Elements of Geometry and Trigonometry |
From inside the book
Page 41
A portion of the circumference , such as FHG , is called An inscribed angle is one which , like BAC , has its vertex in the circumference , and is formed by two chords . B an arc . The chord , or subtense of an arc , is the straight ...
A portion of the circumference , such as FHG , is called An inscribed angle is one which , like BAC , has its vertex in the circumference , and is formed by two chords . B an arc . The chord , or subtense of an arc , is the straight ...
Page 42
... otherwise there would , in the one or the other , be points unequally distant from the centre , which is contrary to the definition of a circle . 44 ! PROPOSITION II . THEOREM . Every chord is less than 42 GEOMETRY . •
... otherwise there would , in the one or the other , be points unequally distant from the centre , which is contrary to the definition of a circle . 44 ! PROPOSITION II . THEOREM . Every chord is less than 42 GEOMETRY . •
Page 43
Every chord is less than the diameter . Let AD be any chord . 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 ...
Every chord is less than the diameter . Let AD be any chord . 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 ...
Page 44
M If the radii AC , EO , are equal , and also the arcs AMD , ENG ; then the chord AD will be equal to the A chord EG . N DD BE K For , since the diameters AB , EF , are equal , the semicircle AMDB may be applied exactly to the ...
M If the radii AC , EO , are equal , and also the arcs AMD , ENG ; then the chord AD will be equal to the A chord EG . N DD BE K For , since the diameters AB , EF , are equal , the semicircle AMDB may be applied exactly to the ...
Page 45
If they were greater , the reverse property would have place ; for , as the arcs increase , the chords would diminish , and conversely . Thus , the arc AKBD is greate than AKBH , and the chord AD , of the first , is less than the chord ...
If they were greater , the reverse property would have place ; for , as the arcs increase , the chords would diminish , and conversely . Thus , the arc AKBD is greate than AKBH , and the chord AD , of the first , is less than the chord ...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Other editions - View all
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 |