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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. "
Elements of Geometry and Trigonometry: With Applications in Mensuration - Page 44
by Charles Davies - 1886 - 324 pages
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The Monthly review. New and improved ser, Volume 26

1798 - 618 pages
...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...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...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...
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - Mathematics - 1811 - 406 pages
...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...
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A Course of Mathematics: In Two Volumes : for the Use of Academies ..., Volume 1

Charles Hutton - Mathematics - 1816 - 610 pages
...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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...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...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...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...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...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...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...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...
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A Treatise on Algebra

George Peacock - Algebra - 1830 - 732 pages
...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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...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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