Elements of Geometry |
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Page 2
... equal , isosceles ( fig . 8 ) , when two only of its sides are equal , and scalene ( fig . 9 ) , when no two of its sides are equal . 16. A right - angled triangle is that which has one right angle . The side opposite to the right angle ...
... equal , isosceles ( fig . 8 ) , when two only of its sides are equal , and scalene ( fig . 9 ) , when no two of its sides are equal . 16. A right - angled triangle is that which has one right angle . The side opposite to the right angle ...
Page 3
... equal ; an equiangular polygon is one which has all its angles equal . • 20. Two polygons are equilateral with respect to each other , when they have their sides equal , each to each , and placed in the same order ; that is , when , by ...
... equal ; an equiangular polygon is one which has all its angles equal . • 20. Two polygons are equilateral with respect to each other , when they have their sides equal , each to each , and placed in the same order ; that is , when , by ...
Page 4
... equal . Demonstration . Let the straight line CD be perpendicular to Fig . 16. AB ( fig . 16 ) , and GH to EF , the angles ACD , EGH , will be equal . Take the four distances CA , CB , GE , GF , equal to each other , the distance AB will be ...
... equal . Demonstration . Let the straight line CD be perpendicular to Fig . 16. AB ( fig . 16 ) , and GH to EF , the angles ACD , EGH , will be equal . Take the four distances CA , CB , GE , GF , equal to each other , the distance AB will be ...
Page 5
... equal to a right angle ; therefore the sum of the two angles ACD , BCD , is equal to two right angles . 29. Corollary 1. If one of the angles ACD , BCD , is a right angle , the other is also a right angle . II . 30. Corollary 11. If the ...
... equal to a right angle ; therefore the sum of the two angles ACD , BCD , is equal to two right angles . 29. Corollary 1. If one of the angles ACD , BCD , is a right angle , the other is also a right angle . II . 30. Corollary 11. If the ...
Page 6
... equal to two right angles ( 28 ) ; but , by hypothesis , the angles ACD , DCB , are together equal to two right angles ; therefore ACD + DCB = ACD + DCE . Take away the common angle ACD , and there will remain the part DCB equal to the ...
... equal to two right angles ( 28 ) ; but , by hypothesis , the angles ACD , DCB , are together equal to two right angles ; therefore ACD + DCB = ACD + DCE . Take away the common angle ACD , and there will remain the part DCB equal to the ...
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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 |