Elements of GeometryAmerican Book Company, 1896 - 540 σελίδες |
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Αποτελέσματα 1 - 5 από τα 83.
Σελίδα 32
... TRIANGLES 55. Def . - A triangle is a figure bounded by three straight lines called its sides . 56. Def . — A right triangle is a triangle one of whose angles is a right angle . 5 % . Def . — An equiangular triangle is one whose angles ...
... TRIANGLES 55. Def . - A triangle is a figure bounded by three straight lines called its sides . 56. Def . — A right triangle is a triangle one of whose angles is a right angle . 5 % . Def . — An equiangular triangle is one whose angles ...
Σελίδα 33
... triangle be produced , the ex- terior angle thus formed equals the sum of the two opposite interior angles ( and hence is greater than either of them ) . b с x OUTLINE PROOF : a + b + c = 2 right angles = x + c , whence a + b = x ...
... triangle be produced , the ex- terior angle thus formed equals the sum of the two opposite interior angles ( and hence is greater than either of them ) . b с x OUTLINE PROOF : a + b + c = 2 right angles = x + c , whence a + b = x ...
Σελίδα 34
... right angles as the figure has sides , less four right angles . A C GIVEN ABCDE , any polygon , having n sides . TO ... triangle is equal to 2 right angles . $ 58 Hence the sum of the angles of the n triangles is equal to 2n right angles ...
... right angles as the figure has sides , less four right angles . A C GIVEN ABCDE , any polygon , having n sides . TO ... triangle is equal to 2 right angles . $ 58 Hence the sum of the angles of the n triangles is equal to 2n right angles ...
Σελίδα 35
... right angles . e d Р a с d ' a c'b GIVEN the polygon P with successive exterior angles a , b , c , d , e . TO PROVE a + b + c + d + e = 4 right ... triangle is a triangle BOOK I 35.
... right angles . e d Р a с d ' a c'b GIVEN the polygon P with successive exterior angles a , b , c , d , e . TO PROVE a + b + c + d + e = 4 right ... triangle is a triangle BOOK I 35.
Σελίδα 37
... right angles . Question . In how many different ways is an equilateral triangle isosceles ? 75. CONSTRUCTION . To bisect any given angle A. X N On the sides of the angle , lay off AX = AY . Join XY . Bisect XY at Z ( § 42 ) . Join AZ ...
... right angles . Question . In how many different ways is an equilateral triangle isosceles ? 75. CONSTRUCTION . To bisect any given angle A. X N On the sides of the angle , lay off AX = AY . Join XY . Bisect XY at Z ( § 42 ) . Join AZ ...
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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.