 | Daniel Cresswell - Geometry - 1819 - 486 pages
...X DA : = BD X DC ; .-. BA X AC ~~ " ~^ AD*. PROP. LVI. 65. THEOREM. If from any angle of a triangle a straight line be drawn perpendicular to the base,...circle described about the triangle. Let ABC be a A , and AD the j_ from the L BAC to the base BC; then is BA X AC equal to the rectangle contained by... | |
 | John Mason Good - 1819 - 800 pages
...the sijuare of the straight line bisecting the angle. Prop. C. Theor. If from any angle of a triangle a straight line be drawn perpendicular to the base;...diameter of the circle described about the triangle. Prop. D. Theor. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle,... | |
 | John Playfair - 1819 - 354 pages
...Q, ED PROP. B. THEOR. If an angle of a triangle be bisected by a straight line, which likentist 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 straight line bisecting the angle* Let... | |
 | Daniel Cresswell - Geometry - 1819 - 446 pages
...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 of' the base, together with the square of the straight line bisecting the angle. Let ABCJ>ea... | |
 | Daniel Cresswell - Euclid's Elements - 1825 - 616 pages
...the square of the straight line bisecting the angle. \ I A" I. TH. If from any angle of a triangle a straight line be drawn perpendicular to the base,...diameter of the circle described about the triangle. LVII. TH. The rectangle contained by the diagonals of a quadrilateral rectilineal figure, inscribed... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...the square of AD. Wherefore, if an angle, &c. QE D PROP C. THEOREM. If from an ansie of a triangle a straight line be drawn perpendicular to the base...rectangle contained by the perpendicular and the diameter ofutt circle described about the triangH Let ABC be a triangle, and AD the perpendicular from the angle... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...an angle, &c. QED PROP. C. THEOR. If 'from any angle of a triangle a straight line be drawn See N. perpendicular to the base ; the rectangle contained...the angle A to the base BC : the rectangle BA, AC shall be equal to the rectangle contained by AD and the diameter of the circle described about the... | |
 | John Playfair - Geometry - 1829 - 210 pages
...be drawn from any angle perpendicular to the opposite side, the rectangle contained by the other two sides of the triangle is equal to the rectangle contained...the perpendicular and the diameter of the circle. Let ABC be a triangle, and AD the perp. drawn from the angle A to the opposite side BC ; the rectangle... | |
 | John Playfair - Euclid's Elements - 1832 - 358 pages
...therefore BA.AC=BD.DC+ DA", Wherefore, if an angle, &c. QED PROP. C. THEOR. If from any angle of a triangle a straight line be drawn perpendicular to the base;...the triangle is equal to the rectangle contained by the perpen dicular, and the diameter of the circle described about the tri angle. Let ABC be a triangle,... | |
 | John Playfair - Euclid's Elements - 1833 - 346 pages
...therefore BA.AC=BD.DC+ DA2. Wherefore, if an angle, &c. QED PROP. C. THEOR. If from any angle of a triangle a straight line be drawn perpendicular to the base...the rectangle contained by the sides of the triangle if equal to the rectangle contained by the perpendicular, and the diameter of the circle described... | |
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Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical 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... 
