 | Education - 1850 - 488 pages
...the vertex to the point of section, divides the vertical angle into two equal angles. SECTION VI. 1. The difference between any two sides of a triangle is less than the third side. 2. The chord of 60° is equal to the radius of the circle. 3. The square of the excess of one straight... | |
 | 1851 - 382 pages
...side and perpendicular of an equilateral triangle, to construct it, 2. Trisect a right angle, .... 3. The difference between any two sides of a triangle is less than the third side< . , . 4. Prove that (A+B) »-)- (AB) » = 2(A»+B«), 5. Describe a square which shall be equal to... | |
 | Alpheus Crosby - Geometry, Plane - 1851 - 192 pages
...of a triangle is less than the sum of the other two. [Proved by the aid of Theor. IX.] COR. i. Tfie difference between any two sides of a triangle is less than the third side. § 80. 4.) Given, OB and OC, drawn from any point O within M.BC, to the extremities of one side BC.... | |
 | Janet Taylor - Nautical astronomy - 1851 - 674 pages
...the third side [Eu. i. 20.] or Theorem IX. page 19. From this it follows also, that the difference of any two sides of a triangle is less than the third side. PRACTICAL RULES For the solution of all the different cases of right-angled plane triangles with their... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...inequality AC<AB+BC' we take away either of the sides, as BC, we shall have (A. 5) AC-BC<AB\ that is, the difference between any two sides of a triangle is less than the third side. PROPOSITION VIII. THEOEEM. If from any point loithin a triangle, two straight lines be drawn to the... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...base, it will bisect the angles at the vertex made by producing the equal sides of the triangle. 3. The difference between any two sides of a triangle is less than the third side. 4. If two straight lines which meet one another be parallel to two other lines which meet one another,... | |
 | Euclid - Geometry - 1853 - 176 pages
...<ma AC are together greater than the third side BC. COROLLARY. It follows from this proposition that the difference between any two sides of a triangle is less than the third side; for since BA and AC are together greater than BC, if AC be subtracted from each, BA will be greater... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...inequality AC<AB+BC we take away either of the sides, as BC, we shall have (JL.5) AC-BC<AB: that is, the difference between any two sides of a triangle is less than the third side. PROPOSITION VIII. TIIEOREM. If from any point within a triangle, two straight lines be drawn to the... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...following problems, until Book V. has been studied. GEOMETRICAL EXERCISES ON BOOK I. THEOREMS. Prop. 1 . The difference between any two sides of a triangle is less than the third side. Prop. 2- The sum of the diagonals of a quadrilateral is less than the sum of any four lines that can... | |
 | Thomas Stantial - Examinations - 1859 - 352 pages
...the angles at the base is half a right angle. 9. Divide a right angle into three equal angles. 10. The difference between any two sides of a triangle is less than the third side. 11. On a given line describe a square of which the given line shall be the diagonal. 12. The diagonals... | |
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The difference between any two sides of a triangle is less than the third side. 
