 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...EF, so is the sector BGC to the sector EHF. Wherefore, in equal circles, &c. QED PROP. B- THEOREM. 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 it equal to the rectangle... | |
 | 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... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...circumference EF, so is the sector BGC to the sector EHF. Wherefore, in equal circles, lac. QED PROP. B. THEOR. If an angle of a triangle be bisected by a straight line. See N. •which likewise cuts the base ; the rectangle contained ly the sides of the triangle is equal... | |
 | John Playfair - Geometry - 1829 - 210 pages
...degrees, and an obtuse angle by an arch which is greater than 90 degrees. PROPOSITION E. THEOREM. SIMSQN. If an angle of a triangle be bisected by a straight line which cuts the opposite side, the square of that line together with the rectangle contained by the segments... | |
 | 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 : Jind if the segments... | |
 | John Playfair - Euclid's Elements - 1833 - 346 pages
...EF, so is the sector BGC to the sector EHF. Wherefore, in equal circles, &c. QED PROP. B. THEOR. tf 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... | |
 | 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... | |
 | Euclid - 1835 - 540 pages
...BGC to the sector EHF. Wherefore, " in equal circles," &c. QED Book VI. v~v~ ' PROP. B. THEOR. See N. 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... | |
 | John Playfair - Euclid's Elements - 1836 - 488 pages
...BC. JVherefore, if a straight line, &c. QED S\ k ___ PROP. III. THEOR. If the 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: And if the segments... | |
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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... 
