Elements of Geometry and Trigonometry |
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Page 15
and since ACE is a straight line , the angle FCE will likewise be a right angle . Hence , the angle FCD is equal to the angle FCE ( Ax . 10. ) ; which can only be the case when the lines CD and CE coincide : therefore , the straight ...
and since ACE is a straight line , the angle FCE will likewise be a right angle . Hence , the angle FCD is equal to the angle FCE ( Ax . 10. ) ; which can only be the case when the lines CD and CE coincide : therefore , the straight ...
Page 20
An equilateral triangle is likewise equiangular , that is to say , has all its angles equal . Scholium . The equality of the triangles BAD , DAC , proves also that the angle BAD , is equal to DAC , and BDA to ADC , hence the latter two ...
An equilateral triangle is likewise equiangular , that is to say , has all its angles equal . Scholium . The equality of the triangles BAD , DAC , proves also that the angle BAD , is equal to DAC , and BDA to ADC , hence the latter two ...
Page 22
But the angle ACB is a right angle , by hypothesis ; therefore , BCF must likewise be a right angle . But if the adjacent angles BCA , BCF , are together equal to two right angles , ACF must be a straight line ( Prop . III . ) ...
But the angle ACB is a right angle , by hypothesis ; therefore , BCF must likewise be a right angle . But if the adjacent angles BCA , BCF , are together equal to two right angles , ACF must be a straight line ( Prop . III . ) ...
Page 24
So , likewise , are the two oblique lines AE , EB , the A two AF , FB , and so on . Therefore every point in the perpendicular is equally distant from the extremities A and B. H B E Secondly , Let I be a point out of the perpendicular .
So , likewise , are the two oblique lines AE , EB , the A two AF , FB , and so on . Therefore every point in the perpendicular is equally distant from the extremities A and B. H B E Secondly , Let I be a point out of the perpendicular .
Page 25
... by hypothesis ; the sum BAC + BAE is likewise equal to two right angles ( Prop . I. ) ; and taking away BAC from both , there will remain the angle ABD = BAE . E A C F C Again , the angles EGA , BGF , are equal ( Prop . IV . ) ...
... by hypothesis ; the sum BAC + BAE is likewise equal to two right angles ( Prop . I. ) ; and taking away BAC from both , there will remain the angle ABD = BAE . E A C F C Again , the angles EGA , BGF , are equal ( Prop . IV . ) ...
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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 |