 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 - Σελίδα 72των George Albert Wentworth - 1881Πλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | Edward Albert Bowser - 1890 - 420 σελίδες
...! to BC and passing through the mid. pt. of the J_ from A to BC. Proposition 4O. Theorem. 160. (1) Every point in the bisector of an angle is equally distant from the sides of the angle; and (2), conversely, even] point within an angle, and equally distant from its sides, is in the bisector... | |
 | Edward Albert Bowser - 1891 - 424 σελίδες
...and produce it to meet BC in E. Then Q is the mid. pt. of AE. (154) Proposition 4O. Theorem. 160. (1) Every point in the bisector of an angle is equally distant from the sides of the angle j and (2), conversely, evenI point within an angle, and equally distant from its sides, is in the bisector... | |
 | Seth Thayer Stewart - 1891 - 428 σελίδες
...following : 1. i. Parallel straight lines are everywhere equally distant. 2. Every point in the bisectrix of an angle is equally distant from the sides of the angle. 3. Two equal straight lines drawn from a point to a straight line make equal angles with that line.... | |
 | William Chauvenet - 1893 - 340 σελίδες
...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... | |
 | Seth Thayer Stewart - 1893 - 262 σελίδες
...the distances AD and В С are equal. (Or, simply by red. ad. abs.) 2. Every point in the bisectrix of an angle is equally distant from the sides of the angle. I. From any point in the bisectrix, let fall _Lsupon the sides. 2. The JS are equal, being corresponding... | |
 | George Albert Wentworth, George Anthony Hill - 1894 - 150 σελίδες
...construct a polygon similar to a given polygon. 6. To inscribe a regular decagon in a given circle. 7. Every point in the bisector of an angle is equally...is unequally distant from the sides of the angle. COLUMBIA COLLEGE, June, 1892. 1. Prove that, in any triangle, the greater side is opposite the greater... | |
 | George Clinton Shutts - 1894 - 412 σελίδες
...points without the _L from the extremities. § 88. 4. What is the required locus ? Ex. 68. Prove that every point in the bisector of an angle is equally distant from the sides of the angle. Suggestion: OM and ON are _L to AB and А С respectively. . § 131. Prove OM equal to О N. RECTILINEAR... | |
 | Webster Wells - 1894 - 394 σελίδες
...O. Then since O is in the bisector AD, it is equally distant from the sides AB and A C. [Any p'(int in the bisector of an angle is equally distant from the sides of the angle.] (§ 99.) In like manner, since O is in the bisector BE, it is equally distant from the sides ^4B and... | |
 | George D. Pettee - 1896 - 272 σελίδες
...B<2,AC<1 3 (preceding theorem), (contradicts hyp.) 38 PLANE GEOMETRY PROPOSITION XXIV 101. Theorem. Every point in the bisector of an angle is equally distant from the sides. Appl. Cons. Dem. B PC DB bisects ABC. Prove P = dist. from sides Draw PE and PF J- to sides of Z. rt.... | |
 | Frederick Harold Bailey - 1897 - 392 σελίδες
...bisector since it does not pass through the angle including the origin. We know by Plane Geometry that every point in the bisector of an angle is equally distant from the sides of the angle. Therefore, if (x, y) is any point of bisector (1), we have, by §32, x cos ^ -(- y sin 0.i — p i... | |
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