Elementary Course of Geometry ...Harper & brothers, 1847 - 103 Seiten |
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Seite ix
... perpendicular planes . Exercises upon planes Definitions . POLYHEDRAL ANGLES . Relations of the plane angles of polyhedral angles 66 66 diedral angles • 1 1 3 5 • 7 Symmetry in polyhedral angles . Exercises upon polyhedral angles ...
... perpendicular planes . Exercises upon planes Definitions . POLYHEDRAL ANGLES . Relations of the plane angles of polyhedral angles 66 66 diedral angles • 1 1 3 5 • 7 Symmetry in polyhedral angles . Exercises upon polyhedral angles ...
Seite 1
... in the unrestricted sense of the term , form one and the same straight line . Or , when two parallel lines coincide , they become one and the same straight line . A 9. One line is Perpendicular to an- other when the Definitions.
... in the unrestricted sense of the term , form one and the same straight line . Or , when two parallel lines coincide , they become one and the same straight line . A 9. One line is Perpendicular to an- other when the Definitions.
Seite 2
... perpendicular to another . Or , when the angles on either side of one line meeting another are equal , they are right angles . 13. Oblique Angles are either Acute or Obtuse . 14. An Acute Angle is less than a right angle . 15. An Obtuse ...
... perpendicular to another . Or , when the angles on either side of one line meeting another are equal , they are right angles . 13. Oblique Angles are either Acute or Obtuse . 14. An Acute Angle is less than a right angle . 15. An Obtuse ...
Seite 7
... points of the former are placed in the sides of the lat- ter . 61. A Secant is a line that cuts a cir- cle , lying partly within and partly with- out it . & 62. The Altitude of a triangle is a perpendicular let DEFINITIONS .
... points of the former are placed in the sides of the lat- ter . 61. A Secant is a line that cuts a cir- cle , lying partly within and partly with- out it . & 62. The Altitude of a triangle is a perpendicular let DEFINITIONS .
Seite 8
... Perpendicular . 64. The altitude of a parallelogram or trapezoid is the perpendicular dis- tance between the parallel sides . The bases of a trapezoid are the par- allel sides . 65. Two triangles , or other right - lined figures , are ...
... Perpendicular . 64. The altitude of a parallelogram or trapezoid is the perpendicular dis- tance between the parallel sides . The bases of a trapezoid are the par- allel sides . 65. Two triangles , or other right - lined figures , are ...
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Häufige Begriffe und Wortgruppen
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
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Seite 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.
Seite 70 - The areas or spaces of circles are to each other as the squares of their diameters, or of their radii.
Seite 50 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.