Elements of Geometry and Trigonometry |
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Page 43
CA , CD , to its extremities . have AD < AC + CD ( Book I. Prop . VII . * ) ; A or AD < AB . Draw the radii We shall then E Cor . Hence the greatest line which can be inscribed in a circle is its diameter . PROPOSITION III . THEOREM .
CA , CD , to its extremities . have AD < AC + CD ( Book I. Prop . VII . * ) ; A or AD < AB . Draw the radii We shall then E Cor . Hence the greatest line which can be inscribed in a circle is its diameter . PROPOSITION III . THEOREM .
Page 45
... distant from its two extremities A and B ( Book I. Prop . XVI . ) . Now , G is one of these points ; therefore AG , BG , are equal . But if the chord AG is equal to the chord GB , the arc AG will be equal to the arc GB ( Prop . IV . ) ...
... distant from its two extremities A and B ( Book I. Prop . XVI . ) . Now , G is one of these points ; therefore AG , BG , are equal . But if the chord AG is equal to the chord GB , the arc AG will be equal to the arc GB ( Prop . IV . ) ...
Page 47
Let BD be perpendicular to the B radius CA , at its extremity A ; then will it be tangent to the circumfeF K H A A straight line perpendicular to a radius , at its extremity , is a tangent to the circumference . E D rence .
Let BD be perpendicular to the B radius CA , at its extremity A ; then will it be tangent to the circumfeF K H A A straight line perpendicular to a radius , at its extremity , is a tangent to the circumference . E D rence .
Page 57
... being each equally distant from the extremities A and B , must both lie in the perpendicular raised from the middle of AB ( Book I. Prop . XVI . Cor . ) . But only one straight line can pass through two given points ; hence the line ...
... being each equally distant from the extremities A and B , must both lie in the perpendicular raised from the middle of AB ( Book I. Prop . XVI . Cor . ) . But only one straight line can pass through two given points ; hence the line ...
Page 59
... D are each equally distant from the extremities A and B of the chord AB ; hence the line CD bisects the chord at right angles ( Book I. Prop . XVI . Cor . ) ; hence , it bisects the arc AB in the point E ( Prop . VI . ) . Secondly .
... D are each equally distant from the extremities A and B of the chord AB ; hence the line CD bisects the chord at right angles ( Book I. Prop . XVI . Cor . ) ; hence , it bisects the arc AB in the point E ( Prop . VI . ) . Secondly .
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Common terms and phrases
ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole
Bibliographic information
| Title | Elements of Geometry and Trigonometry DAVIES' COURSE OF MATHEMATICS |
| Author | Adrien Marie Legendre |
| Editor | Charles Davies |
| Translated by | David Brewster |
| Publisher | A.S. Barnes and Company, 1839 |
| Original from | Harvard University |
| Digitized | 14 Jan 2008 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |