Elements of Geometry and Trigonometry |
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Page 41
From the definition of a circle , it follows that all the radii are equal ; that all the diameters are equal also , and each double of the radius . 3. A portion of the circumference , such as FHG , is called an arc .
From the definition of a circle , it follows that all the radii are equal ; that all the diameters are equal also , and each double of the radius . 3. A portion of the circumference , such as FHG , is called an arc .
Page 42
Every diameter divides 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 ...
Every diameter divides 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 ...
Page 43
Every chord is less than the diameter . Let AD be any chord . Draw the radii CA , CD , to its extremities . We shall then have AD < AC + CD ( Book I. Prop . VII . * ) ; A or AD < AB . Cor . Hence the greatest line which can be inscribed ...
Every chord is less than the diameter . Let AD be any chord . Draw the radii CA , CD , to its extremities . We shall then have AD < AC + CD ( Book I. Prop . VII . * ) ; A or AD < AB . Cor . Hence the greatest line which can be inscribed ...
Page 44
For , since the diameters AB , EF , are equal , the semi- circle AMDB may be applied M ཤིས་ ཡོད་ ས exactly to the semicircle ENGF , and the curve line AMDB will coincide entirely with the curve line ENGF . But the part AMD is equal to ...
For , since the diameters AB , EF , are equal , the semi- circle AMDB may be applied M ཤིས་ ཡོད་ ས exactly to the semicircle ENGF , and the curve line AMDB will coincide entirely with the curve line ENGF . But the part AMD is equal to ...
Page 54
Draw the diameter AE , and the radii CB , CD . The angle BCE , being exterior to the triangle ABC , is equal to the sum of the two interior angles CAB , ABC ( Book I. Prop . XXV . Cor . 6. ) : but the triangle BAC being isosceles ...
Draw the diameter AE , and the radii CB , CD . The angle BCE , being exterior to the triangle ABC , is equal to the sum of the two interior angles CAB , ABC ( Book I. Prop . XXV . Cor . 6. ) : but the triangle BAC being isosceles ...
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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 |