(1) A Treatise on Plane Trigonometry (2) A Shorter Geometry (3) A New Geometry (4) Lessons in Geometry (5) Examples in Arithmetic (6) Solutions of the Examples in Godfrey and Siddons's Solid Geometry (7) A B C of Hydrodynamics (8) A New Algebra (9) A Treatise on the Analytical Geometry of Three Dimensions (10) Fergusson's Percentage Unit of Angular Measurement, with Logarithms; also a Description of his Percentage Theodolite and Percentage Compass (11) An Elementary Treatise on Statics

Nature ◽  
1912 ◽  
Vol 90 (2245) ◽  
pp. 275-277
Keyword(s):  
Three Dimensions ◽  
Angular Measurement ◽  
Analytical Geometry ◽  
Solid Geometry ◽  
Percentage Unit

Analytical Geometry of Three Dimensions

1934 ◽  
Vol 18 (231) ◽  
pp. 340
Author(s):  
H. W. Turnbull ◽  
D. M. Y. Sommerville
Keyword(s):  
Three Dimensions ◽  
Analytical Geometry

scholarly journals XII. On the Equations of Loci traced upon the Surface of the Sphere, as expressed by Spherical Co-ordinates

1834 ◽  
Vol 12 (1) ◽  
pp. 259-362
Author(s):  
Thomas Stephens Davies
Keyword(s):  
Three Dimensions ◽  
Orthogonal Projections ◽  
Analytical Geometry ◽  
Ground Plan ◽  
Modern System

The modern system of analytical geometry of three dimensions originated with Clairault, and received its final form from the hands of Monge. Descartes, it is true, had remarked, that the orthogonal projections of a curve anyhow situated in space, upon two given rectangular planes, determined the magnitude, species, and position of that curve; but this is, in fact, only an appropriation to scientific purposes of a principle which must have been employed from the earliest period of architectural delineation—the orthography and ichnography, or the ground-plan and section of the system of represented lines. Had Descartes, however, done more than make the suggestion—had he pointed out the particular aspect under which it could have been rendered available to geometrical research—had he furnished a suitable notation and methods of investigation—and, finally, had he given a few examples, calculated to render his analytical processes intelligible to other mathematicians;—then, indeed, this branch of science would have owed him deeper obligations than it can now be said to do.

ON THE COUPLER CURVE OF 3R2C LINKAGES

1998 ◽  
Vol 22 (3) ◽  
pp. 251-267
Author(s):  
H.S. Yan ◽  
W.H. Hsieh
Keyword(s):  
Algebraic Curve ◽  
Three Dimensions ◽  
Critical Properties ◽  
Dimensional Synthesis ◽  
Analytical Geometry ◽  
Loop Closure ◽  
Input And Output ◽  
Closure Equation

The purpose of this paper is to investigate the properties of the coupler curves generated by all 3R2C linkages. First, the 3x3 matrix with dual elements is used to derive the loop closure equation, the displacement equations are derived, and all joints variables are expressed in terms of input and output variables. Then, the parametric equations of the coupler curve are found by the D-H matrix. Finally, homogeneous coordinate is introduced to those displacement equations, and the order and some critical properties of the coupler curve are investigated based on the theories of algebraic curve and analytical geometry of three dimensions. In addition, RCRCR and RRCCR linkages are used as examples for illustration. Moreover, the results on the application of dimensional synthesis are discussed.

scholarly journals Classification of Geometries with Projective Metric

1909 ◽  
Vol 28 ◽  
pp. 25-41 ◽  
Author(s):  
D. M. Y. Sommerville
Keyword(s):  
Dihedral Angle ◽  
Plane Geometry ◽  
Three Dimensions ◽  
Angular Measurement ◽  
Plane Angle ◽  
Degenerate Form ◽  
Projective Metric ◽  
The Absolute ◽  
Straight Lines

In the Cayley-Klein projective metric it is ordinarily assumed that the measure of angles, plane and dihedral, is always elliptic, i.e. in a sheaf of planes or lines there is no actual plane or line which makes an infinite angle with the others. With this restriction there are only three kinds of geometry—Parabolic, Hyperbolic and Elliptic, i.e. the geometries of Euclid, Lobachevskij and Riemann ; and the form of the absolute is also limited. Thus in plane geometry the only degenerate form of the absolute which is possible is two coincident straight lines and a pair of imaginary points ; in three dimensions the absolute cannot be a ruled quadric, other than two coincident planes. If, however, this restriction as to angular measurement is removed, there are 9 systems of plane geometry and 27 in three dimensions; for the measure of distance, plane angle and dihedral angle may be parabolic, hyperbolic, or elliptic.

Network Theory—An Enrichment Topic

1974 ◽  
Vol 67 (2) ◽  
pp. 175-178
Author(s):  
Charles A. Reeves
Keyword(s):  
High School ◽  
Network Theory ◽  
Two Dimensions ◽  
Three Dimensions ◽  
High School Geometry ◽  
Solid Geometry ◽  
School Geometry

The last decade has ushered in numerous changes in the teaching of high school geometry—changes due primarily to the impetus of curriculum committees such as the Commission on Mathematics. One trend is that of integrating plane and solid geometry “topicwise” into one course; that is, as each topic is studied in two dimensions, the concept is immediately extended to three dimensions if possible. This pedagogical technique undoubtedly helps students grasp related ideas more readily than if those ideas were presented as separate entities.

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