Elements of Geometry and Trigonometry |
From inside the book
Page 42
A tangent is a line which has but one point in common with the circumference . CD is a tangent . The point M , where the tangent touches the circumference , is called the point of contact . In like manner , two circumferences touch each ...
A tangent is a line which has but one point in common with the circumference . CD is a tangent . The point M , where the tangent touches the circumference , is called the point of contact . In like manner , two circumferences touch each ...
Page 47
Let BD be perpendicular to the B radius CA , at its extremity A ; then will it be tangent to the circumfeF K H A A straight line perpendicular to a radius , at its extremity , is a tangent to the circumference . E D rence .
Let BD be perpendicular to the B radius CA , at its extremity A ; then will it be tangent to the circumfeF K H A A straight line perpendicular to a radius , at its extremity , is a tangent to the circumference . E D rence .
Page 48
At a given point A , only one tangent AD can be drawn to the circumference ; for , if another could be drawn , it would not be perpendicular to the radius CA ( Book I. Prop . XIV . Sch . ) ; hence in reference to this new tangent ...
At a given point A , only one tangent AD can be drawn to the circumference ; for , if another could be drawn , it would not be perpendicular to the radius CA ( Book I. Prop . XIV . Sch . ) ; hence in reference to this new tangent ...
Page 50
All circles which have their centres on the right line AD . and which pass through the point A , are tangent to each other . For , they have only the point A common , and if through the point A , AE be drawn perpendicular to AD ...
All circles which have their centres on the right line AD . and which pass through the point A , are tangent to each other . For , they have only the point A common , and if through the point A , AE be drawn perpendicular to AD ...
Page 56
... or half the difference of BEC and DF . PROPOSITION XXI . THEOREM . D A. E F The angle formed by a tangent and a chord , is measured by half of the arc included between its sides . 4 - d Let BE be the tangent , and 56 GEOMETRY .
... or half the difference of BEC and DF . PROPOSITION XXI . THEOREM . D A. E F The angle formed by a tangent and a chord , is measured by half of the arc included between its sides . 4 - d Let BE be the tangent , and 56 GEOMETRY .
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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 |