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The plan of grouping the fundamental theorems in each book, adopted in "Essentials of Plane Geometry" in this series, has been carried through to the work in solid geometry. In this way the basal propositions command the attention which they deserve. The other propositions are either indicated as subsidiary or are given in the Supplement, where they may be studied if time allows.

A new and important feature of this Supplement is the treatment of the practical mensuration of plane and solid figures along the lines recognized by the College Entrance Examination Board as furnishing valuable replacement material for some of the more formal work in Books VI-VIII. This feature satisfies a frequent demand for a modern type of training in spatial perception and supplements the logical presentation of the standard propositions.

Among the special features of the book may be mentioned the selection and arrangement of propositions, the simplicity of language and of proofs, the careful selection of real and interesting applications, the improvements made in the typography and illustrations in order to relieve eyestrain, and the emphasis secured through the framing of the diagrams.

My long and intimate association with my lamented colleague, George Wentworth, who, unfortunately, died before this book was undertaken, and the life-long influence of the sound principles established by his father, George A. Wentworth, have, I venture to hope, qualified me to write in the spirit which has made the mathematical textbooks bearing the Wentworth name of such inestimable service to more than one generation of teachers and students.

DAVID EUGENE SMITH

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SYMBOLS AND ABBREVIATIONS

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A",

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The following are the most important symbols used : plus

Z

angle minus

Δ

triangle X, times

rectangle *,),: divided by

parallelogram square root of

circle cube root of

st.

straight is equal to, equals, rt.

right is equivalent to A', A", A-prime, A-second, square of a

A-third, a3 cube of a

A1, A, A-one, A-two, and so on

A,

A-three, is greater than Ax.

axiom is less than

Post.

postulate therefore

Const. construction tends to

Def.

definition parallel

Cor.

corollary 1 perpendicular

Iden.

identical There is no generally accepted symbol for "is congruent to.” The sign = is commonly employed, the context telling whether equality, equivalence, identity, or congruence is to be understood ; but teachers often use 3, 5, or = for congruence, and - or for similarity. The symbol = is also used for identity, but is rarely needed in geometry. There is no generally accepted symbol for "arc.

arc.” Some teachers recommend using AB for "arc AB," and this symbol has certain advantages; the word "arc,” however, is so short that a symbol is hardly necessary.

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