 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...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,... | |
 | Horatio Nelson Robinson - Conic sections - 1854 - 350 pages
...scholium), therefore, AC is common to the two A's ABC, ADC; and the A's are identical. QED THEOREM 18. The difference of any two sides of a triangle is less than the third tide. Let ABC be the A, and let AC be greater than AB; then we are to prove that AC — AB is less... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...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... | |
 | Euclides - 1858 - 248 pages
...make the opposite vertical angles equal, each alternate pair of lines will be in the same st. line. 3. The difference of any two sides of a triangle is less than the remaining side. 4. Each angle of an equilateral triangle is equal to one-third of two right angles,... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...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
...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... | |
 | Euclides - 1860 - 142 pages
...CAO (I. 8), and the line AO bisects the angle BAC. EXERCISE Vill.— THEOREM. The difference between two sides of a triangle is less than the third side. Let ABC be a triangle ; then the differ- C ence between any two of its sides, as AB and AC, is less than the third side BC. For... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...however near the point A may be to the line BC. It may be easily shewn from this proposition, that the difference of any two sides of a triangle is less than the third side. Prop. xxn. When the sum of two of the lines is equal to, and when it is less than, the third line;... | |
 | Elias Loomis - Conic sections - 1860 - 246 pages
...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... | |
 | Euclides - 1862 - 140 pages
...the perpendicular. 17. Prove I. 20, without producing any side, by bisecting one of the angles. 18. The difference of any two sides of a triangle is less than the third side. 19. If from any point within a triangle straight lines be drawn to the vertices of the three angles,... | |
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THE Difference of any Two Sides of a Triangle, is Less than the Third Side. 
