Elements of Geometry |
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Page v
... distance of these same points . I have preferred , in order not to render the introduction to geometry too difficult , to sacrifice something of the exactness at which I aimed . Accordingly , I shall call a straight line that which is ...
... distance of these same points . I have preferred , in order not to render the introduction to geometry too difficult , to sacrifice something of the exactness at which I aimed . Accordingly , I shall call a straight line that which is ...
Page 4
... distances CA , CB , GE , GF , equal to each other , the distance AB will be equal to the distance EF , and the line EF may be applied to AB , so that the point E will fall upon A , and the point F upon B. These two lines , thus placed ...
... distances CA , CB , GE , GF , equal to each other , the distance AB will be equal to the distance EF , and the line EF may be applied to AB , so that the point E will fall upon A , and the point F upon B. These two lines , thus placed ...
Page 11
... distances BC , BE , from it , are equal to one another ; 3. Of any two oblique lines AC , AD , or AE , AD , that which is more remote from the perpendicular is the greater . Demonstration . Produce the perpendicular AB , so that BF BA ...
... distances BC , BE , from it , are equal to one another ; 3. Of any two oblique lines AC , AD , or AE , AD , that which is more remote from the perpendicular is the greater . Demonstration . Produce the perpendicular AB , so that BF BA ...
Page 12
... distance of any point from a straight line . 54. Corollary II . From the same point , there cannot be drawn three equal straight lines terminating in a given straight line ; for , if this could be done , there would be on the same side ...
... distance of any point from a straight line . 54. Corollary II . From the same point , there cannot be drawn three equal straight lines terminating in a given straight line ; for , if this could be done , there would be on the same side ...
Page 18
... distance MN equal to FM . It follows from the same demonstration , that if we take NP = FN , we determine , upon the ... distance of the points of intersection from the fixed point F , is not exactly double the distance of the preceding ...
... distance MN equal to FM . It follows from the same demonstration , that if we take NP = FN , we determine , upon the ... distance of the points of intersection from the fixed point F , is not exactly double the distance of the preceding ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids 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 |