Elements of Geometry and Trigonometry |
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Page 79
... square of the hypothenuse diminished by the square of the other side ; which is thus ex- pressed : AB2BC - AC2 . Cor . 2. It has just been shown that the square AH is equi- valent to the rectangle BDEF ; but by reason of the common ...
... square of the hypothenuse diminished by the square of the other side ; which is thus ex- pressed : AB2BC - AC2 . Cor . 2. It has just been shown that the square AH is equi- valent to the rectangle BDEF ; but by reason of the common ...
Page 80
... square of a side opposite an acute angle is less than the sum of the squares of the other two sides , by twice the rectangle contained by the base and the distance from the acute angle to the foot of the perpendicular let fall from the ...
... square of a side opposite an acute angle is less than the sum of the squares of the other two sides , by twice the rectangle contained by the base and the distance from the acute angle to the foot of the perpendicular let fall from the ...
Page 81
... 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 , it will be less . PROPOSITION XIV . THEOREM . In any ...
... 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 , it will be less . PROPOSITION XIV . THEOREM . In any ...
Page 86
... square of the hypothenuse , are the most important and fertile in results of any in geometry : they are almost sufficient of themselves for every application to subsequent reasoning , and for solving every problem . The reason is , that ...
... square of the hypothenuse , are the most important and fertile in results of any in geometry : they are almost sufficient of themselves for every application to subsequent reasoning , and for solving every problem . The reason is , that ...
Page 89
... square described on the hypothenuse BC is equivalent to the squares described on the two sides AB , AC . Thus we again arrive at the property of the square of the hypothenuse , by a path very different from that which formerly conducted ...
... square described on the hypothenuse BC is equivalent to the squares described on the two sides AB , AC . Thus we again arrive at the property of the square of the hypothenuse , by a path very different from that which formerly conducted ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex