## Elements of Geometry |

### From inside the book

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**four**of which treat of plane geometry , and**four**of solid geometry . The first section , entitled first principles , & c . contains the pro- perties of straight lines which meet those of perpendiculars , the theorem upon the sum of the ... Page 2

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**angles**DCE , BCE . Fig . 3 . Fig .**4**. Fig . 5 . 10. When a straight line AB ( fig . 3 ) meets another straight line CD in such a manner that the adjacent**angles**BAC , BAD , are equal , each of these**angles**is called a**right**...**four**sides is ... Page 4

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**right angles**are equal . Demonstration . Let the straight line CD be perpendicular to Fig . 16. AB ( fig . 16 ) , and GH to EF , the angles ACD , EGH , will be equal . Take the**four**distances CA , CB , GE , GF , equal to each other ... Page 6

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**right angles**, the two exterior sides AC , CB , are in the same straight line . Demonstration . For if CB is not the ...**four**angles , formed about a point by two straight lines which cut each other , are together equal to**four**right ... Page 15

... angles BAI , ABD , the sum of which is less than two right angles , the lines AI , BD , produced , will meet ... four angles taken together would be equal to

... angles BAI , ABD , the sum of which is less than two right angles , the lines AI , BD , produced , will meet ... four angles taken together would be equal to

**four right angles**. But the sum of the two angles BAM , ABD , is greater than ...### 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