Elements of Geometry and Trigonometry |
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Page 11
... triangle ABC , right - angled at A , the side BC is the hypothenuse . B 17. Among the quadrilaterals , we distinguish : The square , which has its sides equal , and its an- gles right - angles . The rectangle , which has its angles ...
... triangle ABC , right - angled at A , the side BC is the hypothenuse . B 17. Among the quadrilaterals , we distinguish : The square , which has its sides equal , and its an- gles right - angles . The rectangle , which has its angles ...
Page 18
... triangle , is greater than the third side . Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the third side AB . For the straight line AB is the short- est distance between the points A and B ...
... triangle , is greater than the third side . Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the third side AB . For the straight line AB is the short- est distance between the points A and B ...
Page 19
... triangle ABC , or upon its base BC , or within it . First Case . The straight line GC < GI + IC , and the straight line AB < AI + IB ; therefore , GC + AB < GI + AI + IC + ÏB , or , which is the same thing , GC + AB < AG + BC . Take ...
... triangle ABC , or upon its base BC , or within it . First Case . The straight line GC < GI + IC , and the straight line AB < AI + IB ; therefore , GC + AB < GI + AI + IC + ÏB , or , which is the same thing , GC + AB < AG + BC . Take ...
Page 21
... triangle are equal , the sides oppo- site them are also equal , and the triangle is isosceles . Let the angle ABC be equal to the angle ACB ; then will the side AC be equal to the side AB . D A For , if these sides are not equal ...
... triangle are equal , the sides oppo- site them are also equal , and the triangle is isosceles . Let the angle ABC be equal to the angle ACB ; then will the side AC be equal to the side AB . D A For , if these sides are not equal ...
Page 29
... ABC be any triangle : then will the an- gle C + A + B be equal to two right angles . B E A D For , produce the side ... ABC , BAE , will be equal : hence the three angles of the triangle ABC make up the same sum as the three angles CAB ...
... ABC be any triangle : then will the an- gle C + A + B be equal to two right angles . B E A D For , produce the side ... ABC , BAE , will be equal : hence the three angles of the triangle ABC make up the same sum as the three angles CAB ...
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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.