## Elements of Geometry |

### From inside the book

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... Fig.20 . ( fig . 20 ) is the sum of the two angles DCB , BCE , and the angle DCB is the difference between the two ...

... 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 . Fig . 12 . Fig ... Page 7

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**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

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**fig**. 23 ) , for example , is the shortest way from B to C ( 3 ) ; BC therefore is less than BA + AC . THEOREM . 41. If from a point ○ (**fig**. 24 ) , within a triangle**ABC**, there be drawn straight lines OB , OC , to the extremities of ... Page 10

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**Fig**. 30 . THEOREM . 48. Reciprocally , if two angles of a triangle are equal , the oppo- site sides are equal , and the triangle is isosceles . Demonstration . Let the angle**ABC**= ACB (**fig**. 29 ) , the side AC will be equal to the ... Page 11

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**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 two ...### Other editions - View all

### 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