 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 than the angle BCA. Because AC is greater than AB, make...  Elements of geometry and mensuration - Page 22by Thomas Lund - 1854 - 192 pagesFull view - About this book
 | Euclid, Thomas Tate - 1849 - 120 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...greater angle, Let ABC be a triangle, of which the side A AC is greater than the side AB ; the angle ABC is also greater than the angle BCA. Because AC is... | |
 | Education - 1849 - 682 pages
...globe is 2000 inches ; what is its diameter* Geometry. Demonstrate the following propositions: — 1. The greater side of every triangle is opposite to the greater angle ; and conversely, the greater angle is opposite to the greater side. 2. In every triangle the sum of... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...inequality between the sides BA, AC j therefore, the triangle BAC is isosceles. PROPOSITION XIII. THEOREM. The greater side of every triangle is opposite to the greater angle ; and conversely, the greater angle is opposite to the greater side. For, make the angle BCD = B. Then,... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...two angles, &c. Cor. Hence, every equiangular triangle is also equilateral. PROPOSITION XII. THEOREM. The greater side of every triangle is opposite to the greater angle; and, conversely, the greater angle is opposite to the greater side. Let ABC be a triangle, having the... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...angle, the angle at D is acute (Bk. I. Th. xvii. Cor. 3), and consequently less than the angle B. But the greater side of every triangle is opposite to the greater angle (Bk. I. Th. xi) ; therefore, the side CD is greater than CB, or its equal CF. Hence, the point D is... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...angle, the angle at D is acute (Bk. I. Th. xvii. Cor. 3), and consequently less than the angle B. But the greater side of every triangle is opposite to the greater angle (Bk. I. Th. xi) ; therefore, the side CD is greater than CB, or its eqnal CF. Hence, the point D is... | |
 | Euclides - 1852 - 152 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...of which the side AC is greater than the side AB; the angle ABC is also greater than the angle BCA. • B Because AC is greater than AB, make" AD equal... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...inequality between the sides BA and AC] therefore, the triangle BAC is isosceles. PROPOSITION XIII. THEOEEM. The greater side of every triangle is opposite to the greater angle ; and conversely, the greater angle is opposite to the greater side. 31 B For, make the angle BCD=B.... | |
 | Euclides - 1853 - 146 pages
...also CAB, ABC, are less than two right Therefore any two angles, &c. QED PROP. XVIII. — THEOREM. The greater side of every triangle is opposite to...triangle, of which the side AC is greater than the side AB ; the angle ABCis also greater than the angle BCA. A Because AC is greater than AB, make (I. 3.) AD... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...ABC, are less than two right angles. Therefore any two angles, etc. QKD PROPOSITION XVIII. TIIEOR. The greater side of every triangle is opposite to...triangle, of which the side AC is greater than the side AB ; the angle ABC is also greater than the angle BCA. Because AC is greater than AB, make (3. i.) AD... | |
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