## Elements of Geometry and Trigonometry |

### From inside the book

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Page 6

Division of the Circumference , General Ideas relating to the Trigonometrical Lines , Theorems and Formulas relating to the Sines ,

Division of the Circumference , General Ideas relating to the Trigonometrical Lines , Theorems and Formulas relating to the Sines ,

**Cosines**, Tangents , & c . Construction and Description of the Tables , Description of Table of ... Page 209

For the sake of brevity , they are called the

For the sake of brevity , they are called the

**cosine**, cotangent , and cosecant , of the arc AM , and are thus designated : MQ = cos AM , or cos ACM , cot AM , or cot ACM , cosec AM , or cosec ACM . In general , A being any arc or angle ... Page 210

When the point M is at A , or when the arc AM is zero , the three points T , M , P , are confounded with the point A ; whence it appears that the sine and tangent of an arc or B ܢ > M N zero , are zero , and the

When the point M is at A , or when the arc AM is zero , the three points T , M , P , are confounded with the point A ; whence it appears that the sine and tangent of an arc or B ܢ > M N zero , are zero , and the

**cosine**and secant of ... Page 211

X. The point M continuing to advance from D towards B , the sines diminish and the

X. The point M continuing to advance from D towards B , the sines diminish and the

**cosines**increase . Thus M'P ' is the sine of the arc AM ' , and M'Q , or CP ' its**cosine**, But the arc M'B is the supplement of AM ' , since AM ' + M'B ... Page 212

The versed sine AP is equal to the radius CA minus CP the

The versed sine AP is equal to the radius CA minus CP the

**cosine**AM : that is , ver - sin AM = R — cos AM . Now when the arc AM becomes AM ' the versed sine AP , becomes AP ' , that is equal to R + CP . But this expression cannot be ...### 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