Bernhard Marks.

Marks' first lessons in geometry, objectively presented online

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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.

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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.
4. Enclosed italics font in _underscores_.







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Online LibraryBernhard MarksMarks' first lessons in geometry, objectively presented → online text (page 6 of 6)