## Elements of Geometry |

### From inside the book

Results 6-10 of 89

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**less**than the sum of the other two . Demonstration . The straight line BC ( 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 ... Page 9

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**less**than BC . Case III . If the point G ( fig . 27 ) fall within the triangle Fig . 27 , BAC , then AG + GC < AB + ...**less**than the angle D , then the side BC would be**less**than EF ; but BC is equal to EF , therefore the angle A can ... Page 10

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**less**than B , then according to what has just been demonstrated we should have ABAC , which is con- trary to the hypothesis ; and if C were equal to B , then it would follow , that AC = AB ( 48 ) , 10 Elements of Geometry . Page 11

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**less**than B , nor equal to it ; it is therefore greater . THEOREM . 50. From a given point A ( fig . 31 ) , without a straight line DE , Fig 31 . only one perpendicular can be drawn to that line . Demonstration . If it be possible , let ... Page 12

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**less**than AC half of AC + CF , that is , the perpendicular is**less**than any one of the oblique lines . 2. If BE = BC , then , as AB is common to the two triangles ABE , ABC , and the right angle ABE = ABC , the triangle ABE is equal to ...### 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