Elements of Geometry |
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Page 2
... above referred to ) ; The parallelogram ( fig . 13 ) , which has its opposite sides parallel ; Fig . 14 . The rhombus or lozenge ( fig . 14 ) , which has its sides equal , without having its angles right angles ; Fig . 15 .
... above referred to ) ; The parallelogram ( fig . 13 ) , which has its opposite sides parallel ; Fig . 14 . The rhombus or lozenge ( fig . 14 ) , which has its sides equal , without having its angles right angles ; Fig . 15 .
Page 21
The opposite sides of a parallelogram are equal , and the opposite angles also are equal . Demonstration . Draw the diagonal BD ( fig . 44 ) ; the two Fig . 44 triangles ADB , DBC , have the side BD common ; moreover , on account of the ...
The opposite sides of a parallelogram are equal , and the opposite angles also are equal . Demonstration . Draw the diagonal BD ( fig . 44 ) ; the two Fig . 44 triangles ADB , DBC , have the side BD common ; moreover , on account of the ...
Page 22
equal ( 38 ) ; consequently the side AB opposite to ADB is equal to the side DC opposite to the equal angle DBC , and likewise the third side AD is equal to the third side BC ; therefore the opposite sides of a parallelogram are equal .
equal ( 38 ) ; consequently the side AB opposite to ADB is equal to the side DC opposite to the equal angle DBC , and likewise the third side AD is equal to the third side BC ; therefore the opposite sides of a parallelogram are equal .
Page 23
... are consequently equal ; whence it follows , that the angle AOB = BOC , and that thus the two diagonals of a rhombus cut each other mutually at right angles . a SECTION SECOND . Of the Circle and the Measure of Of Parallelograms .
... are consequently equal ; whence it follows , that the angle AOB = BOC , and that thus the two diagonals of a rhombus cut each other mutually at right angles . a SECTION SECOND . Of the Circle and the Measure of Of Parallelograms .
Page 40
83 ) of a parallelogram being given together with the included angle C , to construct the parallelogram . Solution . Draw the line DE = A ; make the angle FDE = C , and take DF = B ; describe two arcs , one from the point F , as a ...
83 ) of a parallelogram being given together with the included angle C , to construct the parallelogram . Solution . Draw the line DE = A ; make the angle FDE = C , and take DF = B ; describe two arcs , one from the point F , as a ...
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Common terms and phrases
ABC fig ABCD adjacent altitude applied base called centre chord circ circle circumference circumscribed common cone consequently construction contained convex surface Corollary cylinder Demonstration described diameter difference distance divided draw drawn entire equal equivalent example extremities faces feet figure follows formed four give given greater half hence inclination inscribed intersection isosceles join less let fall manner mean measure meet moreover multiplied namely opposite parallel parallelogram parallelopiped pass perimeter perpendicular plane plane angles polyedron polygon prism PROBLEM produced proportional proposition pyramid radii radius ratio reason rectangle regular polygon respect right angles Scholium sector segment similar solid angle Solution sphere spherical square straight line suppose surface taken tangent THEOREM third triangle ABC vertex vertices whence
Bibliographic information
| Title | Elements of Geometry |
| Author | Adrien Marie Legendre |
| Translated by | John Farrar |
| Publisher | Hilliard, Gray, and Company, 1833 |
| Original from | University of Chicago |
| Digitized | 11 Apr 2012 |
| Length | 235 pages |
| Export Citation | BiBTeX EndNote RefMan |