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In any triangle, the difference of the squares of the two sides w equal to the difference of the squares of the segments of the base, or of the two lines or distances included between the extremes of the base and the perpendicular.
A Course of Mathematics: For the Use of Academies as Well as Private Tuition - Page 301
by Charles Hutton - 1812
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...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 perpendicular from the...
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## Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Geometry - 1819 - 377 pages
...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 ; the sum of the squares...
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## Geometrical Problems Deducible from the First Six Books of Euclid: Arranged ...

Miles Bland - Geometry - 1819 - 377 pages
...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 base ; the difference...
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## The Elements of geometry [Euclid book 1-3] in general terms, with ..., Part 3

Euclides - 1821
...fall on the opposite side, the difference between the squares of the sides which contain that angle, is equal to the difference of the squares of the segments of the sides on which the perpendicular falls. For the Q2 of one side is = to n1 of adjacent seg. »nd Q«...
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## A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822
...said hypothenuse and other side (th. 33). Coral. 2. Hence also, if two right-angled triangles have two sides of the one equal to two corresponding sides...of the two Sides, is Equal to the Difference of the Squnres of the Segments of the Base, or of the two Lines, or Distances, included between the Extremes...
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## The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 324 pages
...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 circumstances...
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## Elements of geometry: Being chiefly a selection from Playfair's geometry

John Playfair - Mathematics - 1829 - 186 pages
...drawn from any angle of a triangle to the opposite side, the difference of the squares of the other two sides is equal to the difference of the squares of the segments of the base made by the perpendicular. For, bv the dem. AB3 — AC3 = BD3 — DC3. J CoB. 2. If a perpendicular...
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## Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 272 pages
...that is, to a right angle.* Therefore, &c. Cor. 1. In a right-angled triangle, the square of either of the two sides is equal to the difference of the squares of the hypotenuse and the other side. Cor. 2. It appears, from the demonstration, that if a perpendicular...
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1835 - 316 pages
...isosceles; BC2=2AB2=2AC2; therefore, BC=ABV2. COR. 3. Hence, also, if two right angled triangles have two sides of the one, equal to two corresponding sides...third sides will also be equal, and the triangles will if, identical. PROP. XXXVIII. THEOR. If the square described upon one of the sides of a triangle,...
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## Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...that is, to a right angle.* Therefore, &c. Cor. 1. In a right-angled triangle, the square of either of the two sides is equal to the difference of the squares of the hypotenuse and the other side. Cor. 2. It appears, from the demonstration, that if a perpendicular...
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