Elements of Geometry and Trigonometry |
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Page 19
Now , there may be three cases in the proposition , according as the point G falls without the triangle ABC , or upon its base BC , or within it . First Case . The straight line GC < GI + IC , and the straight line ABAI + IB ; therefore ...
Now , there may be three cases in the proposition , according as the point G falls without the triangle ABC , or upon its base BC , or within it . First Case . The straight line GC < GI + IC , and the straight line ABAI + IB ; therefore ...
Page 20
Let the side BA be equal to the side AC ; then will the angle C be equal to the angle B. For , join the vertex A , and D the middle point of the base BC . Then , the triangles BAD , DAC , will have all the sides of the one equal to ...
Let the side BA be equal to the side AC ; then will the angle C be equal to the angle B. For , join the vertex A , and D the middle point of the base BC . Then , the triangles BAD , DAC , will have all the sides of the one equal to ...
Page 21
1 that side is generally assumed as the base , which is not equal to either of the other two . PROPOSITION XII . THEOREM . Conversely , if two angles of a triangle are equal , the sides opposite them are also equal , and the triangle is ...
1 that side is generally assumed as the base , which is not equal to either of the other two . PROPOSITION XII . THEOREM . Conversely , if two angles of a triangle are equal , the sides opposite them are also equal , and the triangle is ...
Page 42
... the circle and its circumference into two equal parts . Let AEDF be a circle , and AB a diameter . Now , if the figure AEB be applied to AFB , their common base AB retaining its position , the curve line AEB must fall exactly on ...
... the circle and its circumference into two equal parts . Let AEDF be a circle , and AB a diameter . Now , if the figure AEB be applied to AFB , their common base AB retaining its position , the curve line AEB must fall exactly on ...
Page 68
The base of any rectilineal figure , is the side on which the figure is supposed to stand . 5. The altitude of a triangle is the perpendicular let fall from the vertex of an angle on the opposite side , taken as a base .
The base of any rectilineal figure , is the side on which the figure is supposed to stand . 5. The altitude of a triangle is the perpendicular let fall from the vertex of an angle on the opposite side , taken as a base .
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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 |