Elements of Geometry and Trigonometry |
From inside the book
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 Solid Angles, Polyedrons, 400mm The Proportions of Figures and the Measurement of Areas,
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 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 .
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 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 .
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 solid angle S to be formed by three plane angles ASB , ASC , BSC ...
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 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 ...
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 ...
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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
Bibliographic information
| Title | Elements of Geometry and Trigonometry DAVIES' COURSE OF MATHEMATICS |
| Author | Adrien Marie Legendre |
| Editor | Charles Davies |
| Translated by | David Brewster |
| Publisher | A.S. Barnes and Company, 1839 |
| Original from | Harvard University |
| Digitized | 14 Jan 2008 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |