## Elements of Geometry and Trigonometry |

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Page 41

From the definition of a circle , it follows that all the radii are equal ; that all the

From the definition of a circle , it follows that all the radii are equal ; that all the

**diameters**are equal also , and each double of the radius . 3. A portion of the circumference , such as FHG , is called An inscribed angle is one ... Page 42

DOO ( Every

DOO ( Every

**diameter**divides the circle and its circumference into two equal parts . Let AEDF be a circle , and AB a**diameter**. Now , if the figure AEB be applied to AFB , their common base AB retaining its position , the curve line AEB ... Page 43

Every chord is less than the

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

N DD BE K For , since the

N DD BE K For , since the

**diameters**AB , EF , are equal , the semicircle AMDB may be applied exactly to the semicircle ENGF , and the curve line AMDB will coincide entirely with the curve line ENGF . But the part AMD is equal to the ... Page 54

Draw the

Draw the

**diameter**AE , and the radii CB , CD . E The angle BCE , being exterior to the triangle ABC , is equal to the sum of the two interior angles CAB , ABC ( Book I. B Prop . XXV . Cor . 6. ) : but the triangle BAC being isosceles ...### 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