Elementary Course of Geometry ...Harper & brothers, 1847 - 103 páginas |
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Página vii
... circle 40 66 tangents to a circle 42 Measures of angles in various positions in a circle 43 Theorems relating to secants of a circle 45 Equiangular triangles 47 Exercises upon the preceding theorems 47 49 Numerical problems Definitions ...
... circle 40 66 tangents to a circle 42 Measures of angles in various positions in a circle 43 Theorems relating to secants of a circle 45 Equiangular triangles 47 Exercises upon the preceding theorems 47 49 Numerical problems Definitions ...
Página viii
... circles Ratios of the elements of a circle Area of the circle Exercises upon the circle Page · 60 62 65 67 69 . 70 71 PROBLEMS IN PLANE GEOMETRY . Problems relating to perpendiculars . . 74 66 66 to the division and construction of ...
... circles Ratios of the elements of a circle Area of the circle Exercises upon the circle Page · 60 62 65 67 69 . 70 71 PROBLEMS IN PLANE GEOMETRY . Problems relating to perpendiculars . . 74 66 66 to the division and construction of ...
Página ix
... circles Tangent plane to the sphere Various measures of spherical angles . Polar or supplemental triangles 4 6 8 8 9 • 9 • 12 13 • 13 16 18 19 2 7 8 9 11 Relations of the sides and angles of spherical triangles Theorems relating to the ...
... circles Tangent plane to the sphere Various measures of spherical angles . Polar or supplemental triangles 4 6 8 8 9 • 9 • 12 13 • 13 16 18 19 2 7 8 9 11 Relations of the sides and angles of spherical triangles Theorems relating to the ...
Página x
... irregular polygon , and example Of a regular polygon Examples and table . Demonstration of the ratio of the circumference of a circle to its diameter 4 12231 1669 5 5 7 00 8 Examples . To find the length of an arc , X CONTENTS .
... irregular polygon , and example Of a regular polygon Examples and table . Demonstration of the ratio of the circumference of a circle to its diameter 4 12231 1669 5 5 7 00 8 Examples . To find the length of an arc , X CONTENTS .
Página xi
... circle , and examples segment of a circle , and examples 66 Table of areas of segments Area of long irregular figures Examples . Page 9 10 10 11 11 12 12 14 14 15 MENSURATION OF SOLIDS . Superficies of a prism 1 Examples . . Superficies ...
... circle , and examples segment of a circle , and examples 66 Table of areas of segments Area of long irregular figures Examples . Page 9 10 10 11 11 12 12 14 14 15 MENSURATION OF SOLIDS . Superficies of a prism 1 Examples . . Superficies ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 70 - The areas or spaces of circles are to each other as the squares of their diameters, or of their radii.
Página 50 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.