 | 1798 - 618 σελίδες
...be true that any two sides of a triangle are greater than the third, neither could it be true that the greater side of every triangle is opposite to the greater angle, nor that the equal sides are opposite to equal angles, nor, lastly, that things equal to the same thing... | |
 | Robert Simson - 1806 - 546 σελίδες
...also CAB, ABC, are less than two right angles. Therefore, any two angles, &c. QED PROP. XVIII. THEOR. THE greater side of every triangle is opposite to the greater angle. Let ABC be a triangle, of which A the side AC is greater than the side AB ; the angle ABC is also greater... | |
 | Charles Hutton - 1811 - 406 σελίδες
...shown that the outward angle ABG, or its equal CBD, is greater than the other angle A. 5TB THEOREM IX. THE Greater Side, of every Triangle, is opposite to the Greater Angle ; and the Greater Angle opposite to the Greater Side. Let ABC be a triangle, having the side AB greater... | |
 | Charles Hutton - 1816 - 610 σελίδες
...shown that the outward angle ABG, or its equal CBD, is greater than the other angle A. THEOREM IX. THE Greater Side, of every Triangle, is opposite to the Greater Angle ; and the Greater Angle opposite to the Greater Side. Let ABC be a triangle, having the side AB greater... | |
 | Euclides - 1816 - 588 σελίδες
...asals6 CAB, ABC, are less than two right angles. Therefore any two angles, &c. QED PROP. XVIII.X THEOR. THE greater side of every triangle is opposite to the greater angle. Let ABC be a triangle, of which the side AC is greater than the side AB ; the angle ABC is also greater... | |
 | John Playfair - 1819 - 354 σελίδες
...be true, that any two sides of a triangle are greater than the third, neither could it be true, that the greater side of every triangle is opposite to the greater angle, nor that the equal sides are opposite to equal angles, nor, lastly, that things equal to the same thing... | |
 | Peter Nicholson - 1825 - 1046 σελίδες
...ABC, are less than two right angles. Therefore, any two angles, &c. QED Proposition XVIII. Theorem. The greater side of every triangle is opposite to the greater angle. Let ABC be a triangle of which the side AC is greater than the side AB ; the angle ABC is also greater... | |
 | Robert Simson - 1827 - 546 σελίδες
...also CAB, ABC, are less than two right angles. Therefore any two angles, &c. QED PROP. XVIII. THEOR. The greater side of every triangle is opposite to the greater angle. Let ABC be a triangle, of which the side AC is greater than the side AB: the angle ABC shall be greater... | |
 | George Peacock - 1830 - 732 σελίδες
...can exist between the sides and opposite angles of a triangle : in this manner it may be shewn that " the greater side of every triangle is opposite to the greater angle, and conversely :" for if a be greater than fe, then sin A is greater than sin B : but inasmuch as the... | |
 | Euclid - 1835 - 540 σελίδες
...CAB, ABC, are less than two right angles. Therefore, " any two angles," &c. QED PROP. XVIII. THEOR. The greater side of every triangle is opposite to the greater angle. Let ABC be a triangle, of which the side AC is greater than the side AB ; the angle ABC is also greater... | |
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Let ABC be a triangle, of which the side AC is greater than the side AB; the angle ABC shall be greater than the angle BCA. 
