Elements of Geometry and Trigonometry |
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Page 41
Every straight line , CA , CE , CD , drawn from the centre to the circum- ference , is called a radius or semidiam- F E eter ; every line which , like AB , passes through the centre , and is terminated on both sides by the circumference ...
Every straight line , CA , CE , CD , drawn from the centre to the circum- ference , is called a radius or semidiam- F E eter ; every line which , like AB , passes through the centre , and is terminated on both sides by the circumference ...
Page 45
But two points are sufficient to determine the position of a straight line ; hence every straight line which passes through two of the points just mentioned , will necessarily pass througl . the third , and be perpendicular to the chord ...
But two points are sufficient to determine the position of a straight line ; hence every straight line which passes through two of the points just mentioned , will necessarily pass througl . the third , and be perpendicular to the chord ...
Page 46
Through three given points not in the same straight line , one cir- cumference may always be made to pass , and but one . Let A , B , and C , be the given points . Draw AB , BC , and bisect these straight lines by the perpendiculars DE ...
Through three given points not in the same straight line , one cir- cumference may always be made to pass , and but one . Let A , B , and C , be the given points . Draw AB , BC , and bisect these straight lines by the perpendiculars DE ...
Page 49
If two circles cut each other in two points , the line which passes through their centres , will be perpendicular to ... Now if a perpendicular 2 be erected from the middle of this chord , it will pass through each of the two centres C ...
If two circles cut each other in two points , the line which passes through their centres , will be perpendicular to ... Now if a perpendicular 2 be erected from the middle of this chord , it will pass through each of the two centres C ...
Page 50
All circles which have their centres on the right line AD , and which pass through the point A , are tangent to each other . For , they have only the point A common , and it through the point A , AE be drawn perpendicular to AD ...
All circles which have their centres on the right line AD , and which pass through the point A , are tangent to each other . For , they have only the point A common , and it through the point A , AE be drawn perpendicular to AD ...
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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 |