uKsm J(MJi^^t^mmigtiM ^wie^im» i>mti PLANED SOLID GEOMETRY SLAUGHT AND MMjHi »w«Bi*Mii^a i<««a *'' ^M*'»w«'M'flt^ (!}arnell Hititteratty ffitbrarij Cornell University Library arV19325 Plane and solid geometry 3 1924 031 226 263 olin.anx Cornell University Library The original of tliis book is in tlie Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924031226263 [...]... formed by two rays proceeding The point is the vertex of the angle and the rays are its The angle formed by two rays sides said to be the angle between is — ^='*™'^ them or simply siai" their angle Two line-segments having a common end-point also form an angle, namely, the angle of the rays on which the segments lie An angle is determined entirely by the relative directions of its rays and not by the... circle Any two portion of a circle lying between of its points Evidently Any u plane is called an arc all radii of the same circle are equal combination of points, segments, is lines, or curves in called a plane geometric figure Plane Geometry deals with plane geometric figures EXERCISES 13 1 How many end-points has a straight line? How many How many lias a ray ? A circle? has a line-scgmont? 2 Can you... of § 4 Historical Note The Egyptians appear to have been the first people to accumulate any considerable body of exact geometrical The building of the great pyramids (before 3000 b.c.) reknowledge of geometric relations They also used geometry in surveying land Thus it is known that Eameses II (about 1400 B.C.) appointed surveyors to measure the amount of land washed away by the Nile, so that the taxes... can you say of them throughout their whole length ? Do you know of any lines other than straight lines of which this must be true ? 6 How differ in 7 by A do the material points and lines made by crayon or pencil magnitude from the ideal points and lines of geometry ? machine has been made which rules 20,000 side within the space of one inch Do distinct lines side such lines have width ? Are they geometrical... its The two rays lie in Z'd, read, A the same straight line and ex- tend from the same end-point in opposite directions they are said to form a straight angle tion, If they extend in the same direc- they coincide and form a zero angle ^ | S'de 'f side — PLANE GEOMETRY 8 17 An angle turning about Thus Z BA C is from the position rotating ray is may its be thought of as generated by a ray end-point as... make whether or not they are equal? a right angle ? PLANE GEOMETRY 10 AC Suppose that in the figure the ray 3 A point from the position takes place in Zl? What more than one position In this way it may of AB rotates AD about the What change Z2? Can there be which Z 1 = Z 2 ? in ^C to the position q for be made clear that any angle has one and only one bisector jy BD g -^^ A 4 How many 5 Pick out three... simply equal if they have the same size or magnitude This is denoted by the symbol =, read is equivalent Two to or fig-urets is equal to may be throughout are said to be congruent ^, read is so This placed is congruent r i I without changing the sliape or they assumed that figures are said to be similar if they same shape similar at as I if , , size of either, I I to coincide denoted by the symbol... Definitions of Chapter Pyramids and Cones Definitions Summary 317 324 Measurement of the Surface and Volume Problems and Applications Theorems on Projection Projection of a Plane Segment Summary of Chapter IX Problems and Application 312 320 Definitions Cylinders of a Cone 362 369 Regular and Similar Polyhedrons Regular Polyhedrons 378 Inscription of Regular Polyhedrons 377 380 Similar Polyhedrons Applications... not based on the formal theory of limits It is believed that for high school pupils the notion of a limit studied as a process of approximation, and that the best preparation for the later understanding of the theory is by a preliminary study of what is meant by " approaches," such as is best is given in Chapters III and IV The important features by which the Solid Geometry seeks accomplish the two main... CONTENTS Similar Polygons Computations by Means of Sines of Angles Problems of Construction Summary of Chapter III Problems and Applications 136 140 145 Chapter IV PAGE 124 146 Areas of Polygons Areas of Rectangles Areas of Polygons Problems of Construction Summary of Chapter IV Problems and Applications 1.54 156 166 169 170 Chapter V Regular Polygons and Circles Regular Polygons 176 Problems and . often study and recite definitions and theorems without really comprehend- ing their meaning. It is sought to check this tendency by giving definitions only when tlioy are to be used, and by imme- diately verifying. later understanding of the theory is by a preliminary study of what is meant by " approaches," such as is given in Chapters III and IV. The important features by which the Solid Geometry seeks to accomplish the two main purposes stated. the essential facts of elementary geometry as properties of the space in which they live, and not merely as statements in a book. The important features by which the Plane Geometry seeks to accomplish