## Elements of Geometry and Trigonometry |

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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**. F H The circle is the space terminated by A this curved line . * 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 . 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 Î ... 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

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Elements of Geometry and Trigonometry from the Works of A. M. Legendre A. M. Legendre No preview available - 2017 |

### 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 produced 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