WeRead Powered by ReaderPub
Marks' first lessons in geometry / In two parts. Objectively presented, and designed for the use of primary classes in grammar schools, academies, etc. cover

Marks' first lessons in geometry / In two parts. Objectively presented, and designed for the use of primary classes in grammar schools, academies, etc.

Chapter 138: APPENDIX.
By Bernhard Marks
Open in WeRead

Explore more books like this:

MathematicsTeaching & Education

About This Book

This elementary geometry manual presents a structured course for primary and grammar school pupils, dividing instruction into a development section that introduces points, lines, angles, polygons, triangles, quadrilaterals, circles, and surface measurement using diagrams and guided exercises, and a second section that states axioms and illustrated theorems. Lessons include teacher notes for large classes or instructors with limited formal training, use repetition and review to reinforce concepts, and pose suggestive questions intended to strengthen reasoning alongside perceptive skills so students can continue geometric study independently.

APPENDIX.

Note A.—To those teachers who think that the line should be derived from a surface, and the surface from a solid, the author would say, that, according to his experience, children apprehend the ideas conveyed by the terms line and surface as readily as they do any ideas whatever; and that, therefore, there seems to be no necessity for extraordinary care in this case to avoid giving wrong impressions.

Still, if it be considered desirable in this manner to derive lines and surfaces, it will be apparent that all that can be done in the matter is to give such instruction only by way of a preliminary lesson.

Note B.—Crooked and curved lines are here treated of before straight lines, because the first two are defined by means of an affirmative property,—they do change direction; while the last is defined by means of the absence of one,—they do not change direction. It is easier for a child to comprehend what is than what is not.

Note C.—If the pupils are old enough, they may be shown that vertical lines cannot be parallel, but only seem so on account of their shortness and nearness to each other.

Note D.—This definition may be considered objectionable because rhomboid means like a rhomb. That the more general figure, the rhomboid, has been named from the more restricted one, the rhomb, is unfortunate, because it interferes with the symmetry of the nomenclature. The rhomb possesses all the properties of the rhomboid, and should, therefore, when these are considered, be called by the same name; its additional property entitles it to a name which should comprehend the other names. If the rectangle had been called a squaroid, the difficulty would have been repeated.

Note E.—If teachers consider it desirable, they may require the class to prove, by way of corollary, such propositions as assert the parallelism of the lines when the interior alternate angles are equal, when the opposite exterior and interior angles are equal, &c., in continuation of what has already been done.

OF THE
CONSTITUTION OF THE UNITED STATES
A CHART of 52 pages on one roller, designed to hang in Class-Rooms. An exposition of the Constitution; making it one of the most interesting as it is the most important study for our young men.
TOWNSEND’S ANALYSIS OF CIVIL GOVERNMENT.
a TEXT-BOOK to accompany the
CHART OF THE CONSTITUTION
WELLS’ SCIENTIFIC SERIES.
CONTAINING THE
LATEST RESEARCHES IN PHYSICAL SCIENCES,
AND THEIR
PRACTICAL APPLICATION TO EVERY-DAY LIFE.
Science of Common Things.
Natural Philosophy.
Principles of Chemistry.
First Principles of Geology.
GRAY’S BOTANICAL SERIES,
By ASA GRAY, Fisher Professor of Natural Science in Harvard University. The leading Botanist in America. They have no equal.
“How Plants Grow.”
Lessons in Botany.
Manual of Botany (New Edition).
Gray’s Lessons and Manual in 1 vol.
Gray’s Field, Forest and Garden Botany.
Gray’s School and Field Book of Botany.
[Consisting of Gray’s Lessons, and Field, Forest and Garden Botany, bound in 1 vol.]
Manual, with Mosses.
Structural and Systematic Botany.
BRYANT & STRATTON’S BOOK-KEEPING SERIES.
The best TEXT-BOOKS ever prepared on this subject.
Common School Edition.
High School Edition.
Counting-House Edition.
WILSON’S SCHOOL HISTORIES.
Primary American History.
History of the United States.
American History, School Edition.
Outlines of General History.
Parley’s Universal History.

TRANSCRIBER’S NOTES

  1. Moved advertisements from before title page to the end.
  2. Silently corrected typographical errors.
  3. Retained anachronistic and non-standard spellings as printed.