Elements of Geometry and Trigonometry |
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Page 41
A straight line is said to be inscribed in a circle , when its extremities are in the cir- cumference , as AB . An inscribed angle is one which , like BAC , has its vertex in the circumference , and is formed by two chords . * Note .
A straight line is said to be inscribed in a circle , when its extremities are in the cir- cumference , as AB . An inscribed angle is one which , like BAC , has its vertex in the circumference , and is formed by two chords . * Note .
Page 42
An inscribed triangle is one which , like BAC , has its three angular points in the circumference . And , generally , an inscribed figure is one , of which all the angles have their vertices in the circumference .
An inscribed triangle is one which , like BAC , has its three angular points in the circumference . And , generally , an inscribed figure is one , of which all the angles have their vertices in the circumference .
Page 43
Hence the greatest line which can be inscribed in a circle is its diameter . PROPOSITION III . THEOREM . A straight line cannot meet the circumference of a circle in more than two points . For , if it could meet it in three , those ...
Hence the greatest line which can be inscribed in a circle is its diameter . PROPOSITION III . THEOREM . A straight line cannot meet the circumference of a circle in more than two points . For , if it could meet it in three , those ...
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 |