Elements of Geometry and Trigonometry |
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Page 38
... then will M ± N : M :: P ± Q : P . For , from the first proportion , we have MxQ = NxP , or NxP = MxQ ; Add each of the members of the last equation to , or subtract it from M.P , and we shall have , M.P ± N.P = M.P ± M.Q ; or ( MN ) ...
... then will M ± N : M :: P ± Q : P . For , from the first proportion , we have MxQ = NxP , or NxP = MxQ ; Add each of the members of the last equation to , or subtract it from M.P , and we shall have , M.P ± N.P = M.P ± M.Q ; or ( MN ) ...
Page 128
Taking the first equation from the second , and observing that the triangles APC , APB , which are both right angled at P , give AC - PC - AP2 , and AB2 - PB2 = AP2 ; we shall have AP2 + AP2 = 2AQ2 — 2PQ2 . Therefore , by taking the ...
Taking the first equation from the second , and observing that the triangles APC , APB , which are both right angled at P , give AC - PC - AP2 , and AB2 - PB2 = AP2 ; we shall have AP2 + AP2 = 2AQ2 — 2PQ2 . Therefore , by taking the ...
Page 211
The arc or angle A has for its supplement 180 ° -A : hence generally , we have sin A sin ( 180 ° -A . ) The same property might also be expressed by the equation sin ( 90 ° + B ) = sin ( 90 ° -B ) , B being the arc DM or its equal DM ' ...
The arc or angle A has for its supplement 180 ° -A : hence generally , we have sin A sin ( 180 ° -A . ) The same property might also be expressed by the equation sin ( 90 ° + B ) = sin ( 90 ° -B ) , B being the arc DM or its equal DM ' ...
Page 217
The formulas of the preceding Article , combined with each other and with the equation sin 2A + cos 2A = R2 , furnish some others worthy of attention . First we have R2 + tang2 AR2 + R1 R2 ( sin2 A + cos2 A ) . cos 2A cos A cos2 A R2 ...
The formulas of the preceding Article , combined with each other and with the equation sin 2A + cos 2A = R2 , furnish some others worthy of attention . First we have R2 + tang2 AR2 + R1 R2 ( sin2 A + cos2 A ) . cos 2A cos A cos2 A R2 ...
Page 236
But from the equation c = 10 - b , we have c - 10 -- b : hence if we substitute for b its value , we shall have a — b = a + c - 10 , which agrees with the enunciation . When we wish the arithmetical complement of a logarithm , we may ...
But from the equation c = 10 - b , we have c - 10 -- b : hence if we substitute for b its value , we shall have a — b = a + c - 10 , which agrees with the enunciation . When we wish the arithmetical complement of a logarithm , we may ...
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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 |