Elements of Geometry and TrigonometryA. S. Barnes and Company, 1838 - 269 σελίδες |
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Αποτελέσματα 1 - 5 από τα 69.
Σελίδα 53
... similar , it may be shown . that the fourth term of the proportion cannot be less than AD ; hence it is AD itself ; therefore we have Angle ACB angle ACD :: arc AB : arc AD . Cor . Since the angle at the centre of a circle , and the arc ...
... similar , it may be shown . that the fourth term of the proportion cannot be less than AD ; hence it is AD itself ; therefore we have Angle ACB angle ACD :: arc AB : arc AD . Cor . Since the angle at the centre of a circle , and the arc ...
Σελίδα 68
... similar figures , are called 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 ...
... similar figures , are called 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 ...
Σελίδα 73
... similar manner , by measuring its sides with the same linear unit ; a second product is thus obtained , and the ratio of the two pro- ducts is the same as that of the rectangles , agreeably to the proposition just demonstrated . For ...
... similar manner , by measuring its sides with the same linear unit ; a second product is thus obtained , and the ratio of the two pro- ducts is the same as that of the rectangles , agreeably to the proposition just demonstrated . For ...
Σελίδα 84
... similar when they have their angles equal , each to each , and their homolo- gous sides proportional ( Def . 1. ) ; consequently the equiangu- lar triangles BAC , CED , are two similar figures . Cor . For the similarity of two triangles ...
... similar when they have their angles equal , each to each , and their homolo- gous sides proportional ( Def . 1. ) ; consequently the equiangu- lar triangles BAC , CED , are two similar figures . Cor . For the similarity of two triangles ...
Σελίδα 85
... similar . In the two triangles BAC , DEF , suppose we have BC : EF :: AB : DE :: AC : DF ; then will the triangles ABC , DEF have their an- gles equal , namely , A = D , B = E , C = F . B 14 At the point E , make the angle FEG = B , and ...
... similar . In the two triangles BAC , DEF , suppose we have BC : EF :: AB : DE :: AC : DF ; then will the triangles ABC , DEF have their an- gles equal , namely , A = D , B = E , C = F . B 14 At the point E , make the angle FEG = B , and ...
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.