Elements of Geometry and Trigonometry |
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Page 46
... are equal ; therefore the circumference described from the centre O , with the radius OB , will pass through the three given points A ... not in the same straight line : we say farther , that but one can be described through them .
... are equal ; therefore the circumference described from the centre O , with the radius OB , will pass through the three given points A ... not in the same straight line : we say farther , that but one can be described through them .
Page 49
And , whenever the triangle CAD can be constructed , it is plain that the circles described from the centres C and D , will cut each other in A and B. E D PROPOSITION XIII . THEOREM . If the distance between the BOOK III . 49.
And , whenever the triangle CAD can be constructed , it is plain that the circles described from the centres C and D , will cut each other in A and B. E D PROPOSITION XIII . THEOREM . If the distance between the BOOK III . 49.
Page 52
Whatever be the ratio of two angles , they will always be to each other as the arcs intercepted between their sides ; the arcs being described from the vertices of the angles as centres with equal radii . Let ACB be the greater and ACD ...
Whatever be the ratio of two angles , they will always be to each other as the arcs intercepted between their sides ; the arcs being described from the vertices of the angles as centres with equal radii . Let ACB be the greater and ACD ...
Page 53
It is only necessary that , in the comparison of angles with each other , the arcs which serve to measure them , be described with equal radii , as is implied in all the foregoing propositions . Scholium 1. It appears most natural to ...
It is only necessary that , in the comparison of angles with each other , the arcs which serve to measure them , be described with equal radii , as is implied in all the foregoing propositions . Scholium 1. It appears most natural to ...
Page 62
But if the angle C is acute , and the side B less than A , then the arc described from the centre E , with the radius EF = B , will cut the side DF in two points F and G , lying on the same side of D : hence there will be two triangles ...
But if the angle C is acute , and the side B less than A , then the arc described from the centre E , with the radius EF = B , will cut the side DF in two points F and G , lying on the same side of D : hence there will be two triangles ...
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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 |