Elements of Geometry |
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Page 2
... Fig.20 . ( fig . 20 ) is the sum of the two angles DCB , BCE , and the angle DCB is the difference between the two ... ABC ( fig . 10 ) is a triangle right - angled at A , and the side BC is the hypothenuse . Fig . 11 . 17. Among ...
... Fig.20 . ( fig . 20 ) is the sum of the two angles DCB , BCE , and the angle DCB is the difference between the two ... ABC ( fig . 10 ) is a triangle right - angled at A , and the side BC is the hypothenuse . Fig . 11 . 17. Among ...
Page 7
... ABC , DEF ( fig . 2 ) let Fig . 23 . the angle A be equal to the angle D , the side AB equal to the side DE , and the side AC equal to the side DF ; the two trian- gles ABC , DEF , will be equal . Indeed the triangles may be so placed ...
... ABC , DEF ( fig . 2 ) let Fig . 23 . the angle A be equal to the angle D , the side AB equal to the side DE , and the side AC equal to the side DF ; the two trian- gles ABC , DEF , will be equal . Indeed the triangles may be so placed ...
Page 8
... ( fig . 23 ) , for example , is the shortest way from B to C ( 3 ) ; BC therefore is less than BA + AC . Fig . 24 . Fig . 25 . THEOREM . 41. If from a point O ( fig . 24 ) , within a triangle ABC , there be drawn straight lines OB , OC ...
... ( fig . 23 ) , for example , is the shortest way from B to C ( 3 ) ; BC therefore is less than BA + AC . Fig . 24 . Fig . 25 . THEOREM . 41. If from a point O ( fig . 24 ) , within a triangle ABC , there be drawn straight lines OB , OC ...
Page 10
... ABC = ACB ( fig . 29 ) , the side AC will be equal to the side AB . For , if these sides are not equal , let AB be the greater . Take BD = AC , and join DC . The angle DBC is , by hypothesis , equal to ACB , and the two sides DB , BC ...
... ABC = ACB ( fig . 29 ) , the side AC will be equal to the side AB . For , if these sides are not equal , let AB be the greater . Take BD = AC , and join DC . The angle DBC is , by hypothesis , equal to ACB , and the two sides DB , BC ...
Page 11
... ( fig . 31 ) , without a straight line DE , Fig 31 . only one perpendicular ... ABC . For the angle CBF is a right angle ( 29 ) , as well as CBA , and the ... ( fig . 17 ) , in the Fig . 17 . line AB , it is also impossible to draw ...
... ( fig . 31 ) , without a straight line DE , Fig 31 . only one perpendicular ... ABC . For the angle CBF is a right angle ( 29 ) , as well as CBA , and the ... ( fig . 17 ) , in the Fig . 17 . line AB , it is also impossible to draw ...
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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