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Page ix
Charles William Hackley. Theory of perpendiculars to planes 66 66 Page 4 8 12 • 14 parallel planes and lines perpendicular planes . Exercises upon planes Definitions . POLYHEDRAL ANGLES . Relations of the plane angles of polyhedral ...
Charles William Hackley. Theory of perpendiculars to planes 66 66 Page 4 8 12 • 14 parallel planes and lines perpendicular planes . Exercises upon planes Definitions . POLYHEDRAL ANGLES . Relations of the plane angles of polyhedral ...
Page 1
Charles William Hackley. GEOMETRY OF PLANES . * DEFINITIONS . 1. THE angle formed by two lines not in the same plane is the angle formed by one of them with a line drawn through any point of it parallel to the other . 2. A plane is a ...
Charles William Hackley. GEOMETRY OF PLANES . * DEFINITIONS . 1. THE angle formed by two lines not in the same plane is the angle formed by one of them with a line drawn through any point of it parallel to the other . 2. A plane is a ...
Page 2
... planes are parallel to each other when they can not meet , to whatever distance both be pro- duced . 8. A plane is ... planes are represented in their rela- tive position not accurately , but by a sort of perspec- tive . PROP . I. A ...
... planes are parallel to each other when they can not meet , to whatever distance both be pro- duced . 8. A plane is ... planes are represented in their rela- tive position not accurately , but by a sort of perspec- tive . PROP . I. A ...
Page 3
... Parallel straight lines are in the same plane , and , by the first case , one plane only can be drawn through either of them , and a point assumed in the other . Cor . Hence the position of a plane is determined GEOMETRY OF PLANES . 3.
... Parallel straight lines are in the same plane , and , by the first case , one plane only can be drawn through either of them , and a point assumed in the other . Cor . Hence the position of a plane is determined GEOMETRY OF PLANES . 3.
Page 7
... parallel to GH , would form a right angle . In like manner , PG and QK , which represent any two straight lines not situated in the same plane , are considered to form with each other the same angle which PG would make with any parallel ...
... parallel to GH , would form a right angle . In like manner , PG and QK , which represent any two straight lines not situated in the same plane , are considered to form with each other the same angle which PG would make with any parallel ...
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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.