Elements of Geometry and Trigonometry |
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Page 116
Cor It is evident that the circumscribed square is greater than the circumscribed octagon by the four triangles , Cnp , kDg , hEf , Git ; and if a regular polygon of sixteen sides be circumscribed about the circle , we may prove in a ...
Cor It is evident that the circumscribed square is greater than the circumscribed octagon by the four triangles , Cnp , kDg , hEf , Git ; and if a regular polygon of sixteen sides be circumscribed about the circle , we may prove in a ...
Page 117
Let P represent the circumscribed polygon , and p the inscribed polygon : then , since the triangles aOb , AOB , are like parts of P and p , we shall have aOb · AOB :: P : p ( Book II . Prop . XI . ) : But the triangles being similar ...
Let P represent the circumscribed polygon , and p the inscribed polygon : then , since the triangles aOb , AOB , are like parts of P and p , we shall have aOb · AOB :: P : p ( Book II . Prop . XI . ) : But the triangles being similar ...
Page 118
Since the circumscribed polygon has the same number of sides as the corresponding inscribed polygon , and since the two polygons are regular , they will be similar ( Prop . I. ) ; and therefore when they become equal , they will exactly ...
Since the circumscribed polygon has the same number of sides as the corresponding inscribed polygon , and since the two polygons are regular , they will be similar ( Prop . I. ) ; and therefore when they become equal , they will exactly ...
Page 119
The perimeters of two regular polygons , having the same number of sides , are to each other as the radii of the circumscribed circles , and also , as the radii of the inscribed circles ; and their areas are to each other as the squares ...
The perimeters of two regular polygons , having the same number of sides , are to each other as the radii of the circumscribed circles , and also , as the radii of the inscribed circles ; and their areas are to each other as the squares ...
Page 120
... until the number of sides of the polygons shall be indefinitely increased , the perimeters of the polygons will become equal to the circumferences of the circumscribed circles ( Prop . VIII . Cor . 2. ) , and we shall have circ .
... until the number of sides of the polygons shall be indefinitely increased , the perimeters of the polygons will become equal to the circumferences of the circumscribed circles ( Prop . VIII . Cor . 2. ) , and we shall have circ .
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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 |