 | John Playfair - Geometry - 1836 - 148 pages
...straight line, &c. QED PROP. IV. THEOR. If the angle of a triangle be divided into two equal angles, by a straight line which also cuts the base ; the...segments of the base shall have the same ratio which the other sides of the triangle have to one another : and if the segments of the base have the same ratio... | |
 | Mathematics - 1836 - 488 pages
...line drawn from the vertex to the point of section, bisects the vertical angle. A. If the exterior angle of a triangle be bisected by a straight line which also cuts the base produced ; the segments between the bisecting line and the extremities of the base have the same ratio... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...the angle BAC is bisected by AD. The straight line, therefore, &c. PROP. A. THEOR.* IF an exterior angle of a triangle be bisected by a straight line which also cuts the base produced,! the segments between the bisecting line and the extremities of the base, have the same ratio... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...the angle BAG is cut into two equal angles by the straight line AD. PROP. A. THEOR. If the exterior angle of a triangle be bisected by a straight line which also cuts the base produced ; the segments between the bisecting line and the extremities of the base have the same ratio... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...angle BAG is cut into two equal angles by the straight line AD. PROPOSITION A. THEOREM. If the exterior angle of a triangle be bisected by a straight line which also cuts the base produced, the segments between the bisecting line and the extremities of the base have the same ratio... | |
 | William Whewell - 1837 - 226 pages
...remaining side of the triangle. *PROP. in. If the angle of a triangle be divided by a straight line cutting the base, the segments of the base shall have the same ratio as the other side of the triangle ; and if the segments of the base are to each other as the other... | |
 | Euclides - 1840 - 82 pages
...points of section, will be parallel to the remaining side of the triangle. PROP. III. THEOR. If an angle of a triangle be bisected by a straight line...also cuts the base, the segments of the base shall be proportional to the other sides of the triangle; or, if the segments of the base be proportional... | |
 | Euclides - Geometry - 1841 - 378 pages
...straight line, &c. QED PROP. III. THEOR. If the angle of a triangle be divided into two equal angles, by a straight line which also cuts the base; the segments of the base shall have the same ratio which the other sides of the triangle have to one another. And if the segments of the base have the same ratio... | |
 | Euclides - 1842 - 316 pages
...straight line, &c. QED PROP. III. THEOR. IF the angle of a triangle be divided into two equal angles, by a straight line which also cuts the base, the segments of the base shall have the same ratio which the other sides of the triangle have to one another ; and if the segments of the base have the same ratio... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...the angle BAC is cut into two equal angles by the straight line AD. PROP. A. THEOR. i If the exterior angle of a triangle be bisected by a straight line which also outs the base produced ; the segments between thebisecting line and the extremities of the base have... | |
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If the angle of a triangle be divided into two equal angles, by a straight line which also cuts the base ; the segments of the base shall have the same ratio which the other sides of the triangle have to one another... 
