Elements of Geometry and TrigonometryA. S. Barnes and Company, 1838 - 269 σελίδες |
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Σελίδα 12
... homologous sides or angles . Definitions of terms employed in Geometry . An axiom is a self - evident proposition . A theorem is a truth , which becomes evident by means of a train of reasoning called a demonstration . A problem is a ...
... homologous sides or angles . Definitions of terms employed in Geometry . An axiom is a self - evident proposition . A theorem is a truth , which becomes evident by means of a train of reasoning called a demonstration . A problem is a ...
Σελίδα 68
... homologous sides or angles . A 3. In two different circles , similar arcs , sectors , or segments , are those which correspond to equal angles at the centre . Thus , if the angles A and O are equal , the arc BC will be similar to DE ...
... homologous sides or angles . A 3. In two different circles , similar arcs , sectors , or segments , are those which correspond to equal angles at the centre . Thus , if the angles A and O are equal , the arc BC will be similar to DE ...
Σελίδα 84
... homologous sides propor · tional , and are similar . Let ABC , CDE be two triangles which have their angles equal each to each , namely , BAC - CDE , ABC - DCE and ACB DEC ; then the homologous sides , or the sides adjacent to the equal ...
... homologous sides propor · tional , and are similar . Let ABC , CDE be two triangles which have their angles equal each to each , namely , BAC - CDE , ABC - DCE and ACB DEC ; then the homologous sides , or the sides adjacent to the equal ...
Σελίδα 85
... homologous to DC ; in like manner , AC and DE are homologous , because opposite to the equal angles ABC , DCE . When the homologous sides are de- termined , it is easy to form the proportions : AB : DC :: AC : DE :: BC : CE ...
... homologous to DC ; in like manner , AC and DE are homologous , because opposite to the equal angles ABC , DCE . When the homologous sides are de- termined , it is easy to form the proportions : AB : DC :: AC : DE :: BC : CE ...
Σελίδα 87
... homologous sides parallel , or perpendicular to each other , are similar . Let BAC , EDF , be two triangles . First ... homologous sides are the perpendicular ones . Thus in the latter case DE is homologous with AB , DF with AC , and EF ...
... homologous sides parallel , or perpendicular to each other , are similar . Let BAC , EDF , be two triangles . First ... homologous sides are the perpendicular ones . Thus in the latter case DE is homologous with AB , DF with AC , and EF ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface Cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex
Δημοφιλή αποσπάσματα
Σελίδα 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Σελίδα 19 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Σελίδα 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Σελίδα 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Σελίδα 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Σελίδα 169 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude, Fig.
Σελίδα 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Σελίδα 86 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Σελίδα 225 - B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
Σελίδα 168 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.