## Elements of Geometry and Trigonometry |

### From inside the book

Page 96

... the radius D B F OD ; hence the area of the triangle ABC is equal to the perimeter multiplied by half the radius of the inscribed circle . PROPOSITION XXXIII . THEOREM . In every

... the radius D B F OD ; hence the area of the triangle ABC is equal to the perimeter multiplied by half the radius of the inscribed circle . PROPOSITION XXXIII . THEOREM . In every

**quadrilateral**inscribed in 96 GEOMETRY . Page 97

Adrien Marie Legendre Charles Davies. PROPOSITION XXXIII . THEOREM . In every

Adrien Marie Legendre Charles Davies. PROPOSITION XXXIII . THEOREM . In every

**quadrilateral**inscribed in a circle , the rectangle of the two diagonals is equivalent to the sum of the rectangles of the opposite sides . In the**quadrilateral**... Page 110

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**quadrilateral**OPBA , they will coincide ; for the side OP is common ; G the angle OPC = OPB , each being a right ...**quadrilaterals**will entirely coincide . The distance OD is therefore equal to AO ; and consequently the circle ... Page 115

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**quadrilateral**PBfa , so that PB shall fall on PB . Then , since the angle dPB is equal to the angle BPa , each being ...**quadrilaterals**will coincide , and the point g will fall at f ; hence , Bg = Bf , dg = af , and the angle dgB ... Page 140

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**quadrilateral**SAOC is equal to the quadri- lateral TDPF : for , place the angle ASC upon its equal DTF ; because SA = TD , and SC = TF , the point A will fall on D , and the point C on F ; and at the same time , AO , which is per ...### Other editions - View all

### 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