## Elements of Geometry and Trigonometry |

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Page 43

CA , CD , to its

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 inscribed in a circle is its diameter . PROPOSITION III . THEOREM . Page 45

... distant from its two

... distant from its two

**extremities**A and B ( Book I. Prop . XVI . ) . Now , G is one of these points ; therefore AG , BG , are equal . But if the chord AG is equal to the chord GB , the arc AG will be equal to the arc GB ( Prop . IV . ) ... Page 47

Let BD be perpendicular to the B radius CA , at its

Let BD be perpendicular to the B radius CA , at its

**extremity**A ; then will it be tangent to the circumfeF K H A A straight line perpendicular to a radius , at its**extremity**, is a tangent to the circumference . E D rence . Page 57

... being each equally distant from the

... being each equally distant from the

**extremities**A and B , must both lie in the perpendicular raised from the middle of AB ( Book I. Prop . XVI . Cor . ) . But only one straight line can pass through two given points ; hence the line ... Page 59

... D are each equally distant from the

... D are each equally distant from the

**extremities**A and B of the chord AB ; hence the line CD bisects the chord at right angles ( Book I. Prop . XVI . Cor . ) ; hence , it bisects the arc AB in the point E ( Prop . VI . ) . Secondly .### 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