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SECOND LESSONS IN GEOMETRY,
IN THE ORDER OF
SIMSON'S AND PLAYFAIR'S EDITIONS
ADAPTED TO THE USE OF
ADVANCED LEARNERS AND PRIVATE STUDENTS.
BY D. M'CURDY,
AUTHOR OF THE "CHART OF GEOMETRY" AND "FIRST LESSONS."
COLLINS, BROTHER & CO.,
NO. 254 PEARL STREET.
Entered, according to Act of Congress, in the year 1846,
In the Clerk's Office of the District Court of the Southern District of New York.
STEREOTYPED BY BURNS & BANER, 11 SPRUCE-ST.
To bring the Elements of Geometry into general use, is the design of this volume, and of the "Chart of Geometry" and "First Lessons" which precede it.
There was once a competition between certain persons to be the first who should see the risen sun; and the prize was awarded to him who turned his face westward: because there the sun's effects were first discovered, in gilding towers, and battlements, and the mountain's brow. To ascertain the existence of geometry by its effects, let us turn from books to the community, and the obvious defect will meet us in every department of life. Few citizens know what these things mean, or what their use.
A question then arises, "Should this be so?" The regrets of thousands prove the contrary. The learning to read and write is a mere preparation to receive instruction after which, the learner should take hold of the properties of things, and examine them in detail, beginning with the most general, and therefore the most useful. But are there any properties more general than those of magnitude, figure, and motion? There are none: the attribute of number itself is not more general, and it is certainly less expedient as a branch of study. The cherished motto, "A place for everything," evinces the necessity of geometry in all the schools. The magnitude and figure of everything, and of the space to contain it, as well as the law of motion and the momentum of force which conveys it to the place, are certainly more worthy of consideration than the mere fact that it counts one.
It is obvious from the perfection in which the elements of geometry have been handed down to us, that the Greeks taught these elements in all their schools; that geometry was to them what arithmetic has been to us, namely, the groundwork of public instruction. See, then, the effects of this practice in their works of art, their architecture, their sculpture, their literature, their philosophy, the spread of their language, the respect paid to them by the Romans after the conquest of Macedonia. The advantages of a right education to a people are incalculable.