Elements of Geometry and Trigonometry |
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Page 76
... square ACDE ; take AF AB ; draw FG parallel to AC , and BH par- allel to AE . E F H D в с G The square ACDE is made up of four parts ; the first ABIF is the square described on AB , since we made AF - AB : the second IDGH is A the square ...
... square ACDE ; take AF AB ; draw FG parallel to AC , and BH par- allel to AE . E F H D в с G The square ACDE is made up of four parts ; the first ABIF is the square described on AB , since we made AF - AB : the second IDGH is A the square ...
Page 77
... Describe the square ABIF ; take AE L F = AC ; draw CG parallel to to BI , HK parallel to AB , and complete the ... described on BC : hence we have ( AB + BC ) × ( AB - BC ) -AB - BC2 . Scholium . This proposition is equivalent to the ...
... Describe the square ABIF ; take AE L F = AC ; draw CG parallel to to BI , HK parallel to AB , and complete the ... described on BC : hence we have ( AB + BC ) × ( AB - BC ) -AB - BC2 . Scholium . This proposition is equivalent to the ...
Page 78
Adrien Marie Legendre Charles Davies. PROPOSITION XI . THEOREM . The square described on the hypothenuse of a right angled tri- angle is equivalent to the sum of the squares described on the other two sides . Let the triangle ABC be ...
Adrien Marie Legendre Charles Davies. PROPOSITION XI . THEOREM . The square described on the hypothenuse of a right angled tri- angle is equivalent to the sum of the squares described on the other two sides . Let the triangle ABC be ...
Page 79
... square of the hypothenuse diminished by the square of the other side ; which is thus ex- pressed : AB2 = BC2 — AC2 ... described on the diagonal AC , is double of the square described on the side AB . A G E B F This property may be ...
... square of the hypothenuse diminished by the square of the other side ; which is thus ex- pressed : AB2 = BC2 — AC2 ... described on the diagonal AC , is double of the square described on the side AB . A G E B F This property may be ...
Page 81
... described on the two sides are together equivalent to the square described on the third ; for if the angle contained by the two sides is acute , the sum of their squares will be greater than the square of the opposite side ; if obtuse ...
... described on the two sides are together equivalent to the square described on the third ; for if the angle contained by the two sides is acute , the sum of their squares will be greater than the square of the opposite side ; if obtuse ...
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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 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
Popular passages
Page 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.
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 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 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 169 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude, Fig.
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 225 - B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
Page 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.