Elements of Geometry |
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Page 18
... reason is this ; if we produce FE toward H , the angle DEH would have its sides parallel to those of the angle BAC , but the two angles would not be equal . In this case the angle DEH and the angle BAC would together make two right ...
... reason is this ; if we produce FE toward H , the angle DEH would have its sides parallel to those of the angle BAC , but the two angles would not be equal . In this case the angle DEH and the angle BAC would together make two right ...
Page 21
... reason AB is parallel to CD ; there- fore the quadrilateral ABCD is a parallelogram . THEOREM . 87. If two opposite sides AB , CD ( fig . 44 ) , of a quadrilateral Fig . 44 . are equal and parallel , the two other sides will also be ...
... reason AB is parallel to CD ; there- fore the quadrilateral ABCD is a parallelogram . THEOREM . 87. If two opposite sides AB , CD ( fig . 44 ) , of a quadrilateral Fig . 44 . are equal and parallel , the two other sides will also be ...
Page 26
... reason ; it will then be in both of these lines at the same time . But two lines can cut each other in only one point ( 32 ) ; there is therefore only one circle , whose circum- ference can pass through three given points . 108 ...
... reason ; it will then be in both of these lines at the same time . But two lines can cut each other in only one point ( 32 ) ; there is therefore only one circle , whose circum- ference can pass through three given points . 108 ...
Page 27
... reason CF > CI . But CF = CG , since the chords AB , DE , are equal . Therefore CG > CI , and of two unequal chords the less is at the greater distance from the centre . THEOREM . 110. The perpendicular BD ( fig . 54 ) , at the ...
... reason CF > CI . But CF = CG , since the chords AB , DE , are equal . Therefore CG > CI , and of two unequal chords the less is at the greater distance from the centre . THEOREM . 110. The perpendicular BD ( fig . 54 ) , at the ...
Page 32
... reasons . Besides , if the measure of angles by the arcs of a circle be in some degree indirect , it is not the less easy to obtain , by means of them , the direct and absolute measure ; for , if we compare the arc , which is used as ...
... reasons . Besides , if the measure of angles by the arcs of a circle be in some degree indirect , it is not the less easy to obtain , by means of them , the direct and absolute measure ; for , if we compare the arc , which is used as ...
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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