## Elements of Geometry and Trigonometry |

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Page 96

For , drawing AE , the triangles ABD , AEC , are right

For , drawing AE , the triangles ABD , AEC , are right

**angled**, the one at D , the E other at A : also the**angle**B - E ; these ... The product of three lines is sometimes called a**solid**, for a reason that shall be seen afterwards . 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 . Page 138

Therefore suppose the

Therefore suppose the

**solid angle**S to be formed by three plane angles ASB , ASC , BSC , whereof the angle ASB is A the greatest ; we are to show that ASB ASC + BSC . P E D 1 PROPOSITION XIX . THEOREM . If a**solid angle**is formed by ... Page 139

The sum of the plane angles which form a

The sum of the plane angles which form a

**solid angle**is always less than four right angles . Cut the**solid angle**S by any plane ABCDE ; from O , a point in that plane , draw to the several angles the straight lines AO , OB , OC , OD ... Page 140

Let the angle ASC = DTF , the angle ASB DTE , and the angle BSC = ETF ; then will the inclination of the planes ASC ... If two

Let the angle ASC = DTF , the angle ASB DTE , and the angle BSC = ETF ; then will the inclination of the planes ASC ... If two

**solid angles**are contained by three plane angles , respectively equal to each other , and if 140 GEOMETRY .### 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