Transcriber's Note:
The cover image was created by the transcriber and is placed in the public domain.
How it ever came to pass that Arithmetic should be taughtto the extent attained in the grammar schools of the civilizedworld, while Geometry is almost wholly excluded from them,is a problem for which the author of this little book hasoften sought a solution, but with only this result; viz., thatArithmetic, being considered an elementary branch, is includedin all systems of elementary instruction; but Geometry, beingregarded as a higher branch, is reserved for systems of advancededucation, and is, on that account, reached by but veryfew of the many who need it.
The error here is fundamental. Instead of teaching theelements of all branches, we teach elementary branches much tooexhaustively.
The elements of Geometry are much easier to learn, andare of more value when learned, than advanced Arithmetic;and, if a boy is to leave school with merely a grammar-schooleducation, he would be better prepared for the active duties oflife with a little Arithmetic and some Geometry, than withmore Arithmetic and no Geometry.
Thousands of boys are allowed to leave school at the ageof fourteen or sixteen years, and are sent into the carpenter-shop,the machine-shop, the mill-wright’s, or the surveyor’soffice, stuffed to repletion with Interest and Discount, but so4utterly ignorant of the merest elements of Geometry, that theycould not find the centre of a circle already described, if theirlives depended upon it.
Unthinking persons frequently assert that young childrenare incapable of reasoning, and that the truths of Geometryare too abstract in their nature to be apprehended by them.
To these objections, it may be answered, that any ordinarychild, five years of age, can deduce the conclusion of a syllogismif it understands the terms contained in the propositions;and that nothing can be more palpable to the mind of a childthan forms, magnitudes, and directions.
There are many teachers who imagine that the perceptivefaculties of children should be cultivated exclusively in earlyyouth, and that the reason should be addressed only at alater period.
...