A Treatise on Elementary Geometry: With Appendices Containing a Collection of Exercises for Students and an Introduction to Modern Geometry |
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ... William Chauvenet No preview available - 2016 |
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... William Chauvenet No preview available - 2015 |
Common terms and phrases
ABCD adjacent angles altitude anharmonic ratio apothem base bisects centre of similitude chord circumference circumscribed coincide common cone convex Corollary cylinder Definition denote diagonals diameter dicular diedral angle distance divided draw equally distant equilateral equivalent exterior angle faces figure find the locus fixed point frustum given circles given plane given point given straight line hence homologous indefinitely inscribed angle isosceles Let ABC measure middle point number of sides one-half opposite sides parallelogram parallelopiped perimeter perpen perpendicular plane MN plane passed polar pole polyedral angle polyedron prism PROPOSITION pyramid quadrilateral radical axis radii radius rectangle regular polygon respectively right angles right triangle Scholium secant segment similar sphere spherical polygon square straight line drawn straight line joining surface symmetrical tangent tetraedron theorem three given triangle ABC triedral vertex vertices volume
Popular passages
Page 19 - The perpendicular is the shortest line that can be drawn from a point to a straight line.
Page 79 - At a given point in a given straight line, to construct an angle equal to a given angle. Let A be the given point in the straight line AB, and O the given angle.
Page 216 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 348 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 254 - The angle of two arcs of great circles is equal to the angle of their planes, and is measured by the arc of a great circle described from its vertex as a pole and included between its sides (produced if necessary).
Page 269 - The shortest line that can be drawn on the surface of a sphere between two points is the arc of a great circle, not greater than a semicircumference, joining the two points.
Page 263 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Page 315 - Find the locus of a point such that the sum of the squares of its distances from two fixed points shall be equivalent to the square of the distance between the fixed points.
Page 262 - Each side of a spherical triangle is less than the sum of the other two sides.
Page 175 - The projection of a point on a plane is the foot of the perpendicular from the point to the plane. The projection of a figure upon a plane is the locus of the projections of all the points of the figure upon the plane. Thus, A'B' represents the projection of AB upon plane MN.