## 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

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 77

This proposition is equivalent to the algebraical

This proposition is equivalent to the algebraical

**formula**, ( a - b ) 2 = a2 - 2ab + b2 . J. PROPOSITION X. THEOREM . D The rectangle contained by the sum and the difference of two lines , is equivalent to the difference of the squares ... Page 207

We shall first explain the properties of those lines , and the principal

We shall first explain the properties of those lines , and the principal

**formulas**derived from them ;**formulas**which are of great use in all the branches of mathematics , and which even furnish means of improvement to algebraical ... Page 211

... may both be expressed analytically , and in the same general

... may both be expressed analytically , and in the same general

**formula**, it is necessary to consider all lines which are estimated in one direction as positive , and those which are estimated in the contrary direction as negative . Page 212

But this expression cannot be derived from the

But this expression cannot be derived from the

**formula**, S ' B N 10 ( R E M S T A ver - sin AM - R - cos AM , unless we suppose the cosine AM to become negative as soon as the arc AM becomes greater than a quadrant .### 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