## Elements of Geometry |

### From inside the book

Results 6-10 of 59

Page 9

...

...

**AC**( fig . 28 ) , then will the Fig . 28 . angle C be equal to B. Draw the straight**line**AD from the vertex A to the point D the middle of the base BC ; the two triangles ABD , ADC , will have the three sides of the one , equal to the ... Page 10

...

...

**line**drawn from the vertex of an isosceles triangle , to the middle of the base , is perpendicular to the base , and ...**AC**will be equal to the side AB . For , if these sides are not equal , let AB be the greater . Take BD =**AC**... Page 11

...

...

**line**. Demonstration . If it be possible , let there be two AB and**AC**; produce one of them AB , so that BF AB , and ...**line**( 33 ) ; and hence it would follow that two straight**lines**ACF , ABF , might be drawn between the same ... Page 12

...

...

**AC**. 3. In the triangle DFA , the sum of the sides AD , DF , is greater than the sum of the sides**AC**, CF ( 41 ) ; therefore AD half of AD + DF is greater than**AC**half of**AC**+ CF , and the oblique**line**, which is more remote from the ... Page 13

...

...

**AC**DF ( fig . 33 ) , and Fig . 33 . the side AB = DE ; the right - angled ...**AC**; whence AG**AC**. But AG cannot be equal to**AC**( 52 ) ; there- fore it is impossible that BC should be ...**line**AE another point Of Parallel**Lines**.. 13.### 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