Elements of Geometry and Trigonometry |
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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 arc .
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 arc .
Page 43
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 in a circle is its diameter . PROPOSITION III . THEOREM .
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 in a circle is its diameter . PROPOSITION III . THEOREM .
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
For , draw the radii CA , CB . Then the two right angled triangles ADC , CDB , will have AC = CB , and CD com- mon ; 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 com- mon ; 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 per- pendiculars CF , CG , and draw the radii CA , CD . D M 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 per- pendiculars CF , CG , and draw the radii CA , CD . D M 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 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 |