Elements of Geometry and Trigonometry |
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Page 5
Polyedrons , 142 BOOK VIII . The three round bodies , 166 BOOK IX . 188 or Spherical Triangles and Spherical Polygons , APPENDIX . The regular Polyedrons , 205 PLANE TRIGONOMETRY . 207 Division of the Circumference , General.
Polyedrons , 142 BOOK VIII . The three round bodies , 166 BOOK IX . 188 or Spherical Triangles and Spherical Polygons , APPENDIX . The regular Polyedrons , 205 PLANE TRIGONOMETRY . 207 Division of the Circumference , General.
Page 6
207 Division of the Circumference , General Ideas relating to the Trigonometrical Lines , Theorems and Formulas relating to the Sines , Cosines , Tan . 208 gents , & c . 215 223 224 228 231 Construction and Description of the Tables ...
207 Division of the Circumference , General Ideas relating to the Trigonometrical Lines , Theorems and Formulas relating to the Sines , Cosines , Tan . 208 gents , & c . 215 223 224 228 231 Construction and Description of the Tables ...
Page 41
The circumference of a circle is a curve line , all the points of which are G equally distant from a point within , called the certre . The circle is the space icrminated by A this curved line . * 2. Every straight line , CA , CE , CD ...
The circumference of a circle is a curve line , all the points of which are G equally distant from a point within , called the certre . The circle is the space icrminated by A this curved line . * 2. Every straight line , CA , CE , CD ...
Page 42
An inscribed triangle is one which , like BAC , has its three angular points in the circumference . And , generally , an inscribed figure is one , of which all the angles have their vertices in the circumference .
An inscribed triangle is one which , like BAC , has its three angular points in the circumference . And , generally , an inscribed figure is one , of which all the angles have their vertices in the circumference .
Page 43
A straight line cannot meet the circumference of a circle in more than two points . For , if it could meet it in three , those three points would be equally distant from the centre ; and hence , there would be three equal straight lines ...
A straight line cannot meet the circumference of a circle in more than two points . For , if it could meet it in three , those three points would be equally distant from the centre ; and hence , there would be three equal straight lines ...
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Common terms and phrases
ABCD adjacent altitude angled triangle base become Book called centre chord circle circumference circumscribed common cone consequently contained corresponding 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 logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid 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
Popular passages
Page 18 - If two triangles have two sides of the one equal to two sides of the...
Page 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Page 31 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon...
Page 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 168 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 287 - How many square feet are there in the convex surface of the frustum of a square pyramid, whose slant height is 10 feet, each side of the lower base 3 feet 4 inches, and each side of the upper base 2 feet 2 inches ? Ans.
Page 64 - To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B by the lines AO and BO, meeting at the point 0.
Bibliographic information
| Title | Elements of Geometry and Trigonometry |
| Author | Adrien Marie Legendre |
| Editor | Charles Davies |
| Translated by | David Brewster |
| Edition | 4 |
| Publisher | A.S. Barnes and Company, 1837 |
| Original from | the University of Michigan |
| Digitized | 9 Jun 2007 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |