 | 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... | |
 | Robert Simson - Trigonometry - 1806 - 546 pages
...line, Stc. QED PROP. III. TIIEOR. See N. IF the angle of a triangle be divided into two equql 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... | |
 | John Mason Good - 1813 - 714 pages
...III. Theor. If the angle of a trUogie be divided ¡oto tiro rqnal angles, by a straight line »liich 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 seginenU of the b.ise have the... | |
 | Euclides - 1816 - 588 pages
...straight line, &c. QED PROP. HI. 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... | |
 | 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... | |
 | 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 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... 
