Elements of Geometry and Trigonometry |
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Page 16
... included angle of the one , equal to two sides and the included angle of the other , each to each , the two triangles will be equal . Let the side ED be equal to the side BA , the side DF to the side AC , and the an- gle D to the angle ...
... included angle of the one , equal to two sides and the included angle of the other , each to each , the two triangles will be equal . Let the side ED be equal to the side BA , the side DF to the side AC , and the an- gle D to the angle ...
Page 17
... included side EF equal to the included side BC , it may be inferred that the remaining three are also respectively equal , namely , the angle D = A , the side ED = BA , and the side DF - AC . Scholium . Two triangles are said to be ...
... included side EF equal to the included side BC , it may be inferred that the remaining three are also respectively equal , namely , the angle D = A , the side ED = BA , and the side DF - AC . Scholium . Two triangles are said to be ...
Page 18
... included angles unequal , the third sides will be unequal ; and the greater side will belong to the triangle which has the greater included angle . Let BAC and EDF be two triangles , having the side AB = DE , AC = DF , and the angle A ...
... included angles unequal , the third sides will be unequal ; and the greater side will belong to the triangle which has the greater included angle . Let BAC and EDF be two triangles , having the side AB = DE , AC = DF , and the angle A ...
Page 21
... included angle in the one , equal to two sides and the included angle in the other , each to each hence they are equal ( Prop . V. ) . But the part cannot be equal to the whole ( Ax . 8. ) ; hence , there is no inequality between the ...
... included angle in the one , equal to two sides and the included angle in the other , each to each hence they are equal ( Prop . V. ) . But the part cannot be equal to the whole ( Ax . 8. ) ; hence , there is no inequality between the ...
Page 32
... included between two other parallels AD , BC , are equal ; and the diagonal DB divides the parallelogram into two equal triangles . PROPOSITION XXIX . THEOREM . If the opposite sides of a quadrilateral are equal , each to each , the ...
... included between two other parallels AD , BC , are equal ; and the diagonal DB divides the parallelogram into two equal triangles . PROPOSITION XXIX . THEOREM . If the opposite sides of a quadrilateral are equal , each to each , the ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn 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 parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall 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
Popular passages
Page 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.
Page 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 11 - A right-angled triangle is one which has a right angle. The side opposite the right angle is called the hypothenuse.
Page 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.
Page 31 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon...
Page 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.
Page 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 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'.
Page 159 - S-ahc be the smaller : and suppose Aa to be the altitude of a prism, which having ABC for its base, is equal to their difference. Divide the altitude AT into equal parts Ax, xy, yz, &c. each less than Aa, and let k be one of those parts ; through the points of division...
Page 64 - To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B by the lines AO and BO, meeting at the point 0.