Elements of GeometryAmerican Book Company, 1896 - 540 σελίδες |
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Σελίδα 287
... hexaedron ; one of eight faces , an octaedron ; one of twelve faces , a dodecaedron ; one of twenty faces , an icosaedron . ICOSAEDRON DODECAEDRON OCTAEDRON HEXAEDRON TETRAEDRON 629. Def . - A polyedron is convex when no. BOOK VII ...
... hexaedron ; one of eight faces , an octaedron ; one of twelve faces , a dodecaedron ; one of twenty faces , an icosaedron . ICOSAEDRON DODECAEDRON OCTAEDRON HEXAEDRON TETRAEDRON 629. Def . - A polyedron is convex when no. BOOK VII ...
Σελίδα 348
... tetraedron cut the tetraedron , the section is a parallelo- gram . 748. Exercise . - If the angles at the vertex of a triangu- lar pyramid are right angles , and the lateral edges 348 GEOMETRY OF SPACE PROBLEMS OF DEMONSTRATION.
... tetraedron cut the tetraedron , the section is a parallelo- gram . 748. Exercise . - If the angles at the vertex of a triangu- lar pyramid are right angles , and the lateral edges 348 GEOMETRY OF SPACE PROBLEMS OF DEMONSTRATION.
Σελίδα 349
... tetraedron . 750. Exercise . - The straight lines joining the middle points of the opposite edges of a tetraedron meet in a point and are each bisected by the point . 751. Exercise . - A plane bisecting two opposite edges of a regular ...
... tetraedron . 750. Exercise . - The straight lines joining the middle points of the opposite edges of a tetraedron meet in a point and are each bisected by the point . 751. Exercise . - A plane bisecting two opposite edges of a regular ...
Σελίδα 371
... . 8531 That is , P is the pole of the great circle AB . 816 Q. E. D. 822. Remark . - The preceding theorems enable us to. that P is the pole of the great circle AB . Form a tetraedron having these points as vertices . BOOK VIII 371.
... . 8531 That is , P is the pole of the great circle AB . 816 Q. E. D. 822. Remark . - The preceding theorems enable us to. that P is the pole of the great circle AB . Form a tetraedron having these points as vertices . BOOK VIII 371.
Σελίδα 377
... tetraedron , and but one . D B GIVEN the tetraedron ABCD . TO PROVE that one , and only one , sphere can be inscribed in it . Bisect the diedral angles BC , CD , and DB by the planes BOC , COD , and DOB . The plane BOC is the locus of ...
... tetraedron , and but one . D B GIVEN the tetraedron ABCD . TO PROVE that one , and only one , sphere can be inscribed in it . Bisect the diedral angles BC , CD , and DB by the planes BOC , COD , and DOB . The plane BOC is the locus of ...
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles allel altitude angles are equal apothem axis bisecting bisector centre chord circumference circumscribed coincide construct Def.-The Defs Defs.-A diagonals diameter diedral angles distance divided draw equally distant equilateral triangle equivalent Exercise.-The face angles figure Find the area frustum geometry given circle given line given point given straight line GIVEN TO PROVE given triangle Hence hypotenuse lateral area lateral edges lateral faces locus meet middle points number of sides parallel lines parallelogram parallelopiped perimeter perpendicular plane geometry plane MN polyedral angle polyedron prism prismatic surface pyramid Q. E. D. PROPOSITION quadrilateral radical axis radii radius ratio of similitude rectangle regular polygon right angles right triangle segment similar slant height sphere spherical polygon spherical triangle square straight line joining surface symmetrical tangent tetraedron THEOREM triangle ABC triangles are equal triangular prism triedral vertex vertices volume
Δημοφιλή αποσπάσματα
Σελίδα 30 - If two triangles have two sides and the included angle of one, equal respectively to two sides and the included angle of the other, the triangles are equal. C...
Σελίδα 466 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Σελίδα 315 - The frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and a mean proportional between the two bases of the frustum.
Σελίδα 205 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems.
Σελίδα 36 - ... 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 379 - Two triangles are congruent if (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other...
Σελίδα 138 - ... twice the product of one of these sides and the projection of the other side upon it.
Σελίδα 57 - 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 137 - If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment.
Σελίδα 147 - The product of two sides of a triangle is equal to the product of the diameter of the circumscribed circle and the altitude upon the third side.