 | Eucleides - 1860 - 396 pages
...VI. 2. ... VI. A. (p. 76). HYPOTHESES. .{ several parallels be drawn to the base of a triangle. .{ an angle of a triangle be bisected by a straight line, which likewise cuts the Idem [fa straight line bisects both the angle and base of a triangle. [f from any... | |
 | War office - 1861 - 260 pages
...are equal to each other. 3. In a given circle inscribe an equilateral and equiangular pentagon. 4. If an angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle... | |
 | Euclides - 1861 - 464 pages
...Cor. 2, VL PROP. 3.— THEOR. If tIie angle of a triangle be divided into two equal angles by a st. line which also cuts the base ; the segments of the base shall hare thâ same ratio which the other sides of the triangle have to one another: and conversely, if... | |
 | Robert Potts - 1863 - 482 pages
...that P, R, Q are in one straight line. 3. 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 conversely. Given... | |
 | Euclides - 1864 - 448 pages
...line, &c. QED PROPOSITION III. THEOREM. 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 conversely, if... | |
 | Woolwich roy. military acad - 1864 - 588 pages
...AD cutting the given circle in P, prove PD and PB each equal to the radius of the given circle. 11. If an angle of a triangle be bisected by a straight line that cuts the base, the rectangle containedby the sides of the triangle is equal to the rectangle contained... | |
 | Euclides - 1865 - 402 pages
...which the circumferences on which they stand have to one another: so also have the sectors. Prop. B. If an angle of a triangle be bisected by a straight line which likewise cuts the base ; the rectangle contained by the sides of the triangle is equal to the rectangle... | |
 | Robert Potts - 1865 - 528 pages
...BGC to the sector EHF. (v. def. 5.) Wherefore, in equal circles, &o. cj. ED PROPOSITION B. THEOREM. If an angle of a triangle be bisected by a straight line which likewise outs the bast ; the rectangle contained by the sides of the triangle is equal to the rectangle... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...a straight line &c. QED PROPOSITION 3. THEOREM. If the vertical angle of a triangle be bisected bi/ 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... | |
 | Euclid - 1868 - 138 pages
...KOuvфrjc IiTÍ rffv тоfiriv èiTi&vyvvfiivri eú0iïa Sí%a TÍfivfi rfjV TOV TOiydivov ywviav. If any angle of a triangle be bisected by a straight line...also cuts the base, the segments of the base shall have the same ratio to one another which the adjacent sides of the triangle have ; and conversely,... | |
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IF an angle of a triangle be bisected by a straight line, which likewise 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 of the... 
