London, 1905

The present work was first published under the title First Book of Geometry, in 1905, at London. A translation into German was published at Leipzig in 1908, under the title Der Kleine Geometer. A translation into Hebrew was published in Dresden, in 1921. The present Edition, published at Bronx, N.Y. [by Chelsea Publishing Company, 1970, under the title Beginner's Book of Geometry] is textually the same as the original edition, except for the correction of errata.

Preface (excerpts)

The study of Geometry at the secondary and primary schools suffers considerably from the fact that the scholars have not previously acquired the habit of geometrical observation. What training they have had, has, for the most part, checked, and not encouraged, the natural practice of thinking in three dimensions. In a certain sense Plane Geometry is more abstract than three-dimensional, or so-called Solid Geometry. It is best taught from the outset as a part of a more natural system. One of the reasons why Plane Geometry has for some many centuries maintained its position as an independent and preliminary course of study is probably because of the didactic value of the method of drawing plane diagrams on paper, or on the blackboard, or their equivalents. This method has the following advantages:—

- It requires no special apparatus:
- It is easy to teach and to grasp, and only requires care and practice;
- The diagrams can be reproduced as often as necessary, so that the scholar, in acquiring the necessary dexterity, becomes at the same time familiar with the truths which the diagrams represent.

....

The bar in the way of the proper development of geometrical insight has been the want of a method to take the place of drawing in Plane Geometry. The drawing of solid figures is too difficult. Modelling, confined for the most part to cardboard modelling, suffers from the same defect; it is also cumbrous, comparatively expensive , and requires constant supervision. Paper *ad lib.*, a pencil and pins, even scissors, any small child may and can always have, but not paste, cardboard or a knife. The methods adopted in the present little book demand no apparatus except paper, occasionally a few pins, and a pencil, and a pair of scissors; the latter indeed can almost always be dispensed with. The models and diagrams which are made with these simple appliances, are, when well-made, accurate and durable. Those made by a child at first will, of course, be imperfect, but he can make them for himself, and he may make them as often as he pleases; as he does so, he acquires not only manual dexterity, but complete familiarity with the truths which each model is meant to represent. Just because he can do this *by himself*, he is not taught, but learns, and he develops what may be called his geometrical sense.

This is the keynote of the present little volume. It is not a text-book to be learnt. It is hoped that it may be a help to the teacher, or to the grown-up person, whoever it is, who wishes to guide and help and not simply to teach. Still more it is meant for the child himself, hence the large number of diagrams. There will be much in the book that will at first seem difficult; much that may be and will be omitted as first, but perhaps digested on a second reading. The book is meant to aid the child to achieve things, and to acquire ideas which will not be uninteresting at the time, and will be subsequently invaluable.

....

To sum up, the main features of the present book may be put as follows:— 1. The presentation of the primary geometrical ideas; 2. The presentation in a graphical form of the primary geometrical theorems; 3. The development of practical methods requiring (a) no special apparatus, (b) no special supervision, (c) no serious expenditure of trouble, or money, for arriving at familiarity with plane and solid objects, and the relations determining their positions and their forms.

**Table of Contents**

- Preliminary Notions
- The Straight Line
- The Plane
- The Cylinder and Cone
- Division of the Plane by a Straight Line
- Angles
- Equal, Greater, Less
- The Circle
- Division of a Straight Line
- Equality of Angles
- Division of Angles
- Comparison of Unequal Angles
- Perpendicularity
- The Rhombus
- The Square
- The Cube
- The Rectangle
- Perpendicularity
- The Isosceles Triangle
- The Equilateral Triangles
- The Regular Hexagon
- The Right-Angled Isosceles Triangle
- The Corner Tetrahedron
- The Triangle
- Congruent Triangles
- Parallel Lines
- Parallel Planes
- The Regular Octahedron
- Properties of a Pair of Parallel Lines
- The Right-Angled Triangle
- Area of a Right-Angled Triangle and a Rectangle
- The Theorem of Pythagoras
- Parallelograms
- Conjugate Triangles
- Isogonal Conjugate Lines

General Index