## Elements of Geometry and Trigonometry |

### From inside the book

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Page 41

A

A

**segment**is the surface or portion of a circle , included between an arc and its chord . 5. A sector is the part of the circle included between an arc DE , and the two radii CD , CE , drawn to the extremities of ... Page 55

All the angles BAC , BDC , BEC , inscribed in the same

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- ... Page 65

On a given straight line to describe a

On a given straight line to describe a

**segment**that shall contain a given angle ; that is to say , a**segment**such , that all the an- gles inscribed in it , shall be equal to the given angle . Let AB be the given straight line , and C ... Page 66

If the given angle were a right angle , the required

If the given angle were a right angle , the required

**segment**would be a semicircle , described on AB as a diameter . · PROBLEM XVII . To find the numerical ratio of two given straight lines , these lines being supposed to have a common ... Page 68

In two different circles , similar arcs , sectors , or

In two different circles , similar arcs , sectors , or

**segments**, are those which correspond to equal angles at the centre . ... the sector BAC to the sector DOE , and the**segment**whose chord is BC , to the seg- ment whose chord is DE .### What people are saying - Write a review

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### Other editions - View all

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 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