Introductory modern geometry of point, ray, and circle Volume 1

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1892 Excerpt: ...and one bisects an angle of the parallelogram. 36. From any point in the base of an isosceles A parallels are drawn to the sides; the parallelogram so formed has a constant perimeter (= measure round = sum of sides). 37. The sum of the distances of any point on the base of an isosceles A from the sides is constant. 38. The sum of the distaaces of any point within a regular A from the sides is constant.--What if the point be without the A? 39. P is on a mid-ray of the angle A in the A ABC; compare the difference of PB and PC: when P is within the A, and when P is without. 40. The inner mid-ray of one angle of a A and the outer mid-ray of another form an angle that is half the third angle of the A. 41. O is the orthocentre of the A ABC; express the angles A OB, BOC, CO A, through the angles A, B, C. 42. Do the like for the circum-centre.Sand the in-centre / 43. The medial to the hypotenuse of a right A equals one-half of that hypotenuse. 44. The mid-rays of two adjacent angles of a parallelogram are normal to each other. 45. In a 5-pointed star the sum of the angles at the points is a straight angle. What is the sum in a 7-pointed star? 46. Parallels are drawn to the sides of a regular A, trisecting the sides; what figures result? 47. A side of a A is cut into 8 equal parts, through each section point parallels are drawn to the other sides; how are the other sides cut and what figures result? 48. Two A are congruent when they have two mid-tracts of two corresponding angles equal, and besides have equal (1) these angles and a pair of the including sides; or (-2) two pairs of corresponding angles; or (3) one pair of corresponding angles and the corresponding angles of the mid-tract with the opposite side; or (4) one pair of including sides and the adjacent segm...