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The difference of the squares of two sides of a triangle is equal to the difference of the squares of the segments made by the altitude upon the third side.
ELEMENTARY SYNTHETIC GEOMETRY OF THE POINT, LINE AND CIRCLE IN THE PLANE - Page 124
by N. F. DUPUIS, M.A., F.R.S.C. - 1894

## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 390 pages
...maximum when the line is bisected. Cor. 4. Since (I. 47. cor. 4.) the difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base, it follows, from the first corollary above, that the rectangle under the...

## The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 352 pages
...maximum when the line is bisected. Cor. 4. Since (I. 47, cor. 4) the difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base, it follows, from the first corollary above, that the rectangle under the...

## Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862
...and also one equal to the difference of two given squares. 49. The difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base made by a perpendicular from the opposite angle. 50. The three straight...

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

Euclides - 1874
...which it is divided is equal to the square on the other side. 63. The difference of the squares on the sides of a triangle is equal to the difference of the squares on the segments of the base made by a perpendicular from the opposite angle. 64. The square on the side subtending...

## Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...BC will be the difference of the given squares. Cor. 3. — a. The difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base made by a perpendicular. For the square of AB is equal to the squares of...

## The Elementary Geometry of the Right Line and Circle ... With Exercises

William Alexander Willock - 1875 - 172 pages
...of CP remains equal to the rectangle AP-BP, as stated. Con. 3. The difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base made by the perpendicular from the vertical angle upon the base. Let ACB...

## Exercises on Euclid and in modern geometry, New ed., revised

James McDowell - 1878
...rectangle under the hypotenuse and its adjacent segment 28 40. The difference of the squares on the sides of a triangle is equal to the difference of the squares on the segments of the base, made by the perpendicular from the vertex on the base or the base produced, and...

## Elements of Geometry

Simon Newcomb - Geometry - 1881 - 399 pages
...c), the required expression. THEOREMS FOR EXERCISE. THEOREM 1. The difference of the squares upon any two sides of a triangle is equal to the difference of the squares of the projections of these sides upon the third side. THEOREM 2. The sum of the squares upon the diagonals...