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 inscribed angle is one ...
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 inscribed angle is one ...
Page 42
DOO ( 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 ...
DOO ( 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 ...
Page 43
Every chord is less than the diameter . Let AD be any chord . CA , CD , to its extremities . have AD < AC + CD ( Book I. Prop . VII . * ) ; A or AD < AB . Draw the radii We shall then E Cor . Hence the greatest line which can be ...
Every chord is less than the diameter . Let AD be any chord . CA , CD , to its extremities . have AD < AC + CD ( Book I. Prop . VII . * ) ; A or AD < AB . Draw the radii We shall then E Cor . Hence the greatest line which can be ...
Page 44
N DD BE K For , since the diameters AB , EF , are equal , the semicircle AMDB may be applied 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 the ...
N DD BE K For , since the diameters AB , EF , are equal , the semicircle AMDB may be applied 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 the ...
Page 54
Draw the diameter AE , and the radii CB , CD . E The angle BCE , being exterior to the triangle ABC , is equal to the sum of the two interior angles CAB , ABC ( Book I. B Prop . XXV . Cor . 6. ) : but the triangle BAC being isosceles ...
Draw the diameter AE , and the radii CB , CD . E The angle BCE , being exterior to the triangle ABC , is equal to the sum of the two interior angles CAB , ABC ( Book I. B 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 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 |