## Elements of Geometry and Trigonometry |

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Page 41

A portion of the circumference , such as FHG , is called An inscribed angle is one which , like BAC , has its vertex in the circumference , and is formed by two

A portion of the circumference , such as FHG , is called An inscribed angle is one which , like BAC , has its vertex in the circumference , and is formed by two

**chords**. B an arc . The**chord**, or subtense of an arc , is the straight ... Page 42

... otherwise there would , in the one or the other , be points unequally distant from the centre , which is contrary to the definition of a circle . 44 ! PROPOSITION II . THEOREM . Every

... otherwise there would , in the one or the other , be points unequally distant from the centre , which is contrary to the definition of a circle . 44 ! PROPOSITION II . THEOREM . Every

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

Every

Every

**chord**is less than the diameter . Let AD be any**chord**. CA , CD , to its extremities . have AD < AC + CD ( Book I. Prop . VII . * ) ; A or AD < AB . Draw the radii We shall then E Cor . Hence the greatest line which can be ... Page 44

M If the radii AC , EO , are equal , and also the arcs AMD , ENG ; then the

M If the radii AC , EO , are equal , and also the arcs AMD , ENG ; then the

**chord**AD will be equal to the A**chord**EG . N DD BE K For , since the diameters AB , EF , are equal , the semicircle AMDB may be applied exactly to the ... Page 45

If they were greater , the reverse property would have place ; for , as the arcs increase , the

If they were greater , the reverse property would have place ; for , as the arcs increase , the

**chords**would diminish , and conversely . Thus , the arc AKBD is greate than AKBH , and the**chord**AD , of the first , is less than the**chord**...### What people are saying - Write a review

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### Common terms and phrases

ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole