Elements of Geometry and Trigonometry |
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Page 57
From A , the point of contact , draw the diameter AD . The angle BAD is a right angle ( Prop . IX . ) , and is measured by half the semicircumference AMD ; the angle DAC is measured by the half of DC : hence , BAD + DAC , or BAC ...
From A , the point of contact , draw the diameter AD . The angle BAD is a right angle ( Prop . IX . ) , and is measured by half the semicircumference AMD ; the angle DAC is measured by the half of DC : hence , BAD + DAC , or BAC ...
Page 66
If the given angle were a right angle , the required segment would be a semicircle , described on AB as a diameter . PROBLEM XVII . To find the numerical ratio of two given straight lines , these lines being supposed to have a common ...
If the given angle were a right angle , the required segment would be a semicircle , described on AB as a diameter . PROBLEM XVII . To find the numerical ratio of two given straight lines , these lines being supposed to have a common ...
Page 90
If from a point A , in the circumference of a circle , two chords AB , AC , be drawn to the extremities of a diameter BC , the triangle BAC will be right angled at A ( Book III . Prop . B D с XVIII . Cor . 2. ) ...
If from a point A , in the circumference of a circle , two chords AB , AC , be drawn to the extremities of a diameter BC , the triangle BAC will be right angled at A ( Book III . Prop . B D с XVIII . Cor . 2. ) ...
Page 96
In every triangle , the rectangle contained by two sides is equivalent to the rectangle contained by the diameter of the circumscribed circle , and the perpendicular let fall upon the third side . In the triangle ABC , let AD be drawn ...
In every triangle , the rectangle contained by two sides is equivalent to the rectangle contained by the diameter of the circumscribed circle , and the perpendicular let fall upon the third side . In the triangle ABC , let AD be drawn ...
Page 99
For , the perpendicular EG , let fall from a point in the circumference upon the diameter , is a mean proportional between DE EF , the two segments of the diameter ( Prop . XXIII . Co. ) ; and these segments are equal to the given lines ...
For , the perpendicular EG , let fall from a point in the circumference upon the diameter , is a mean proportional between DE EF , the two segments of the diameter ( Prop . XXIII . Co. ) ; and these segments are equal to the given lines ...
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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 |