## Elements of Geometry and Trigonometry |

### From inside the book

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Page 5

Planes and

Planes and

**Solid**Angles , Polyedrons , The Proportions of Figures and the Measurement of Areas , - Problems relating to the Fourth Book , Oman BOOK V. Regular Polygons and the Measurement of the Circle , BOOK VI . Page 9

A

A

**solid**or body is that which has length , breadth , and thickness ; and therefore combines the three dimensions of extension . 9. When two straight lines , AB , AC , 2 The principles, Page 96

therefore the product of three sides of a triangle is equal to its area multiplied by twice the diameter of the circumscribed circle . The product of three lines is sometimes called a

therefore the product of three sides of a triangle is equal to its area multiplied by twice the diameter of the circumscribed circle . The product of three lines is sometimes called a

**solid**, for a reason that shall be seen afterwards . Page 125

... whole circumference must be 3.1415926 , when the diameter is 1 : hence the ratio of the circumference to the diameter , formerly expressed by π , is equal to 3.1415926 . BOOK VI . PLANES AND

... whole circumference must be 3.1415926 , when the diameter is 1 : hence the ratio of the circumference to the diameter , formerly expressed by π , is equal to 3.1415926 . BOOK VI . PLANES AND

**SOLID**ANGLES . Definitions . BOOK V. 125. Page 126

PLANES AND

PLANES AND

**SOLID**ANGLES . Definitions . 1. A straight line is perpendicular to a plane , when it is perpendicular to all the straight lines which pass through its foot in the plane . Conversely , the plane is perpendicular to the line .### 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