 | 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 ; and if the segments... | |
 | 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... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...straight line, &c. QED PROP. III. THEOR. If the angle of a triangle be divided into tmo equal angles, by a straight line which also cuts the base ; the segments of the base shall have the tame ratio nhich the other sides of the triangle have to one another : And if the segments of the bate... | |
 | 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... | |
 | Euclides - 1826 - 226 pages
...THEOREM. If the angle of a triangle be bisected, and the right line cutting the angle cuts the base also ; the segments of the base shall have the same ratio which the remaining sides of the triangle have; and if the segments of the base have the same ratio which the... | |
 | Euclid - 1826 - 234 pages
...THEOREM. If the angle of a triangle be bisected, and the right line cutlina the angle cuts the base also ; the segments of the base shall have the same ratio which the remaining sides of the triangle have ; and if the segments of the base have the same ratio which the... | |
 | George Lees - 1826 - 276 pages
...of a triangle ABC, be bisected by a straight line AD, which also cuts the base, the segments BD, DC of the base shall have the same ratio, which the other sides BA, AC of the triangle have to one another : And if the segments of the base have the same ratio which... | |
 | Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...Q . ED PROP. III. THEOR. If the angle of a triangle be hiseeted by a straight line whieh also euts the base ; the segments of the base shall have the same ratio whieh the other sides of the triangle have to one another : And if the segments of the base have the... | |
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If the vertical 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 of the base, together with the square on the straight... 
