Elements of Geometry |
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Page 1
... extremities of a line are called points . A point , therefore , has no extension . 3. A straight or right line is the shortest way from one point to another . 4. Every line , which is neither a straight line nor composed of straight ...
... extremities of a line are called points . A point , therefore , has no extension . 3. A straight or right line is the shortest way from one point to another . 4. Every line , which is neither a straight line nor composed of straight ...
Page 8
... extremities of BC , one of its sides , the sum of these lines will be less than that of AB , AC , the two other sides . Demonstration . Let BO be produced till it meet the side AC in D ; the straight line OC is less than OD + DC ; to ...
... extremities of BC , one of its sides , the sum of these lines will be less than that of AB , AC , the two other sides . Demonstration . Let BO be produced till it meet the side AC in D ; the straight line OC is less than OD + DC ; to ...
Page 12
... extremities of the line AB ; 2. any point without the perpendicular is at unequal distances from the same extremities A and B. Demonstration . 1. Since AC CB , the two oblique lines AD , DB , are drawn to points which are at the same ...
... extremities of the line AB ; 2. any point without the perpendicular is at unequal distances from the same extremities A and B. Demonstration . 1. Since AC CB , the two oblique lines AD , DB , are drawn to points which are at the same ...
Page 22
... extremities ** . 93. A segment of a circle is the portion comprehended be- tween an arc and its chord . 94. A sector is the part of a circle comprehended between an arc DE and the two radii CD , CE , drawn to the extremities of this arc ...
... extremities ** . 93. A segment of a circle is the portion comprehended be- tween an arc and its chord . 94. A sector is the part of a circle comprehended between an arc DE and the two radii CD , CE , drawn to the extremities of this arc ...
Page 23
... extremities of the chord AD , we shall have the straight line AD < AC + CD , that is , AD < AB ( 91 ) . 100. Corollary . Hence the greatest straight line that can be inscribed in a circle is equal to its diameter . THEOREM . 101. A ...
... extremities of the chord AD , we shall have the straight line AD < AC + CD , that is , AD < AB ( 91 ) . 100. Corollary . Hence the greatest straight line that can be inscribed in a circle is equal to its diameter . THEOREM . 101. A ...
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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