Elements of Geometry and Trigonometry |
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Page 28
and since CD is parallel to EF , PR will for a like reason be perpen - C dicular to CD . Hence AB and CD are . perpendicular to the same straight line ; hence they are parallel ( Prop . XVIII . ) . A R Q P B PROPOSITION XXIII .
and since CD is parallel to EF , PR will for a like reason be perpen - C dicular to CD . Hence AB and CD are . perpendicular to the same straight line ; hence they are parallel ( Prop . XVIII . ) . A R Q P B PROPOSITION XXIII .
Page 33
For a like reason AB is parallel to CD therefore the quadrilateral ABCD is a parallelogram . PROPOSITION XXX . THEOREM . If two opposite sides of a quadrilateral are equal and parallel , the remaining sides will also be equal and ...
For a like reason AB is parallel to CD therefore the quadrilateral ABCD is a parallelogram . PROPOSITION XXX . THEOREM . If two opposite sides of a quadrilateral are equal and parallel , the remaining sides will also be equal and ...
Page 46
neither could it be out of the line FG , for a like reason ; therefore , it would be in both the lines DE , FG . But two straight lines cannot cut each other in more than one point ; hence there is but one circumference which can pass ...
neither could it be out of the line FG , for a like reason ; therefore , it would be in both the lines DE , FG . But two straight lines cannot cut each other in more than one point ; hence there is but one circumference which can pass ...
Page 53
It has been found more simple to measure them by arcs of a circle , on account of the facility with which arcs can be made equal to given arcs , and for various other reasons . At all events , if the measurement of angles by arcs of a ...
It has been found more simple to measure them by arcs of a circle , on account of the facility with which arcs can be made equal to given arcs , and for various other reasons . At all events , if the measurement of angles by arcs of a ...
Page 54
For a like reason , the angle CAD will be measured by the half of ED ; hence BAC + CAD , or BAD will be measured by half of BE + ED , or of BED . Suppose , in the second place , that the centre C lies without the angle BAD .
For a like reason , the angle CAD will be measured by the half of ED ; hence BAC + CAD , or BAD will be measured by half of BE + ED , or of BED . Suppose , in the second place , that the centre C lies without the angle BAD .
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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 |