Describes how many of the geometrical and physical properties of the binary elastic collision of two particles can be represented by an isoceles trapezoid in the velocity space. (BB)

An activity is presented which involves making a stadia tube from a cardboard mailing tube and using it to measure horizontal and vertical distances using the properties of similar triangles. (MN)

The use of basis matrix methods to rotate axes is detailed. It is felt that persons who have need to rotate axes often will find that the matrix method saves considerable work. One drawback is that most students first learning to rotate axes will not yet have studied linear algebra. (MP)

Some ways of thinking and acting geometrically are described which are related to the approach used by ancient humans. The focus is on intuitive geometric imagery, an attempt to resurrect a way of describing possible viewpoints of geometry outside of those commonly accepted. (MP)

Activities designed to lead pupils through the process of using the basic measuring and drawing devices of geometry are presented and move to the discovery of several surprising generalizations about arbitrary triangles. (MP)

Describes an activity in which students observe a simple situation, explore conjectures, and generate conclusions from their exploration of the conjectures to develop the essential triangle-congruence theorems. Includes teacher's guide. (KHR)

Presents Heron's original geometric proof to his formula to calculate the area of a triangle. Attempts to improve on this proof by supplying a chain of reasoning that leads quickly from premises to the conclusion. (MDH)

This textbook commences with a brief sketch of the history of Elementary Geometry. The definitions throughout have been somewhat amplified, and several notes have been added which it is hoped may be found useful and suggestive. The subject of Ratio has been expanded; a few new propositions have been added; and there is a considerable collection of…

This textbook is designed to be used in a geometry course incorporating the writings of Euclid. The object of this edition now offered to the public, is not so much to give the writings of Euclid the form which they originally had, as that which may at present render them most useful. The author believes that the use of algebraic signs and…

This textbook covers the first six books of the elements of Euclid, the 11th and 12th books, and the book of Euclid's data. Elements of plane and spherical trigonometry are included.

This textbook is a course in surveying. Geometry, land surveying, chain surveying, plain-table surveying, theodolite surveying, hilly-ground surveying, laying out land, division of land, and levelling are covered.

This textbook covers geometry and trigonometry with addition of a fuller explanation of rectangular surveying, as well as a more particular explanation of the use of natural sines. The book's primary goal is teaching common field surveying. This edition adds practical matter, as well as the only table of natural tangents ever published in this…

The impossibility of a trapezoid having the sum of two adjacent sides equal to the sum of the remaining two sides is proved. (DT)

Develops a model of a non-Euclidean geometry and relates this to the metric approach to Euclidean geometry. (JG)