Plane and Solid Geometry |
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Page v
... pyramid , cylinder , cone , sphere , etc. Mensuration much more largely than demonstration motivates student activity in high school geometry , and mensuration of sur- faces and volumes seems to the student worth learning . When a ...
... pyramid , cylinder , cone , sphere , etc. Mensuration much more largely than demonstration motivates student activity in high school geometry , and mensuration of sur- faces and volumes seems to the student worth learning . When a ...
Page x
... pyramids with cones , and polyedral angles with spherical polygons . 3. In the theorems regarding the areas and volumes of solids , and requiring a use of limits , great care is taken to make the treatment logical and still keep it ...
... pyramids with cones , and polyedral angles with spherical polygons . 3. In the theorems regarding the areas and volumes of solids , and requiring a use of limits , great care is taken to make the treatment logical and still keep it ...
Page 5
... PYRAMIDS AND CONES Definitions and Theorems 343 • Areas of Pyramids and Cones . 349 Area of Frustum of Pyramid or Cone 353 Volumes of Pyramids and Cones 357 Similar Pyramids and Cones 365 General Exercises . 367 CHAPTER IX . PRISMATOIDS ...
... PYRAMIDS AND CONES Definitions and Theorems 343 • Areas of Pyramids and Cones . 349 Area of Frustum of Pyramid or Cone 353 Volumes of Pyramids and Cones 357 Similar Pyramids and Cones 365 General Exercises . 367 CHAPTER IX . PRISMATOIDS ...
Page 8
... pyramids , temples , and mausoleums , which could not have been erected without a knowledge of geo- metric principles . The subject was of special importance to the Egyptians because of the frequent land surveys necessitated by the ...
... pyramids , temples , and mausoleums , which could not have been erected without a knowledge of geo- metric principles . The subject was of special importance to the Egyptians because of the frequent land surveys necessitated by the ...
Page 342
... straight line has more than two points common to the curved surface of a right circular cylinder , the line is an element of the surface . CHAPTER VIII PYRAMIDS AND CONES 693. A moving straight line 342 SOLID GEOMETRY.
... straight line has more than two points common to the curved surface of a right circular cylinder , the line is an element of the surface . CHAPTER VIII PYRAMIDS AND CONES 693. A moving straight line 342 SOLID GEOMETRY.
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Common terms and phrases
AABC ABCD acute angle altitude angles are equal angles equal base bisects chord circumference circumscribed congruent diagonals diameter diedral angles distance divided Draw drawn equal respectively equilateral triangle equivalent EXERCISES face angles figure Find the area Find the length Find the number Find the radius Find the volume formula frustum given circle given line given point hypotenuse inch interior angles intersecting isosceles trapezoid isosceles triangle lateral area lateral edges locus median middle point number of sides parallel lines parallelepiped parallelogram perimeter plane geometry plane Q polyedral angle polyedron prism prismatoid Proof prove pyramid quadrilateral radii ratio rectangle regular polygon rhombus right angle right circular cone right triangle segment semicircle Show similar slant height sphere spherical angles spherical polygon spherical triangle straight line surface tangent tetraedron Theorem trapezoid triangle ABC triedral vertex angle vertices
Popular passages
Page 169 - In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other side upon it.
Page 75 - 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.
Page 19 - If two triangles have two angles and the included side of one equal respectively to two angles and the included side of the other, the triangles are congruent.
Page 155 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 89 - 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.
Page 164 - Two triangles which have an angle of one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles.
Page 155 - ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.
Page 248 - ... as the squares of their radii, or as the squares of their...
Page 296 - Axiom. Through a given point only one straight line can be drawn parallel to a given straight line.
Page 39 - In an isosceles triangle the angles opposite the equal sides are equal.