum of the squares on the medians drawn to the other two sides. 16. Three times the square on a side...

## The Practical Teacher, Volume 3

Education - 1884
...and a diagonal is 8,545 feet ; determine whether the parallelogram is a rectangle. By Euclid I. 47, the square on the hypotenuse of a rightangled triangle is equal to the sum of the squares on the sides. Here the diagonal corresponds with the hypotenuse. Now 75842 +...

## An introduction to geometry, consisting of Euclid's Elements, book ..., Volume 1

Euclides - 1884 - 182 pages
...each side of which shall be equal to a given straight line." 9. Give the proposition equivalent to : " The square on the hypotenuse of a right-angled triangle is equal to the sum of the squares upon the other two sides." 10. In the construction to XLVIII., show that it...

## The New Physics

John Trowbridge - 1884 - 408 pages
...have forgotten the philosophical proofs. Thus we can by actual measurement ascertain the truth that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the base and altitude of the triangle, and, knowing this fact, we can make...