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" Every point in the bisector of an angle is equally distant from the sides of the angle ; and every point not in the bisector, but within the angle, is unequally distant from the sides of the angle. "
Elements of Geometry - Page 72
by George Albert Wentworth - 1881 - 250 pages
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The Elements of Geometry

George Bruce Halsted - Geometry - 1885 - 389 pages
...its perpendicular on any one of the three given lines as radius, will touch all three. PROOF. By 186, every point in the bisector of an angle is equally distant from its arms ; 416. The four tangents common to two circles occur in two pairs intersecting on the common...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...to one half the sum of the other two angles. IV. THEOREM. — Show that any point in the bisectrix of an angle is equally distant from the sides of the angle. V. THEOREM. — If two sides of a triangle are prolonged beyond the third side, show that the bisectrices...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...the base of an isosceles triangle to the opposite sides are equal. PROPOSITION XXX. THEOREM. 98. Any point in the bisector of an angle is equally distant from the sides of the angle. /A N Let BD be the bisector of the angle ABC and let P be any point in BD. To prove that P is equally...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 394 pages
...its perpendicular on any one of the three given lines as radius, will touch all three. PROOF. By 186, every point in the bisector of an angle is equally distant from its arms ; 416. The four tangents common to two circles occur in two pairs intersecting on the common...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 332 pages
...point not on the perpendicular is unequally distant from the extremities of the line. PROPOSITION XIX. Every point in the bisector of an angle is equally...of the angle ; and every point not in the bisector is unequally distant from the sides of the angle ; that is, the bisector of an angle is the locus of...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...point not on the perpendicular is unequally distant from the extremities of the line. PROPOSITION XIX. Every point in the bisector of an angle is equally...of the angle ; and every point not in the bisector is unequally distant from the sides of the angle ; that is, the bisector of an angle is the locus of...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1887 - 364 pages
...on the perpendicular is unequally from the extremities of the line. PROPOSITION XIX. , J W ""T " , f point in the bisector of an angle is equally distant from the the angle; and every point not in the bisector, but within the , unequally distant from the sides of...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1888 - 826 pages
...Be = B'C', Cd = C'D'; therefore, PROPOSITION XXXIX.— THEOREM. 126. Every point in the bisector o/ an angle is equally distant from the, sides of the...is unequally distant from the sides of the angle. 1st. Let AD be the bisector of the angle BA C, P any point in it, and PE, PF, the perpendicular distances...
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Wentworth & Hills's Exercise Manuals: Geometry, Issue 3

George Albert Wentworth - 1889 - 264 pages
...middle point of the IvaQ.^s" ^&- Theorem. Every p'oint in the bisector of an angle is equidistant from the sides of the angle, and every point not in the bisector is unequally distant from the sides. 70. Theorem. The line joining the middle points of two sides of...
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Exercise Manuals, Issue 3

George Albert Wentworth - 1889 - 276 pages
...through the middle point of the line. 69. Theorem. Every point in the bisector of an angle is equidistant from the sides of the angle, and every point not in the bisector is unequally distant from the sides. 70. Theorem. The line joining the middle points of two sides of...
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