## Elements of Geometry and Trigonometry |

### From inside the book

Results 1-5 of 67

Page 41

The circumference of a circle is a curved line , all the points of which are equally distant from a point within , called the

The circumference of a circle is a curved line , all the points of which are equally distant from a point within , called the

**centre**. The circle is the space terminated by A this curved line . *酱 F H G 2. Page 42

... otherwise there would , in the one or the other , be points unequally distant from the

... otherwise there would , in the one or the other , be points unequally distant from the

**centre**, which is contrary to the definition of a circle . 44 ! PROPOSITION II . THEOREM . Every chord is less than 42 GEOMETRY . • Page 43

For , if it could meet it in three , those three points would be equally distant from the

For , if it could meet it in three , those three points would be equally distant from the

**centre**; and hence , there would be three equal straight lines drawn from the same point to the same straight line , which is impossible ( Book I. Page 45

The

The

**centre**C , the middle point D , of the chord AB , and the middle point G , of the arc subtended by this chord , are three points of the same line perpendicular to the chord . But two points are sufficient to determine the position ... Page 46

For , if there were a second circumference passing through the three given points A , B , C , its

For , if there were a second circumference passing through the three given points A , B , C , its

**centre**could not be out of the line DE , for then it would be unequally distant from A and B ( Book I. Prop . XVI . ) ...### 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