Elementary Course of Geometry ...Harper & brothers, 1847 - 103 páginas |
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Página vii
... 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 RATIOS AND ...
... 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 RATIOS AND ...
Página viii
... tangents · 83 84 · 88 66 66 similar figures 92 General note upon the method of solution of problems Miscellaneous exercises in plane geometry 93 100 Of triangles APPENDIX I. ISO PERIMETRY . Of polygons Of plane figures Centers of ...
... tangents · 83 84 · 88 66 66 similar figures 92 General note upon the method of solution of problems Miscellaneous exercises in plane geometry 93 100 Of triangles APPENDIX I. ISO PERIMETRY . Of polygons Of plane figures Centers of ...
Página ix
... Tangent planes to cylinders , and development of their surface Ratios of similar prisms and cylinders Propositions relating to sections of pyramids and cones Relations of pyramids and prisms Tangent planes to cones , and development of ...
... Tangent planes to cylinders , and development of their surface Ratios of similar prisms and cylinders Propositions relating to sections of pyramids and cones Relations of pyramids and prisms Tangent planes to cones , and development of ...
Página 6
... Tangent Exter- nally , Tangent Internally , or , finally , the two circum- ferences may intersect . 52. An Angle in a Segment is that which is contained by two lines , drawn from any point in the arc of the segment , to the two ...
... Tangent Exter- nally , Tangent Internally , or , finally , the two circum- ferences may intersect . 52. An Angle in a Segment is that which is contained by two lines , drawn from any point in the arc of the segment , to the two ...
Página 7
... Tangent to a circle , or touches it , when it has but one point in common with the circle . 57. Two circles Touch each other when they have but one point common , or when they have a common tangent . 58. A right - lined figure is ...
... Tangent to a circle , or touches it , when it has but one point in common with the circle . 57. Two circles Touch each other when they have but one point common , or when they have a common tangent . 58. A right - lined figure is ...
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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.