# The Elements of Plane and Solid Geometry

Longmans, Green, and Company, 1872 - Geometry - 285 pages

### Contents

 On the Circle 16 MISCELLANEOUS PROPOSITIONS 58 ON ANGLES IN CIRCLES 68 ON THE CONTACT OF STRAIGHT LINES AND CIRCLES 77 ON LOCI CONNECTED WITH THE CIRCLE 90 BOOK III 96
 BOOK V 143 58 148 OF MAGNITUDES OF LIKE KINDS 168 BOOK VI 175 68 189 BOOK VII 242

### Popular passages

Page 101 - Through a given point to draw a straight line 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 line BC.
Page 285 - Price 31. 6d. On the STRENGTH of MATERIALS and STRUCTURES : the Strength of Materials as depending on their quality and as ascertained by Testing Apparatus ; the Strength of Structures, as depending on their form and arrangement, and on the materials of which they are composed. By Sir J.
Page 126 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 285 - Fcp. 8vo. , 41. 6d. INTRODUCTION TO THE STUDY OF INORGANIC CHEMISTRY. By WILLIAM ALLEN MILLER, MD, LL.D., FRS With 72 Illustrations.
Page 19 - If two triangles have two sides of the one equal to two sides of the other, each to each, and" have likewise their bases equal ; the angle which is contained by the two sides of the one shall be equal to the angle contained by the two sides equal to them, of the other.
Page 222 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R
Page 188 - If the angle of a triangle be divided into two equal angles, by a straight line which also cuts the base ; the segments of the base shall have the same ratio which the other sides of the triangle have to one another...
Page 285 - THEORY OF HEAT. By J. CLERK MAXWELL. MA, LL.D., Edin., FRSS., L. & E. With 38 Illustrations. Fcp. 8vo. , 41. 6d. PRACTICAL PHYSICS. By RT GLAZEBROOK. MA, FRS, and W. N. SHAW, MA * With 134 Illustrations. Fcp. 8vo. , 71. 6d. PRELIMINARY SURVEY AND ESTIMATES. By THEODORE GRAHAM GRIBBLE, Civil Engineer.
Page 204 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Page 30 - Any two angles of a triangle are together less than two right angles.