New Elementary Geometry: With Practical Applications : a Shorter Course Upon the Basis of the Larger WorkRobert S. Davis & Company, 1874 - 176 páginas |
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Página 141
... sphere is any section made by a plane not passing through the center . A Plane is Tangent to a sphere , when it meets the sphere in but one point , however far it may be produced . 331. A Spherical Polygon is a portion of the surface of a ...
... sphere is any section made by a plane not passing through the center . A Plane is Tangent to a sphere , when it meets the sphere in but one point , however far it may be produced . 331. A Spherical Polygon is a portion of the surface of a ...
Página 142
... spherical polygon intercepted by the same planes . 337. The cylinder , cone , and sphere are termed the Three Round Bodies of Elementary Geometry . THEOREM I. 338. The convex surface of a cylinder is equal to the circumference of its ...
... spherical polygon intercepted by the same planes . 337. The cylinder , cone , and sphere are termed the Three Round Bodies of Elementary Geometry . THEOREM I. 338. The convex surface of a cylinder is equal to the circumference of its ...
Página 149
... sphere , its radius will be the radius of the sphere ; hence all great circles are equal . 355. Cor . 2. Two great circles always bisect each other . For , since the two circles have the same center , their common intersection , passing ...
... sphere , its radius will be the radius of the sphere ; hence all great circles are equal . 355. Cor . 2. Two great circles always bisect each other . For , since the two circles have the same center , their common intersection , passing ...
Página 150
... sphere is equal to the product of its diameter by the circumference of a great circle . Let A B C D E F be a semicircle in which is inscribed any regular semi - polygon ; from the center , O , draw OI perpen- dicular to one of the sides ...
... sphere is equal to the product of its diameter by the circumference of a great circle . Let A B C D E F be a semicircle in which is inscribed any regular semi - polygon ; from the center , O , draw OI perpen- dicular to one of the sides ...
Página 151
... sphere is equal to the area of four of its great circles . For the area of a circle is equal to the product of the ... sphere , are to each other as their altitudes ; and any zone or segment is to the surface of the sphere as the ...
... sphere is equal to the area of four of its great circles . For the area of a circle is equal to the product of the ... sphere , are to each other as their altitudes ; and any zone or segment is to the surface of the sphere as the ...
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New Elementary Geometry with Practical Applications Benjamin Greenleaf Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD ABCDEF alti altitude Theo angle A CD axis base multiplied bisect chord circum circumference circumscribed cone convex surface D E F diagonal diameter divided ELEMENTARY ALGEBRA ellipse entire surface equal Theo equivalent formed frustum greater GREENLEAF'S half the sum hence homologous homologous sides hypothenuse inches inscribed circle inscribed square intersection magnitudes mean proportional measured by half Metric System number of sides parallelogram parallelopipedon perimeter perpendicular prism PROBLEM quadrilateral radii radius ratio rectangle rectangular regular polygon Required the area Required the volume rhombus right angles Theo right pyramid rods Scholium SCHOOLS sector semicircle side A B side B C similar slant hight solid sphere is equal spherical square described square feet square root tangent THEOREM third triangles A B C triangular triangular prism tude vertex
Pasajes populares
Página 23 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Página 83 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar.
Página 29 - 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 61 - At a point in a given straight line to make an angle equal to a given angle.
Página 85 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Página 93 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Página 62 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Página 100 - The circumferences of circles are to each other as their radii, and their areas are to each other as the squares of their radii. Let C denote the circumference of one of ^ the circles, R its radius OA, A its area; and let C...
Página 88 - FIK are similar ; hence the similar polygons may be divided into the same number of triangles similar each to each, and similarly situated.
Página 124 - But the solidity of each triangular prism is equal to the product of its base by its altitude ; and.