| Benjamin Greenleaf - Geometry - 1862 - 520 pages
...Scholium. This proposition is restricted to the case where the side EF lies in the same direction with BC, **since if FE were produced toward H, the angles DEH,...THEOREM. 94. If any side of a triangle be produced, the** exteriorangle is equal to the sum of the two interior and. opposite angles. Let ABC be a triangle,... | |
| S. M. Saxby - Marine engines - 1862 - 200 pages
...double of ECB, so must the whole angle ADB be the double of the angle AC B. *28. Euc. I. Prop. XXXII.— **If any side of a triangle be produced, the exterior angle is equal to the** two interior and opposite angles ; and the three interior angles of any triangle are equal to two right... | |
| Benjamin Greenleaf - Geometry - 1863 - 502 pages
...Scholium. This proposition is restricted to the case where the side EF lies in the same direction with BC, **since if FE were produced toward H, the angles DEH,...angle is equal to the sum of the two interior and** opposite angles. Lot ABC bo a triangle, and lot one of its sides, BC be produced towards D ; then the... | |
| Benjamin Greenleaf - Geometry - 1863 - 320 pages
...the side EF lies in the same direction with BC, since if FE were produced toward H, the angles DE H", **ABC would only be equal when they are right angles....angle is equal to the sum of the two interior and** opposite angles. Let ABC be a triangle, and AE lot one of its sides, BC be pro- /\ duced towards D... | |
| John Robertson (LL.D., of Upton Park sch.) - Examinations - 1865 - 144 pages
...in the same, and thence show that two straight lines cannot have a common segment. [ECS] 43. If the **side of a triangle be produced, the exterior angle is equal to the** two interior opposite angles : and the three interior angles of every triangle are together equal to... | |
| Euclides - 1865
...is one-third of two right angles, or two thirds of one right angle. PROPOSITION XXXI. THEOR. If one **side of a triangle be produced, the exterior angle is equal to the** two interior opposite angles. Let BC, one of the sides of the triangle ABC, be produced to D, the exterior... | |
| Horatio Nelson Robinson - Conic sections - 1865 - 472 pages
...angles. Hence the theorem ; the sum of the three angles, etc. THEOREM XII. If any side of a triangle is **produced, the exterior angle is equal to the sum of the two interior** opposite angles. Let ABC be a triangle. Produce AB to D; and we are to prove that the angle CBD is... | |
| Benjamin Greenleaf - Geometry - 1866 - 328 pages
...the case where the side EF lies in the same direction with BC, since if FE were produced toward II, **the angles DEH, ABC would only be equal when they...angle is equal to the sum of the two interior and** opposite angles. Let ABC be a triangle, and let one of its sides, BC be produced towards D ; then the... | |
| Benjamin Greenleaf - 1868 - 338 pages
...Scholium. This proposition is restricted to the case where the side EF lies in the same direction with BC, **since if FE were produced toward H, the angles DEH,...side of a triangle be produced, the exterior angle** ii equal to the sum of the two interior and ojipositu angles. Let ABC be a triangle, and let one of... | |
| Benjamin Greenleaf - 1869 - 516 pages
...Scholium. This proposition is restricted to the case where the side EF lies in the same direction with BC, **since if FE were produced toward H, the angles DEH,...only be equal when they are right angles. PROPOSITION** XX VII. r— THEOREM. 94. If any side of a triangle be produced, the exterior angle is equal lo the... | |
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