Elements of Geometry and Trigonometry |
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Page 45
Sch . ) ; and hence that the arc AH is greater than AD ; since the whole is greater than its part . Scholium . The arcs here treated of are each less than the semicircumference . If they were greater , the reverse property would have ...
Sch . ) ; and hence that the arc AH is greater than AD ; since the whole is greater than its part . Scholium . The arcs here treated of are each less than the semicircumference . If they were greater , the reverse property would have ...
Page 48
If the two parallels DE , IL , are tangents , the one at H , the other at K , draw the parallel secant AB ; and , from what has just been shown , we shall have MH = HP , MK = KP ; and hence the whole arc HMK = HPK .
If the two parallels DE , IL , are tangents , the one at H , the other at K , draw the parallel secant AB ; and , from what has just been shown , we shall have MH = HP , MK = KP ; and hence the whole arc HMK = HPK .
Page 51
... AB is equal to DE ; hence AI must be equal to AB , or a part to the whole , which is absurd ( Ax . 8. ) ... if two angles at the centre are to each other in the proportion of two whole numbers , the intercepted arcs will be to each ...
... AB is equal to DE ; hence AI must be equal to AB , or a part to the whole , which is absurd ( Ax . 8. ) ... if two angles at the centre are to each other in the proportion of two whole numbers , the intercepted arcs will be to each ...
Page 52
Therefore the whole arc AB will be to the whole arc DE , as 7 is to 4. But the same reasoning would evidently apply , if in place of 7 and 4 any numbers whatever were employed ; hence , if the ratio of the angles ACB , DCE , can be ...
Therefore the whole arc AB will be to the whole arc DE , as 7 is to 4. But the same reasoning would evidently apply , if in place of 7 and 4 any numbers whatever were employed ; hence , if the ratio of the angles ACB , DCE , can be ...
Page 53
The arcs AB , AI , will be to each other as two whole numbers , and by the preceding theorem , we shall have , the angle ACB : angle ACI :: arc AB arc AI . Comparing these two proportions with each other , we see that the antecedents ...
The arcs AB , AI , will be to each other as two whole numbers , and by the preceding theorem , we shall have , the angle ACB : angle ACI :: arc AB arc AI . Comparing these two proportions with each other , we see that the antecedents ...
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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 |