Elements of Geometry and Trigonometry |
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Page 13
A number placed before a line , or a quantity , serves as a multiplier to that line or quantity ; thus , 3AB signifies that the line AB is taken three times ; A signifies the half of the angle A. The square of the line AB is designated ...
A number placed before a line , or a quantity , serves as a multiplier to that line or quantity ; thus , 3AB signifies that the line AB is taken three times ; A signifies the half of the angle A. The square of the line AB is designated ...
Page 23
therefore , AB , the half of ABF , is shorter than AC , the half of ACF ; hence , the per- pendicular is shorter than any oblique line . Secondly . Let us suppose BC = BE ; then will the triangle CAB be equal to the the triangle BAE ...
therefore , AB , the half of ABF , is shorter than AC , the half of ACF ; hence , the per- pendicular is shorter than any oblique line . Secondly . Let us suppose BC = BE ; then will the triangle CAB be equal to the the triangle BAE ...
Page 47
D M A In the right angled triangles CAF , DCG , the hypothenuses CA , CD , are equal ; and the side AF , the half of AB , is equal to the side DG , the half of DE : hence the triangles are equal , and CF is equal to CG ( Book I. Prop .
D M A In the right angled triangles CAF , DCG , the hypothenuses CA , CD , are equal ; and the side AF , the half of AB , is equal to the side DG , the half of DE : hence the triangles are equal , and CF is equal to CG ( Book I. Prop .
Page 54
An inscribed angle is measured by half the arc included between its sides . Let BAD be an inscribed angle , and let us first suppose that the centre of the cir- cle lies within the angle BAD . Draw the diameter AE , and the radii CB ...
An inscribed angle is measured by half the arc included between its sides . Let BAD be an inscribed angle , and let us first suppose that the centre of the cir- cle lies within the angle BAD . Draw the diameter AE , and the radii CB ...
Page 55
All the angles BAC , BDC , BEC , inscribed in the same segment are equal ; because they are all measured by the half of the same arc BOC . B Cor . 2. Every angle BAD , inscribed in a semicircle is a right angle ; because it is mea- ...
All the angles BAC , BDC , BEC , inscribed in the same segment are equal ; because they are all measured by the half of the same arc BOC . B Cor . 2. Every angle BAD , inscribed in a semicircle is a right angle ; because it is mea- ...
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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 |