Elementary Course of Geometry ... |
From inside the book
Results 1-5 of 25
Page viii
... axes of symmetry . Of diameters Center of mean distances Centers of similitude 66 66 APPENDIX II . in circles Radical axis and radical center Conjugate points , poles , and polar lines Definitions GEOMETRY OF PLANES . Sections of planes ...
... axes of symmetry . Of diameters Center of mean distances Centers of similitude 66 66 APPENDIX II . in circles Radical axis and radical center Conjugate points , poles , and polar lines Definitions GEOMETRY OF PLANES . Sections of planes ...
Page x
... axis with reference to a plane Diametral planes Center of mean distances Of centers of similitude Centers of similitude of spheres . · REGULAR POLYHEDRONS . Proof that there can be but five Construction of the regular tetrahedron 66 64 ...
... axis with reference to a plane Diametral planes Center of mean distances Of centers of similitude Centers of similitude of spheres . · REGULAR POLYHEDRONS . Proof that there can be but five Construction of the regular tetrahedron 66 64 ...
Page 96
... axis , to find a third point such that the line drawn from this third point to the first shall meet the given axis at equal dis- tances from the second and third points . Solution . The geometric locus which resolves this problem is a ...
... axis , to find a third point such that the line drawn from this third point to the first shall meet the given axis at equal dis- tances from the second and third points . Solution . The geometric locus which resolves this problem is a ...
Page 1
... AXES OF SYMMETRY . Two polygons , or portions of one polygon , are said to be symmet- rical with respect to a line when ... axis of symmetry . Theorem 2. Prove that the isosceles trapezoid may be inscribed in a circle . General Theorem ...
... AXES OF SYMMETRY . Two polygons , or portions of one polygon , are said to be symmet- rical with respect to a line when ... axis of symmetry . Theorem 2. Prove that the isosceles trapezoid may be inscribed in a circle . General Theorem ...
Page 5
... AXIS AND RADICAL CENTER . Definitions . A radical axis of two circles is the locus of points from each of which equal tangents can be drawn to the two circles . Construction . Divide the line joining the centers of the two circles in ...
... AXIS AND RADICAL CENTER . Definitions . A radical axis of two circles is the locus of points from each of which equal tangents can be drawn to the two circles . Construction . Divide the line joining the centers of the two circles in ...
Other editions - View all
Common terms and phrases
ABCD altitude angles equal axis bisect center of similitude chord circumference cone consequently construct cylinder diagonal diameter dicular divided draw equal angles equal bases equal distances equiangular equilateral triangle figure find a point find the area frustum geometric locus given angle given circle given line given point given triangle gles Hence hypothenuse indeterminate problems inscribed intersection isosceles isosceles triangle Let ABC line drawn line joining locus which resolves measured meet parallel planes parallelogram pendicular pentagon perimeter perpen perpendicular plane angles plane XZ polygon polyhedral angle polyhedrons prism Prob Prop proportional Prove pyramid radical axis radii radius ratio rectangle regular polygon regular polyhedrons resolves this problem rhombus right line right-angled triangle Scholium segment semicircle side AC similar Solution sphere spherical polygon spherical triangle straight line surface symmetric tangent tetrahedrons triangle ABC trihedral angles vertex
Popular passages
Page 33 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle.
Page 70 - The areas or spaces of circles are to each other as the squares of their diameters, or of their radii.
Page 50 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Page 50 - Four quantities are said to be proportional when the ratio of the first to the second is the same as the ratio of the third to the fourth.
Page 60 - Carol. 4. Parallelograms, or triangles, having an angle in each equal, are in proportion to each other as the rectangles of the sides which are about these equal angles. THEOREM LXXXII. IF a line be drawn in a triangle parallel to one of its sides, it will cut the other two sides proportionally.
Page 23 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 1 - A straight line is said to be perpendicular to a plane when it is perpendicular to every straight line which passes through its foot in that plane, and the plane is said to be perpendicular to the line.
Page 51 - Proportion, when the ratio is the same between every two adjacent terms, viz. when the first is to the second, as the second to the third, as the third to the fourth, as the fourth to the fifth, and so on, all in the same common ratio.
Page 5 - ... 07958 in using the circumferences j then taking one-third of the product, to multiply by the length, for the content. Ex. 1. To find the number of solid feet in a piece of timber, whose bases are squares, each side of the greater end being 15 inches, and each side of the less end 6 inches ; also, the length or perpendicular altitude 2-1 feet.
Page 2 - What is the upright surface of a triangular pyramid, the slant height being 20 feet, and each side of the base 3 feet ? • Ans.