| Webster Wells - Trigonometry - 1883 - 234 pages
...sides of a spherical triangle are equal, the angles opposite them are equal ; and conversely. (c) . **If two sides of a spherical triangle are unequal,...angle lies opposite the greater side ; and conversely.** (cZ) . The perpendicular from the vertex to the base of an isosceles spherical' triangle bisects the... | |
| George Clinton Shutts - Geometry - 1894 - 412 pages
...prove that CD is perpendicular to the hypotenuse AB, PROPOSITION XXXIV. 128. Theorem. // two sides of a **triangle are unequal the angles opposite them are unequal, and the greater angle** is opposite the greater side. A Let ABC represent a triangle in which the side AB is greater than the... | |
| George Albert Wentworth - Trigonometry - 1897 - 234 pages
...is called a quadrantal triangle. It is shown in Solid Geometry, that in every spherical triangle I. **If two sides of a spherical triangle are unequal,...angles opposite them are unequal, and the greater angle** is opposite the greater side ; and conversely. II. The sum of the sides is less than 360°. III. The... | |
| George Albert Wentworth - Logarithms - 1897 - 384 pages
...is called a quadrantal triangle. It is shown in Solid Geometry, that in every spherical triangle I. **If two sides of a spherical triangle are unequal,...angles opposite them are unequal, and the greater angle** is opposite the greater side; and conversely. II. The sum of the sides is less than 360°. III. The... | |
| Webster Wells - Geometry - 1899 - 180 pages
...of a great O meeting AC at D, and making Z CBD equal to Z C.) 614. Cor. (Converse of Prop. XXVII.) **If two sides of a spherical triangle are unequal, the angles opposite** are unequal, and the greater angle lies opposite the greater side. (Prove by Reductio ad Absurdum.')... | |
| Webster Wells - Geometry - 1899 - 450 pages
...of a great O meeting AC at D, and making Z CBD equal to Z C.) 614. Cor. (Converse of Prop. XXVII.) **If two sides of a spherical triangle are unequal, the angles opposite** are unequal, and the greater angle lies opposite the greater side. PROP. XXVIII. THEOREM. 615. The... | |
| Alan Sanders - Geometry - 1903 - 392 pages
...angle. Let ABC be a triangle having ZC greater than ZA . To Prove AB > BC. SOLID GEOMETRY CONVERSE. **If two sides of a spherical triangle are unequal, the angles opposite them are unequal,** the greater angle lying opposite the greater side. [Prove indirectly.] 1150. EXERCISE. Prove the converse... | |
| George Clinton Shutts - 1905 - 260 pages
...that CD is perpendicular to the hypotenuse A B. PROPOSITION XXXIV. 128. Theorem. // two sides of a **triangle are unequal the angles opposite them are unequal, and the greater angle** is opposite the greater side. A Let ABC represent a triangle in which the side AB is greater than the... | |
| Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...= BC (?). QED 121. THEOREM. An equiangular triangle is equilateral. 122. THEOREM. If two sides of a **triangle are unequal, the angles opposite them are unequal, and the greater** side subtends the greater angle. A Given: A ^BC; AB>AC. To Prove : Z 4CB > Z B. Proof : On AB take... | |
| Isaac Newton Failor - Geometry - 1906 - 431 pages
...unequal, the sides opposite are unequal, and the greater side is opposite the greater angle ; conversely, **if two sides of a spherical triangle are unequal, the angles opposite** are unequal, and the greater angle is opposite the greater side. HYPOTHESIS. In the spherical A ABC,... | |
| |