Elements of plane (solid) geometry (Higher geometry) and trigonometry (and mensuration), being the first (-fourth) part of a series on elementary and higher geometry, trigonometry, and mensuration |
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Page 25
... convex surface of the prism ; the equal straight lines AF , BG , CH , & c . are called the sides of the prism . 6. The altitude of a prism is the distance between its two bases , or the perpendicular drawn from a point in the upper base ...
... convex surface of the prism ; the equal straight lines AF , BG , CH , & c . are called the sides of the prism . 6. The altitude of a prism is the distance between its two bases , or the perpendicular drawn from a point in the upper base ...
Page 27
... surface . Note 1. By the vertices of a polyedron , we mean the points . situated at the vertices of its different solid angles . 2. The only polyedrons we intend at present to treat of , are polyedrons with salient angles , or convex ...
... surface . Note 1. By the vertices of a polyedron , we mean the points . situated at the vertices of its different solid angles . 2. The only polyedrons we intend at present to treat of , are polyedrons with salient angles , or convex ...
Page 34
... convex surface of a right prism is equal to the perimeter of its base multiplied by its altitude . Let ABCDE - K be a right prism : then will its convex surface be equal to ( AB + BC + CD F + DE + EA ) × AF . K H For , the convex ...
... convex surface of a right prism is equal to the perimeter of its base multiplied by its altitude . Let ABCDE - K be a right prism : then will its convex surface be equal to ( AB + BC + CD F + DE + EA ) × AF . K H For , the convex ...
Page 44
... convex surface multiplied by half the radius of the circle inscribed in the base . Scholium 1. As all the triangular ... surfaces will be to each 44 ELEMENTS OF SOLID GEOMETRY .
... convex surface multiplied by half the radius of the circle inscribed in the base . Scholium 1. As all the triangular ... surfaces will be to each 44 ELEMENTS OF SOLID GEOMETRY .
Page 46
... convex surface of a regular pyramid is equal to the perime- ter of its base multiplied by half its slant height . For , since the pyramid is regular , the point O , in which axis meets the base , is the centre of the polygon ABCDE ( Def ...
... convex surface of a regular pyramid is equal to the perime- ter of its base multiplied by half its slant height . For , since the pyramid is regular , the point O , in which axis meets the base , is the centre of the polygon ABCDE ( Def ...
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Elements of Plane (Solid) Geometry (Higher Geometry) and Trigonometry (and ... Nathan Scholfield No preview available - 2015 |
Common terms and phrases
ABCD abscissa altitude axis bisect chord circle circular segment circum circumference circumscribing cone conjugate construction convex surface cosec cosine cube curve cylinder described diameter distance divided draw ellipse equal to half equation equivalent feet figure formed frustum Geom geometry given hence hyperbola hypothenuse inches inscribed inscribed sphere latus rectum length logarithm magnitude measured multiplied by one-third number of sides opposite ordinates parabola parallel parallelogram perimeter perpendicular plane polyedroid polyedron polygon portion prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon revoloid rhomboid right angled triangle right line root Scholium sector segment similar similar triangles sine slant height solid angle sphere spherical square straight line tangent THEOREM triangle ABC triangular triangular prism ungula vertex vertical virtual centre
Popular passages
Page 36 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Page 35 - The sum of any two sides of a triangle, is greater than the third side.
Page 60 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 56 - In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Page 38 - The volumes of similar solids are to each other as the cubes of their like dimensions.
Page 75 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 86 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...
Page 211 - To find the solidity of a hyperbolic conoid, or otherwise called a hyperboloid. RULE. To the square of the radius of the base, add the square of the diameter...
Page 48 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon has sides, and consequently, equal to the sum of the interior angles plus the exterior angles.