## Elements of Geometry and Trigonometry |

### From inside the book

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Page 41

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**chord**, or subtense of an arc , is the straight line FG , which joins its two extremities . † 4. A segment is the surface or portion of a circle , included between an arc and its**chord**. 5. A sector is the part of the circle included ... Page 42

... , otherwise there would , in the one or the other , be points unequally dis- tant from the centre , which is contrary to the definition of a circle . PROPOSITION II . THEOREM . -Every

... , otherwise there would , in the one or the other , be points unequally dis- tant from the centre , which is contrary to the definition of a circle . PROPOSITION II . THEOREM . -Every

**chord**is less than 42 GEOMETRY . Page 43

Adrien Marie Legendre Charles Davies. PROPOSITION II . THEOREM . -Every

Adrien Marie Legendre Charles Davies. PROPOSITION II . THEOREM . -Every

**chord**is less than the diameter . Let AD be ...**chords**; and , conversely , equal**chords**subtend equal arcs . Note . When reference is made from one proposition ... Page 44

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**chord**EG . For , since the diameters AB , EF , are equal , the semi- circle AMDB may be applied M H N DO • exactly ...**chord**AD is equal to the**chord**EG . Conversely , supposing again the radii AC , EO , to be equal , if the**chord**... Page 45

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**chord**AD , of the first , is less than the**chord**AH of the second . PROPOSITION VI . THEOREM . The radius which is perpendicular to a**chord**, bisects the**chord**, and bisects also the subtended arc of the**chord**. Let AB be a**chord**...### 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