## Elements of Geometry and Trigonometry |

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Page 41

A straight line is said to be

A straight line is said to be

**inscribed**in a circle , when its extremities are in the cir- cumference , as AB . An**inscribed**angle is one which , like BAC , has its vertex in the circumference , and is formed by two chords . * Note . Page 42

An

An

**inscribed**triangle is one which , like BAC , has its three angular points in the circumference . And , generally , an**inscribed**figure is one , of which all the angles have their vertices in the circumference . Page 43

Hence the greatest line which can be

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 . For , if it could meet it in three , those ... Page 54

An

An

**inscribed**angle is measured by half the arc included between its sides . Let BAD be an**inscribed**angle , and let us first suppose that the centre of the cir- cle lies within the angle BAD . Draw the diameter AE , and the radii CB ... Page 55

All the angles BAC , BDC , BEC ,

All the angles BAC , BDC , BEC ,

**inscribed**in the same segment are equal ; because they are all measured by the half of the same arc BOC . B Cor . 2. Every angle BAD ,**inscribed**in a semicircle is a right angle ; because it is mea- ...### 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 construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole