Elements of Geometry and Trigonometry |
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Page 57
4 - d Let BE be the tangent , and AC the chord . 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 ...
4 - d Let BE be the tangent , and AC the chord . 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 ...
Page 62
If the arc described with E as a centre , should be tangent to the line DG , the triangle would be right angled , and there would be but one solution . The problem would be impossible in all cases , if the side B were less than the ...
If the arc described with E as a centre , should be tangent to the line DG , the triangle would be right angled , and there would be but one solution . The problem would be impossible in all cases , if the side B were less than the ...
Page 64
Through a given point , to draw a tangent to a given circle . If the given point A lies in the circumference , draw the radius CA , and erect AD perpendicular to it : AD will be the tangent required ( Prop . IX . ) .
Through a given point , to draw a tangent to a given circle . If the given point A lies in the circumference , draw the radius CA , and erect AD perpendicular to it : AD will be the tangent required ( Prop . IX . ) .
Page 65
Now , if from the point O as a centre , with the radius OD , a circle be described , this circle will evidently be inscribed in the triangle ABC ; for the side AB , being perpendicular to the radius at its extremity , is a tangent ; and ...
Now , if from the point O as a centre , with the radius OD , a circle be described , this circle will evidently be inscribed in the triangle ABC ; for the side AB , being perpendicular to the radius at its extremity , is a tangent ; and ...
Page 95
If from the same point without a circle , a tangent and a secant be drawn , the tangent will be a mean proportional between the secant and its external segment . From the point O , let the tangent OA , and the secant OC be be drawn ...
If from the same point without a circle , a tangent and a secant be drawn , the tangent will be a mean proportional between the secant and its external segment . From the point O , let the tangent OA , and the secant OC be be drawn ...
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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 |