The Elements of GeometryLeach, Shewell & Sanborn, 1894 - 378 σελίδες |
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Σελίδα 280
... by their altitudes . Ex . 16. Find the lateral area and volume of a regular hexagonal prism , each side of whose base is 3 , and whose altitude is 9 . PYRAMIDS . DEFINITIONS . 510. A pyramid is a polyedron 280 SOLID GEOMETRY . -BOOK VII .
... by their altitudes . Ex . 16. Find the lateral area and volume of a regular hexagonal prism , each side of whose base is 3 , and whose altitude is 9 . PYRAMIDS . DEFINITIONS . 510. A pyramid is a polyedron 280 SOLID GEOMETRY . -BOOK VII .
Σελίδα 281
Webster Wells. PYRAMIDS . DEFINITIONS . 510. A pyramid is a polyedron bounded by a polygon , and a series of triangles having a common vertex ; as 0 - ABCDE . The polygon is called the ... pyramid is that portion of a pyramid PYRAMIDS . 281.
Webster Wells. PYRAMIDS . DEFINITIONS . 510. A pyramid is a polyedron bounded by a polygon , and a series of triangles having a common vertex ; as 0 - ABCDE . The polygon is called the ... pyramid is that portion of a pyramid PYRAMIDS . 281.
Σελίδα 285
... pyramids with their bases in the same plane , and let PQ be their common altitude . Divide PQ into any number of equal parts ; and through the points of division pass planes parallel to the plane of the bases , cutting o - abc in the ...
... pyramids with their bases in the same plane , and let PQ be their common altitude . Divide PQ into any number of equal parts ; and through the points of division pass planes parallel to the plane of the bases , cutting o - abc in the ...
Σελίδα 287
... pyramid O - ACDE . Divide O - ACDE into two triangular pyramids , O - ACE and O - CDE , by passing a plane through O , C , and E. Now , O - ACE and O - CDE have the same altitude . And since CE is a diagonal of the parallelogram ACDE ...
... pyramid O - ACDE . Divide O - ACDE into two triangular pyramids , O - ACE and O - CDE , by passing a plane through O , C , and E. Now , O - ACE and O - CDE have the same altitude . And since CE is a diagonal of the parallelogram ACDE ...
Σελίδα 288
Webster Wells. PROPOSITION XIX . THEOREM . 527. The volume of any pyramid is equal to one - third the product of its base and altitude . Any pyramid may be divided into triangular pyramids by passing planes through one of the lateral ...
Webster Wells. PROPOSITION XIX . THEOREM . 527. The volume of any pyramid is equal to one - third the product of its base and altitude . Any pyramid may be divided into triangular pyramids by passing planes through one of the lateral ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles altitude angles are equal approach the limit arc BC area ABC base and altitude BC² bisector bisects centre chord circle circumference circumscribed cone of revolution construct the triangle Converse of Prop cylinder diagonals diameter diedral Draw BC equal respectively equally distant equilateral triangle equivalent exterior angle Find the area frustum given point given straight line Hence homologous hypotenuse intersection isosceles triangle lateral area lateral edges Let ABC measured by arc middle point number of sides O-ABC parallelogram parallelopiped perimeter perpendicular to MN plane MN polyedral polyedron prism produced PROPOSITION prove pyramid quadrilateral radii radius rectangle regular polygon rhombus right angles right triangle secant line segment similar slant height sphere spherical polygon spherical triangle square surface tangent tetraedron THEOREM trapezoid triangle ABC triangles are equal triangular prism triedral vertex volume Whence
Δημοφιλή αποσπάσματα
Σελίδα 165 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 39 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Σελίδα 65 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Σελίδα 172 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.
Σελίδα 122 - In any proportion the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Σελίδα 355 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Σελίδα 52 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.
Σελίδα 140 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Σελίδα 123 - In any proportion the terms are in proportion by composition and division ; that is, the sum of the first two terms is to their difference as the sum of the last two terms to their difference.
Σελίδα 207 - S' denote the areas of two © whose radii are R and R', and diameters D and D', respectively. Then, | = "* § = ££ = £• <§337> That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters.