# A Treatise on Elementary Geometry: With Appendices Containing a Collection of Exercises for Students and an Introduction to Modern Geometry

J.B. Lippincott & Company, 1884 - 368 СЕКъДЕР

### тИ КщМЕ ОИ ВЯчСТЕР -сЩМТАНГ ЙЯИТИЙчР

дЕМ ЕМТОПъСАЛЕ ЙЯИТИЙщР СТИР СУМчХЕИР ТОПОХЕСъЕР.

### пЕЯИЕВЭЛЕМА

 INTRODUCTION 9 BOOK IV 126 BOOK V 142 GEOMETRY OF SPACE 171
 BOOK VIII 238 BOOK IX 271 INTRODUCTION TO MODERN GEOMETRY 883 335

### дГЛОЖИКч АПОСПэСЛАТА

сЕКъДА 338 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
сЕКъДА 106 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
сЕКъДА 120 - The area of a rectangle is equal to the product of its base and altitude.
сЕКъДА 189 - The lateral area of a prism is equal to the product of the perimeter of a right section of the prism by a lateral edge. Let AD...
сЕКъДА 19 - The perpendicular is the shortest line that can be drawn from a point to a straight line. Let PC be the perpendicular, and PD any oblique line, from the point P to the line AB. Then PC < PD. For, produce PC to P', making CP
сЕКъДА 206 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
сЕКъДА 79 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
сЕКъДА 244 - The angle of two arcs of great circles is equal to the angle of their planes, and is measured by the arc of a great circle described from its vertex as a pole and included between its sides (produced if necessary). Let AB and AB...
сЕКъДА 117 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.
сЕКъДА 253 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180╟ and less than 540╟. (gr). If A'B'C' is the polar triangle of ABC...