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In any triangle, if a line be drawn from the vertex at right angles to the base; the difference of the squares of the sides is equal to the difference of the squares of the segments of the base.
A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the ... - Page 153
by Thomas Malton - 1774 - 440 pages

## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 320 pages
...THEOR. IF a perpendicular be drawn from any angle of a triangle to the opposite side, the difference of the squares of the sides is equal to the difference of the squares of the segments of the base. Book IT. Let ABC be a. triangle, having the side AB greater than AC, and AD a...

## Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 444 pages
...(29.) In any triangle if a line be drawn from the vertex at right angles to the base, the difference of the squares of the sides is equal to the difference of the squares of the segments of the base. S From A the vertex of the triangle ABC, let AD be drawn perpendicular to the...

## Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 442 pages
...In any triangle, if a line be drawn from the vertex at right angles to the base ; the difference of the squares of the sides is equal to the difference of the squares of the segments of the base. 30. In any triangle, if a line be drawn from the vertex bisecting the base ;...

## Glasgow Mechanics' Magazine, and Annals of Philosophy, Volume 2

Industrial arts - 1825 - 490 pages
...Theorem. In any triangle, if a perpendicular be let fall from the vertex to the base, the difference of the squares of the sides is equal to the difference of the squares of the two segments of the base. 14. Problem. To construct a square that shall be equal to two given squares....

## The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 544 pages
...the sides be given, the problem to determine the triangle is indeterminate, because the difference of the squares of the sides is equal to the difference of the squares of the segments of the base, and may, therefore, be inferred from the base and the point of section. The geometrical...

## Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...(</) In every triangle, if a perpendicular be drawn from the vertex to the base, the difference of the squares of the sides is equal to the difference of the squares of the segments of the base, ie the base is to the sum of the sides as the difference of the sides to the...

## Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...if a perpendicular be drawn from the vertex to the base, or to the base produced, the difference of the squares of the sides is equal to the difference of the squares of the segments of the base, or of the base produced, may be staled thus : — the base is to the sum of the...

## Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 544 pages
...vertex of a plane triangle, a perpendicular fall upon the base or the base produced, the difference of the squares of the sides is equal to the difference of the squares of the segments of the base. 74. If from the middle point of one of the sides of a right-angled triangle a...