Elements of Geometry and Trigonometry |
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Page 9
A straight line is the shortest distance from one point to another . 4. Every line which is not straight , or composed of straight lines , is a curved line . Thus , AB is a straight line ; ACDB is a broken line , or one composed of ...
A straight line is the shortest distance from one point to another . 4. Every line which is not straight , or composed of straight lines , is a curved line . Thus , AB is a straight line ; ACDB is a broken line , or one composed of ...
Page 13
... but this expression should not be employed , when there is any danger of confounding it with that of the line AB , which expresses the distance between the points A and B. The expression Ax ( B + C - D ) represents the product of A ...
... but this expression should not be employed , when there is any danger of confounding it with that of the line AB , which expresses the distance between the points A and B. The expression Ax ( B + C - D ) represents the product of A ...
Page 22
2d , Any two oblique lines , drawn on different sides of the perpen- dicular , cutting off equal distances on the other line , will be equal . 3d , Of two oblique lines , drawn at pleasure , that which is farther from the perpendicular ...
2d , Any two oblique lines , drawn on different sides of the perpen- dicular , cutting off equal distances on the other line , will be equal . 3d , Of two oblique lines , drawn at pleasure , that which is farther from the perpendicular ...
Page 23
The perpendicular measures the shortest distance of a point from a line . Cor . 2. From the same point to the same straight line , only two equal straight lines can be drawn ; for , if there could be more , we should have at least two ...
The perpendicular measures the shortest distance of a point from a line . Cor . 2. From the same point to the same straight line , only two equal straight lines can be drawn ; for , if there could be more , we should have at least two ...
Page 28
therefore , the side EG , which measures the distance of the parallels AB and CD at the point E , is equal to the side FH , which measures the distance of the same parallels at the point F. PROPOSITION XXIV . THEOREM .
therefore , the side EG , which measures the distance of the parallels AB and CD at the point E , is equal to the side FH , which measures the distance of the same parallels at the point F. PROPOSITION XXIV . THEOREM .
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Common terms and phrases
ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied 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 shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole
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, 1834 |
| Original from | the University of California |
| Digitized | 14 Oct 2010 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |