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EUCLID.

EUCLID,

BOOK I., PROPOSITIONS I. TO XXVI.

WITH EXERCISES ON EACH PROPOSITION,

AND ALTERNATIVE PROOFS FOR SOME OF THE

MORE DIFFICULT THEOREMS.

OBLIOTHER · MAY 1980 PODLE LACE

ETON : WILLIAMS AND SON.
LONDON: SIMPKIN, MARSHALL AND CO.

1877.

183. e. 55

LONDON : R. CLAY, SONS, AND TAYLOR, BREAD STREET HILL, E.C.

INTRODUCTION.

In commencing any new subject the student will generally find that he has first to learn the rules or the methods of notation which are peculiar to the subject on which he is entering : thus, in Arithmetic there are certain signs (such as those for addition, subtraction, &c.) which he has not used before ; and in Algebra there are besides these some others whose meaning he must know before he can attempt to proceed; so again in languages he finds there are rules and principles which come before him at the very outset, and in some cases even the alphabet or character in which the language is written is altogether new to him. This, then, which he has experienced in other branches of study, he will find also in Geometry; there are certain principles and explanations which must be understood before he can attain to any real comprehension of its object.

In Euclid's system of Geometry these elementary principles and explanations are arranged in three divisions :

(1) He gives first his DEFINITIONS ; as Plane Geometry treats of the relations and properties of lines and figures lying in one plane, the Definitions give descriptions of the various lines and figures fulfilling that condition :

(2) His next division consists of three POSTULATES, which are demands he makes as to constructions which he is entitled to assume; in them he takes it for granted that he may use a

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