Elements of Geometry and Trigonometry |
From inside the book
Results 1-5 of 42
Page 20
... follow , that the side EF must be less than BC : but EF is equal to BC , by hypothesis ; therefore , the angle D can neither be greater nor less than A ; therefore it must be equal to it . In the same manner it may be shown that the ...
... follow , that the side EF must be less than BC : but EF is equal to BC , by hypothesis ; therefore , the angle D can neither be greater nor less than A ; therefore it must be equal to it . In the same manner it may be shown that the ...
Page 21
... follows , from what has just been proved , that AB < AC ; which is contrary to the hypothesis . It the angle C = B , then the side AB = AC ( Prop . XII . ) ; which is also contrary to the supposition . Therefore , when AB > AC , the ...
... follows , from what has just been proved , that AB < AC ; which is contrary to the hypothesis . It the angle C = B , then the side AB = AC ( Prop . XII . ) ; which is also contrary to the supposition . Therefore , when AB > AC , the ...
Page 32
... follows that the angle A is equal to the angle C ; and also that the angle ADC com- posed of the two ADB , BDC , is equal to ABC , composed of the two equal angles DBC , ABD : hence the opposite angles of a parallelogram are also equal ...
... follows that the angle A is equal to the angle C ; and also that the angle ADC com- posed of the two ADB , BDC , is equal to ABC , composed of the two equal angles DBC , ABD : hence the opposite angles of a parallelogram are also equal ...
Page 33
... therefore equal : whence it follows that the angles AEB , BEC , are equal , and therefore , that the two diagonals of a rhombus cut each other at right angles . BOOK II . OF RATIOS AND PROPORTIONS . Definitions . BOOK I. 33.
... therefore equal : whence it follows that the angles AEB , BEC , are equal , and therefore , that the two diagonals of a rhombus cut each other at right angles . BOOK II . OF RATIOS AND PROPORTIONS . Definitions . BOOK I. 33.
Page 34
... follows , that magnitudes may be rep- resented by numbers to any degree of exactness , or they will differ from their numerical representatives by less than any assignable quantity . Therefore , of two magnitudes , A and B , we may ...
... follows , that magnitudes may be rep- resented by numbers to any degree of exactness , or they will differ from their numerical representatives by less than any assignable quantity . Therefore , of two magnitudes , A and B , we may ...
Other editions - View all
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.