« ForrigeFortsett »
AUTHOR OF A SERIES OF TEXT-BOOKS IN MATHEMATICS
BOSTON, U.S.A., AND LONDON
Entered, according to Act of Congress, in the year 1896, by
G. A. WENTWORTH, in the Office of the Librarian of Congress, at Washington.
This pamphlet contains the enunciations of the propositions and corollaries of the author's text-book in Geometry, numbered as they are in the text-book.
The Syllabus is not designed to take the place of the Geometry, but it can be used with great advantage in the recitation room, especially in connection with the author's pamphlet of Geometrical Exercises.
G. A. WENTWORTH. EXETER, N. H.
66. A proof or demonstration is a course of reasoning by which the truth or falsity of any statement is logically established.
67. A theorem is a statement to be proved.
68. A theorem consists of two parts: the hypothesis, or that which is assumed; and the conclusion, or that which is asserted to follow from the hypothesis.
69. An axiom is a statement the truth of which is admitted without proof.
70. A construction is a graphical representation of a geometrical figure.
71. A problem is a question to be solved. 72. The solution of a problem consists of four parts:
(1) The analysis, or course of thought by which the construction of the required figure is discovered ;
(2) The construction of the figure with the aid of ruler and compasses ;
(3) The proof that the figure satisfies all the given conditions ;
(4) The discussion of the limitations, which often exist, within which the solution is possible.
73. A postulate is a construction admitted to be possible.
74. A proposition is a general term for either a theorem or a problem,