Books Books
AB>AC-BC: that is, the difference of any two sides of a triangle is less than the third side.
A Course of Mathematics: In Two Volumes. For the Use of Academies, as Well ... - Page 257
by Charles Hutton - 1818

## The Elements of Plane Geometry ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...Similarly it may be shown that AC and CB are together greater than AB, and CB and BA than AC. QED COR. The difference of any two sides of a triangle is less than the third side. *Ex. 1 8. The straight line drawn from the vertex of a triangle to the middle point of the base is...

## Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...sides AB, BC, as BC, for example, there remains (A. 5), AC - BC < AB ; that is, the difference between any two sides of a triangle is less than the third side. resent the sides of a triangle, the sum of any two must be greater than the third, and the difference...

## First Steps in Geometry: A Series of Hints for the Solution of Geometrical ...

Richard Anthony Proctor - Geometry - 1887 - 202 pages
...than P Q. Let QD cut AB in E, and join EP : with this construction the proof is obvious. PROP. 20. 54. The difference of any two sides of a triangle is less than the third side. 55. A point P is taken within the triangle ABC; show that the sum of the distances PA, PB, and PC is...

## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 460 pages
...respectively: shew that, if AB is greater than AC, then OB is greater than OC. ON PROPOSITION 20. 7. The difference of any two sides of a triangle is less than the third side. 8. In a quadrilateral, if two opposite sides which are not parallel are produced to meet one another;...

## The First Book of Euclid's Elements: Arranged for Beginners

Euclid, John Bascombe Lock - Euclid's Elements - 1892 - 184 pages
...of the sides of a quadrilateral is greater tftan the sum of the diagonals. 5. The difference between any two sides of a triangle is less than the third side. 6. Given two points C, D and a straight line AB, find P in AB such that the difference between PC and...

## Annual Report

1894 - 1186 pages
...every respect. Prove Part i. only that is two angles and the adjacent side being given. (Prop. a6 V 7. The difference of any two sides of a triangle is less than> the third side. (From Prop-. 20) 8. .Construct a triangle, having given the base, one of the angles at the base, and...

## Plane and Solid Geometry: Suggestive Method

Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 520 pages
...and AD and BC intersect at O. Prove tkat AOB is an isosceles triangle. Ex. 60. The difference between any two sides of a triangle is less than the third side. PROPOSITION XXXIII. THEOREM. 108. Converse of Prop.XXXII,!. The shortest lin* from, a point- to a line...

## Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...VZACD = ZDCB. Stepl 4. .'.b>AD. Th. 7. State it 5. Similarly a> DB. 6. .'.a+b>c. Add 4 and 5 COROLLARY. The difference of any two sides of a triangle is less than the third side. For if a + b > c, and c > b, then a > c — b, by ax. 5. EXERCISES. 55. State the converse of each...