Elements of Geometry and Trigonometry |
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Page 41
The chord , or subtense of an arc , is the straight line FG , which joins its two extremities . † 4. A segment is the surface or portion of a circle , included between an arc and its chord . 5. A sector is the part of the circle ...
The chord , or subtense of an arc , is the straight line FG , which joins its two extremities . † 4. A segment is the surface or portion of a circle , included between an arc and its chord . 5. A sector is the part of the circle ...
Page 42
... the curve line AFB , otherwise there would , in the one or the other , be points unequally dis- tant from the centre , which is contrary to the definition of a circle . PROPOSITION II . THEOREM . Every chord is less than 42 GEOMETRY .
... the curve line AFB , otherwise there would , in the one or the other , be points unequally dis- tant from the centre , which is contrary to the definition of a circle . PROPOSITION II . THEOREM . Every chord is less than 42 GEOMETRY .
Page 43
Every chord is less than the diameter . Let AD be any chord . Draw the radii CA , CD , to its extremities . We shall then have AD < AC + CD ( Book I. Prop . VII . * ) ; A or AD < AB . Cor . Hence the greatest line which can be inscribed ...
Every chord is less than the diameter . Let AD be any chord . Draw the radii CA , CD , to its extremities . We shall then have AD < AC + CD ( Book I. Prop . VII . * ) ; A or AD < AB . Cor . Hence the greatest line which can be inscribed ...
Page 44
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 . For , since the diameters AB , EF , are equal , the semi- circle AMDB may be applied M ཤིས་ ཡོད་ ས exactly to the ...
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 . For , since the diameters AB , EF , are equal , the semi- circle AMDB may be applied M ཤིས་ ཡོད་ ས exactly to the ...
Page 45
If they were greater , the reverse pro- perty would have place ; for , as the arcs increase , the chords would diminish , and conversely . Thus , the arc AKBD is greater than AKBH , and the chord AD , of the first , is less than the ...
If they were greater , the reverse pro- perty would have place ; for , as the arcs increase , the chords would diminish , and conversely . Thus , the arc AKBD is greater than AKBH , and the chord AD , of the first , is less than the ...
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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 |