## Elements of Geometry and Trigonometry |

### From inside the book

Results 1-5 of 18

Page 76

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**square described**on the whole line is equivalent to the sum of the squares described on the parts , together with twice the rectangle contained by the parts . Let AC be the line , and B the point of division ; then , is AC2 or ( AB + ... Page 77

... square ABIF ; take AE L F = AC ; draw CG parallel to to BI , HK parallel to AB , and complete the square K EFLK . The two rectangles CBIG , GLKD , are each measured by AB × BC ; take them away ...

... square ABIF ; take AE L F = AC ; draw CG parallel to to BI , HK parallel to AB , and complete the square K EFLK . The two rectangles CBIG , GLKD , are each measured by AB × BC ; take them away ...

**square described**on the BOOK IV . 77. Page 78

Adrien Marie Legendre. PROPOSITION XI . THEOREM . The

Adrien Marie Legendre. 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 right angled at ... Page 79

... square of the hypothenuse diminished by the square of the other side ; which is thus ex- pressed : AB2BC - AC2 . Cor ... described on the diagonal AC , is double of the

... square of the hypothenuse diminished by the square of the other side ; which is thus ex- pressed : AB2BC - AC2 . Cor ... described on the diagonal AC , is double of the

**square described**on the side AB . E B F G This property may be ... Page 81

... described on the two sides are together equivalent to the

... 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 ...### Other editions - View all

### Common terms and phrases

adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine 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 Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex