Elements of Geometry |
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Page v
... drawn be- tween two points from the shortest line which measures the 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 ...
... drawn be- tween two points from the shortest line which measures the 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 ...
Page 3
... drawn between two points . 26. Two magnitudes , whether they be lines , surfaces , or solids , are equal , when , being applied the one to the other , they coin- cide with each other entirely , that is , when they exactly fill the same ...
... drawn between two points . 26. Two magnitudes , whether they be lines , surfaces , or solids , are equal , when , being applied the one to the other , they coin- cide with each other entirely , that is , when they exactly fill the same ...
Page 5
... drawn from A to B , which is impossi- ble ( 25 ) . Now let us suppose , if it be possible , that the lines , when produced , separate from each other at a point C , the one becoming CD , and the other CE . At the point C , let CF be . drawn ...
... drawn from A to B , which is impossi- ble ( 25 ) . Now let us suppose , if it be possible , that the lines , when produced , separate from each other at a point C , the one becoming CD , and the other CE . At the point C , let CF be . drawn ...
Page 8
... drawn straight lines OB , OC , to the 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 ...
... drawn straight lines OB , OC , to the 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 ...
Page 10
... drawn from the vertex of an isosceles triangle , to the middle of the base , is perpendicular to the base , and ... Draw CD making the angle BCD = B . In the triangle BDC , BD is equal to DC ( 48 ) ; but AD + DC > AC , and AD + DC = AD + ...
... drawn from the vertex of an isosceles triangle , to the middle of the base , is perpendicular to the base , and ... Draw CD making the angle BCD = B . In the triangle BDC , BD is equal to DC ( 48 ) ; but AD + DC > AC , and AD + DC = AD + ...
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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