OBSERVATIONAL GEOMETRY

BY

WILLIAM T. CAMPBELL, A.M.

INSTRUCTOR IN MATHEMATICS IN THE BOSTON LATIN SCHOOL

WITH AN INTRODUCTION BY

ANDREW W. PHILLIPS, PH.D.

PROFESSOR OF MATHEMATICS AND DEAN OF THE
GRADUATE SCHOOL, YALE UNIVERSITY

Edus T 148.99.

260

WARVARD COLLEGE LIBRARY
GIFT CF

GINN AND COMPANY
DEC. 20, 1923

THE PHILLIPS-LOOMIS MATHEMATICAL SERIES.

ELEMENTS OF GEOMETRY. By ANDREW W. PHILLIPS, Ph.D., and IRVING FISHER, Ph.D. Crown 8vo, Half Leather, $1 75. [By mail, $1 92.]

ABRIDGED GEOMETRY. By ANDREW W. PHILLIPS, Ph.D., and
IRVING FISHER, Ph.D. Crown 8vo, Half Leather, $1 25. [By
mail, $1 40.]

PLANE GEOMETRY. BY ANDREW W. PHILLIPS, Ph.D., and IRVING
FISHER, Ph.D. Crown 8vo, Cloth, 80 cents. [By mail, 90 cents.]
GEOMETRY OF SPACE. By ANDREW W. PHILLIPS, Ph.D., and
IRVING FISHER, Ph.D. Crown 8vo, Cloth, $1 25. [By mail, $1 35.]
OBSERVATIONAL GEOMETRY, BY WILLIAM T. Campbell, A.M.
Crown 8vo, Cloth.

ELEMENTS OF TRIGONOMETRY, Plane and Spherical. By
ANDREW W. PHILLIPS, Ph.D., and WENDELL M. STRONG, Ph.D., Yale
University. Crown 8vo, Cloth, 90 cents. [By mail, 98 cents.]
LOGARITHMIC AND TRIGONOMETRIC, TABLES. Five-Place
and Four-Place. By ANDREW W. PHILLIPS, Ph.D., and WENDELL
M. STRONG, Ph.D. Crown 8vo, Cloth, $1 00. [By mail, $1 08.]
TRIGONOMETRY AND TABLES. By ANDREW W. PHILLIPS,
Ph.D., and WENDELL M. STRONG, Ph.D. In One Volume. Crown
8vo, Half Leather, $1 40. [By mail, $1 54.]
LOGARITHMS OF NUMBERS.

Five-Figure Table to Accompany the "Elements of Geometry," by ANDREW W. PHILLIPS, Ph.D., and IRVING FISHER, Ph.D. Crown 8vo, Cloth, 30 cents. [By mail, 35 cents.]

NEW YORK AND LONDON:

HARPER & BROTHERS, PUBLISHERS.

Copyright, 1899, by HARPER & BROTHERS.

All rights reserved.

INTRODUCTION

CONTENTS

PAGE

vii

PART I

ELEMENTARY FORMS AND CONSTRUCTION OF MODELS.

SIMPLE EXPERIMENTS IN MENSURATION

Chapter I. The cube. Squares; right angles; construction of a dia-
gram; cutting out a diagram; horizontal surfaces; parallel
faces; vertical planes; a test of geometric equality; the three
dimensions in geometry; area of a square, volume of a cube.

II. A parallelopiped. Construction; description; quadrilat-

erals; straight lines and their measurement; area of a rect-

angle; volume of a parallelopiped; a practical experiment in

volumes

Construction; description; variety in prisms;

I

17

III. A prism.

triangles.

31

IV. Angles. Construction and measurement of angles with the

aid of a protractor

37

V. Construction of some plane figures. Triangles; sum of
the angles of a triangle; a right triangle; parallel lines; paral-
lelograms

45

VI. A truncated prism. Construction; description

VII. A pyramid.

area of a triangle; volume of a pyramid

VIII. A triangular pyramid. Construction; solid angles

IX. A pentagonal pyramid. Construction

Construction; description; diedral angles;

58

65

68

X. A hexagonal pyramid. Construction

70