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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...
The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... - Page 169
by Robert Simson - 1827 - 513 pages

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...Wherefore, if an anele,&c. Q, E. U PROP. C. THEOR. If from any angle of a triangle a straight line be 'drawn perpendicular to the base ; the rectangle contained...perpendicular from the angle A to the base BC ; the rectangle BA.AC is equal to the rectangle contained by AD and tke diameter of the circle described about the...

A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 486 pages
...X AC ~~ " ~^ AD*. PROP. LVI. 65. THEOREM. If from any angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained...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...

Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 800 pages
...line bisecting the angle. Prop. C. Theor. If from any angle of a triangle a straight line be drawn perpendicular to the base; the rectangle contained...diameter of the circle described about the triangle. Prop. D. Theor. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle,...

A Supplement to the Elements of Euclid

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...

Elements of Geometry: Containing the First Six Books of Euclid: With a ...

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...

A Supplement to the Elements of Euclid

Daniel Cresswell - Euclid's Elements - 1825 - 616 pages
...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, the rectangle contained...diameter of the circle described about the triangle. LVII. TH. The rectangle contained by the diagonals of a quadrilateral rectilineal figure, inscribed...

A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...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 ; the rectangle contained...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...

Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

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...