## Elements of Geometry and Trigonometry |

### From inside the book

Results 1-5 of 64

Page 13

A number placed before a line , or a quantity , serves as a multiplier to that line or quantity ; thus , 3AB signifies that the line AB is taken three times ; A signifies the

A number placed before a line , or a quantity , serves as a multiplier to that line or quantity ; thus , 3AB signifies that the line AB is taken three times ; A signifies the

**half**of the angle A. The square of the line AB is designated ... Page 23

therefore , AB , the

therefore , AB , the

**half**of ABF , is shorter than AC , the**half**of ACF ; hence , the perpendicular is shorter than any oblique line . BE Secondly . Let us suppose BC = BE ; then will the triangle CAB be equal to the the triangle BAE ... Page 47

M D A In the right angled triangles CAF , DCG , the hypothenuses CA , CD , are equal ; and the side AF , the

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 , the**half**of DE : hence the triangles are equal , and CF is equal to CG ( Book I. Prop . Page 54

An inscribed angle is measured by

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 circle lies within the angle BAD . Draw the diameter AE , and the radii CB ... Page 55

All the angles BAC , BDC , BEC , inscribed in the same segment are equal ; because they are all measured by the

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 measured ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### 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