Elements of Geometry and Trigonometry |
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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
A straight line perpendicular to a radius , at its extremity , is a tangent to the circumference . Let BD be perpendicular to the B radius CA , at its extremity A ; then will it be tangent to the circumfe- rence .
A straight line perpendicular to a radius , at its extremity , is a tangent to the circumference . Let BD be perpendicular to the B radius CA , at its extremity A ; then will it be tangent to the circumfe- 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 it 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 it through the point A , AE be drawn perpendicular to AD ...
Page 56
... or half the difference of BEC and DF . A. E PROPOSITION XXI . THEOREM . The angle formed by a tangent and a chord , is measured by half of the arc included between its sides . Let BE be the tangent , and AC the chord 56 GEOMETRY .
... or half the difference of BEC and DF . A. E PROPOSITION XXI . THEOREM . The angle formed by a tangent and a chord , is measured by half of the arc included between its sides . Let BE be the tangent , and AC the chord 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 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 |