Elements of Geometry and Trigonometry |
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Page 10
When a straight line AB meets another straight line CD , so as to make the adjacent angles BAC , BAD , equal to each other , each of those angles is called a right angle ; and the line AB is said to be perpendicular to CD . 11.
When a straight line AB meets another straight line CD , so as to make the adjacent angles BAC , BAD , equal to each other , each of those angles is called a right angle ; and the line AB is said to be perpendicular to CD . 11.
Page 14
A B At the point C , erect CE perpendicular to AB . The angle ACD is the sum of the an-gles ACE , ECD : therefore ACD + DCB is the sum of the three angles ACE , ECD , DCB : but the first of these three angles is a right angle , and the ...
A B At the point C , erect CE perpendicular to AB . The angle ACD is the sum of the an-gles ACE , ECD : therefore ACD + DCB is the sum of the three angles ACE , ECD , DCB : but the first of these three angles is a right angle , and the ...
Page 16
... if four right angles were formed about the point C , by two lines perpendicular to each other , the same space would be occupied by the four right angles , as by the successive angles ACB , BCD , DCE , ECF , FCA .
... if four right angles were formed about the point C , by two lines perpendicular to each other , the same space would be occupied by the four right angles , as by the successive angles ACB , BCD , DCE , ECF , FCA .
Page 20
... hence the latter two are right angles ; therefore , the line drawn from the vertex of an isosceles triangle to the middle point of its base , is perpendicular to the base , and divides the angle at the vertex into two equal parts .
... hence the latter two are right angles ; therefore , the line drawn from the vertex of an isosceles triangle to the middle point of its base , is perpendicular to the base , and divides the angle at the vertex into two equal parts .
Page 22
From a given point , without a straight line , only one perpendicular can be drawn to that line . Let A be the point , and DE the given line . A Let us suppose that we can draw two perpendiculars , AB , AC .
From a given point , without a straight line , only one perpendicular can be drawn to that line . Let A be the point , and DE the given line . A Let us suppose that we can draw two perpendiculars , AB , AC .
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre A. M. Legendre No preview available - 2017 |
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 produced 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 | Harvard University |
| Digitized | 9 Dec 2008 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |