Elements of Geometry |
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Page 2
... equal , isosceles ( fig . 8 ) , when two only of its sides Fig . 9. 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 ...
... equal , isosceles ( fig . 8 ) , when two only of its sides Fig . 9. 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 ...
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 . 30. Corollary 11. If the line ...
... 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 . 30. Corollary 11. If the line ...
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 BAD 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 and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence