Elements of Geometry and Trigonometry |
From inside the book
Page 13
The whole is greater than any of its parts . 9. The whole is equal to the sum of all its parts . 10. All right angles are equal to each other . 11 From one point to another only one straight line can be drawn . 12.
The whole is greater than any of its parts . 9. The whole is equal to the sum of all its parts . 10. All right angles are equal to each other . 11 From one point to another only one straight line can be drawn . 12.
Page 14
Two straight lines , which have two points common , coincide with each other throughout their whole extent , and form one ana the same straight line . B E I D pose , however , that on being produced , these 14 GEOMETRY .
Two straight lines , which have two points common , coincide with each other throughout their whole extent , and form one ana the same straight line . B E I D pose , however , that on being produced , these 14 GEOMETRY .
Page 21
But the part cannot be equal to the whole ( Ax . 8. ) ; hence , there is no inequality between the sides BA , AC ; therefore , the triangle BAC is isosceles . PROPOSITION XIII . THEOREM .
But the part cannot be equal to the whole ( Ax . 8. ) ; hence , there is no inequality between the sides BA , AC ; therefore , the triangle BAC is isosceles . PROPOSITION XIII . THEOREM .
Page 22
and the line CD would coincide with CE ; otherwise , a part would be equal to the whole , which is impossible ( Ax . 8. ) . A C B PROPOSITION XV . THEOREM . If from a point without a straight line , a perpendicular be let fall on the ...
and the line CD would coincide with CE ; otherwise , a part would be equal to the whole , which is impossible ( Ax . 8. ) . A C B PROPOSITION XV . THEOREM . If from a point without a straight line , a perpendicular be let fall on the ...
Page 34
Thus , of two magnitudes , one of them may be considered to be divided into some number of equal parts , each of the same kind as the whole , and one of those parts being considered as an unit of measure , the inagnitude may be ...
Thus , of two magnitudes , one of them may be considered to be divided into some number of equal parts , each of the same kind as the whole , and one of those parts being considered as an unit of measure , the inagnitude may be ...
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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 |