## Elements of Geometry and Trigonometry |

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Page 68

Similar figures are those which have the angles of the one equal to the angles of the other , each to each , and the sides about ... BOOK IV Planes and

Similar figures are those which have the angles of the one equal to the angles of the other , each to each , and the sides about ... BOOK IV Planes and

**Solid Angles**, Polyedrons, 400mm The Proportions of Figures and the Measurement of Areas, Page 96

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

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

**angled**, the one at D , the 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

F The proposition requires demonstration only when the plane angle , which is compared to the sum of the other two , is greater than either of them . Therefore suppose the

F The proposition requires demonstration only when the plane angle , which is compared to the sum of the other two , is greater than either of them . Therefore suppose the

**solid angle**S to be formed by three plane angles ASB , ASC , BSC ... 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 ...### What people are saying - Write a review

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### Common terms and phrases

ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole