Elements of Geometry and Trigonometry |
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Page 10
The point of intersection A is the vertex of the angle , and the lines AB , AC , are its sides .. -B The angle is sometimes designated simply by the letter at the vertex A ; sometimes by the three letters BAC , or CAB , the letter at ...
The point of intersection A is the vertex of the angle , and the lines AB , AC , are its sides .. -B The angle is sometimes designated simply by the letter at the vertex A ; sometimes by the three letters BAC , or CAB , the letter at ...
Page 15
PROPOSITION IV . THEOREM . When two straight lines intersect each other , the opposite or ver tical angles , which they form , are equal . Let AB and DE be two straight lines , intersecting BOOK I. 15.
PROPOSITION IV . THEOREM . When two straight lines intersect each other , the opposite or ver tical angles , which they form , are equal . Let AB and DE be two straight lines , intersecting BOOK I. 15.
Page 16
The four angles formed about a point by two straight lines , which intersect each other , are together equal to four right angles : for the sum of the two angles ACE , ECB , is equal to two right angles ; and the sum of the other two ...
The four angles formed about a point by two straight lines , which intersect each other , are together equal to four right angles : for the sum of the two angles ACE , ECB , is equal to two right angles ; and the sum of the other two ...
Page 17
Hence , the point D , falling at the same time in the two straight lines BA and CA , must fall at their intersection A : hence , the two triangles EDF , BAC , coincide with each other , and are therefore equal ( Ax . 13. ) . Cor .
Hence , the point D , falling at the same time in the two straight lines BA and CA , must fall at their intersection A : hence , the two triangles EDF , BAC , coincide with each other , and are therefore equal ( Ax . 13. ) . Cor .
Page 49
If two circles cut each other in two points , the line which passes through their centres , will be perpendicular to the chord which joins the points of intersection , and will divide it into two equal parts .
If two circles cut each other in two points , the line which passes through their centres , will be perpendicular to the chord which joins the points of intersection , and will divide it into two equal parts .
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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 |