Elements of Geometry and Trigonometry |
From inside the book
Page 41
From the definition of a circle , it follows that all the radii are equal ; that all the diameters are equal also , and each double of the radius . 3. A portion of the circumference , such as FHG , is called An inscribed angle is one ...
From the definition of a circle , it follows that all the radii are equal ; that all the diameters are equal also , and each double of the radius . 3. A portion of the circumference , such as FHG , is called An inscribed angle is one ...
Page 43
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 . A straight line cannot meet the circumference of a circle in more than two points .
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 . A straight line cannot meet the circumference of a circle in more than two points .
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
For , draw the radii CA , CB . Then the two right angled triangles_ADC , CDB , will have AC = CB , and CD common ; hence , AD is equal to DB ( Book I. Prop . XVII . ) . Again , since AD , DB , are equal , CG is a perpendicular erected ...
For , draw the radii CA , CB . Then the two right angled triangles_ADC , CDB , will have AC = CB , and CD common ; hence , AD is equal to DB ( Book I. Prop . XVII . ) . Again , since AD , DB , are equal , CG is a perpendicular erected ...
Page 47
Bisect these chords by the perpendiculars CF , CG , and draw the radii CA , CD . M D A In the right angled triangles CAF , DCG , the hypothenuses CA , CD , are equal ; and the side AF , the half of AB , is equal to the side DG ...
Bisect these chords by the perpendiculars CF , CG , and draw the radii CA , CD . M D A In the right angled triangles CAF , DCG , the hypothenuses CA , CD , are equal ; and the side AF , the half of AB , is equal to the side DG ...
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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 |