 | John Playfair - Mathematics - 1806 - 320 pages
...ratios are equal to one another, which may be inferred from 11. 5. PROP. III. THEOR. Book VI. IF the angle of a triangle be bisected by a straight line which also cuts the base, the segments of the base will have the same ratio which the other sides of the triangle have to each other... | |
 | Daniel Cresswell - Geometry - 1819 - 486 pages
...FL, and it is manifest, that the segment CL is equal to the segment BK. PROP. LV. 64. THEOREM. If an angle of a triangle be bisected by a straight line, which also cuts the base, the rectangle, contained by the sides of the triangle, is equal to the rectangle contained by the segments... | |
 | John Playfair - 1819 - 354 pages
...angles by the straight line AD. Therefore, if the angle, &c. Q,. ED 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... | |
 | John Martin Frederick Wright - Mathematics - 1825 - 798 pages
...triangle and the three angles to construct it. PROPOSITIONS IN PLANE GEOMETRY. 1816. 1 . 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... | |
 | Daniel Cresswell - Euclid's Elements - 1825 - 616 pages
...FL, and it is manifest, that the segment CL is equal to the segment BK. PROP. LV. 64. THEOREM. If an angle of a triangle be bisected by a straight line, which also cutis the base, the rectangle, contained by the sidea of the triangle. is equal to the rectangle contained... | |
 | John Martin Frederick Wright - 1827 - 358 pages
...a spherical triangle. And the Freshmen had these PROPOSITIONS IN PLANE GEOMETRY. 1. 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... | |
 | John Martin F. Wright - 1827 - 632 pages
...a spherical triangle. And the Freshmen had these PROPOSITIONS IN PLANE GEOMETRY. 1. 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... | |
 | John Playfair - Euclid's Elements - 1832 - 358 pages
...therefore DE is parallel to BC. Wherefore, if a straight line, &c. QED PROP. III. THEOR. If the angle nfa triangle be bisected by a straight line which also cuts the base; the segments of the base shall have the satne ratio which the other sides of the triangle have to one another... | |
 | John Playfair - Euclid's Elements - 1833 - 346 pages
...1.) ; therefore DE is parallel to BC. Wherefore, if a straight line, &c. QED PROP. III. THEOR. If the angle of a triangle be bisected by a straight line which also ctits the base ; the segments of the base shall have the same ratio which the other sides of the triangle... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...between the same parallels (33. 1.) ; therefore DE is parallel to BC. A PROP. III. THEOR. If the anfrle of a triangle be bisected by a straight line which also cuts the base; V hesejmeni of the base shall have the same ratio whu-h the other «<*» of the triangle have to one... | |
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If the vertical angle of a triangle be bisected 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... 
