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" B', B, or B" according as KD is less than, equal to, L FIG. 18. B'B B" AB FIG. 19. or greater than LB. In these three cases 2^D is greater than, equal to, or less than, 2ħB respectively. Hence: Each summit angle of an isosceles birectangular quadrilateral... "
Monographs on Topics of Modern Mathematics, Relevant to the Elementary Field - Page 111
edited by - 1911 - 416 pages
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...is also a right angle. This proposition may be extended thus : The vertical angle of a triangle is less than, equal to, or greater than a right angle, according as the square of the base is less than, equal to, or greater than the sum of the squares of the sides. For...
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Mathews' Euclid examination papers ... on Euc. i.-iv

Edward Harri Mathews - 1879 - 94 pages
...parallelogram if the diagonals bisect each other. j. Prove that the angle at the vertex of a triangle is less than, equal to, or greater than a right angle, according as the line joining the vertex to the middle point of the base is greater than, equal to, or less than half...
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Class lessons on Euclid

Marianne Nops - 1882 - 278 pages
...straight lines. How many such lines may be drawn ? 72. Prove that the angle at the vertex of a triangle is less than, equal to, or greater than a right angle according as the line joining the vertex to the middle point of the base is greater than, equal to, or less than half...
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Elementary Geometry: Plane

James McMahon - Geometry, Plane - 1903 - 380 pages
...to, or greater than, a right angle. Let ACB be an angle in the segment ABC. D To prove that ACB is less than, equal to, or greater than, a right angle, according as the arc ACB is greater than, equal to, or less than, a semicircle. Take the center O, and draw OA, OB....
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Monographs on Topics of Modern Mathematics, Relevant to the Elementary Field

Jacob William Albert Young - Mathematics - 1911 - 434 pages
...point D will fall at B', B, or B" according as KD is less than, equal to, L FIG. 18. B'B B" AB FIG. 19. or greater than LB. In these three cases 2^D is greater...however, the following theorem : In the Lobachevskian and Riemannian geometries, a summitangle of an isosceles birectangular quadrilateral cannot equal a right...
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The Elements of Non-Euclidean Plane Geometry and Trigonometry

Horatio Scott Carslaw - Geometry - 1916 - 193 pages
...the proof concisely : 1. In any triangle ABC in which the angle C is a right angle, the angle A is less than, equal to, or greater than a right angle, according as the segment BC is less than, equal to, or greater than JJ. Let P be the pole of the side AC. FIG. 90. Then...
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