## Elements of Geometry and Trigonometry |

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Page 41

From the definition of a circle , it follows 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 43

Draw the

Draw the

**radii**We shall then E Cor . Hence the greatest line which can be inscribed in a circle is its diameter . PROPOSITION III . THEOREM . A straight line cannot meet the circumference of a circle in more than two points . Page 44

M If 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

For , draw the

For , draw the

**radii**CA , CB . Then the two right angled triangles_ADC , CDB , will have AC = CB , and CD common ; hence , AD is equal to DB ( Book I. Prop . XVII . ) . Again , since AD , DB , are equal , CG is a perpendicular erected ... Page 47

Bisect these chords by the perpendiculars CF , CG , and draw the

Bisect these chords by the perpendiculars CF , CG , and draw the

**radii**CA , CD . M D A In the right angled triangles CAF , DCG , the hypothenuses CA , CD , are equal ; and the side AF , the half of AB , is equal to the side DG ...### 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