Elements of Geometry and Trigonometry |
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Page 47
... XV . ) ; hence the E D point E is without the circle ; therefore , BD has no point but A common to it and the circumference ; . consequently BD is a tangent ( Def . 8. ) . Scholium . At a given point A , only one BOOK III . 47.
... XV . ) ; hence the E D point E is without the circle ; therefore , BD has no point but A common to it and the circumference ; . consequently BD is a tangent ( Def . 8. ) . Scholium . At a given point A , only one BOOK III . 47.
Page 69
... consequently equal ( Book I. Prop . X. ) . But if from the quadrilateral ABED , we take away the tri- angle ADF , there will remain the parallelogram ABEF ; and if from the same quadrilateral ABED , we take away the equal triangle CBE ...
... consequently equal ( Book I. Prop . X. ) . But if from the quadrilateral ABED , we take away the tri- angle ADF , there will remain the parallelogram ABEF ; and if from the same quadrilateral ABED , we take away the equal triangle CBE ...
Page 78
... consequently the triangle HBC , and the square AH , which have the common base BH , have also the common altitude AB ; hence the triangle is half of the square . The triangle ABF has already been proved equal to the tri- angle HBC ...
... consequently the triangle HBC , and the square AH , which have the common base BH , have also the common altitude AB ; hence the triangle is half of the square . The triangle ABF has already been proved equal to the tri- angle HBC ...
Page 80
... consequently BD - BC + CD2—2BC × CD ( Prop . IX . ) . Adding AD to each , and observing that the right angled trian- gles ABD , ADC , give AD + BD = AB , and AD2 + CD2 AC , we have ' AB2 = BC2 + AC2-2BC x CD . Secondly . When the ...
... consequently BD - BC + CD2—2BC × CD ( Prop . IX . ) . Adding AD to each , and observing that the right angled trian- gles ABD , ADC , give AD + BD = AB , and AD2 + CD2 AC , we have ' AB2 = BC2 + AC2-2BC x CD . Secondly . When the ...
Page 81
... consequently the triangle ABC gives AB2 + BC2-2AE2 + 2BE2 . The triangle ADC gives , in like manner . AD2 + DC2-2AE2 + 2DE2 . A T Adding the corresponding members together , and observing that BE and DE are equal , we shall have AB2 + ...
... consequently the triangle ABC gives AB2 + BC2-2AE2 + 2BE2 . The triangle ADC gives , in like manner . AD2 + DC2-2AE2 + 2DE2 . A T Adding the corresponding members together , and observing that BE and DE are equal , we shall have AB2 + ...
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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 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 Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment side BC 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 18 - If two triangles have two sides of the one equal to two sides of the...
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 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 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 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'.
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Page 287 - How many square feet are there in the convex surface of the frustum of a square pyramid, whose slant height is 10 feet, each side of the lower base 3 feet 4 inches, and each side of the upper base 2 feet 2 inches ? Ans.
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.