## Elements of Geometry |

### From inside the book

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Page iii

... spherical isoperimetrical polygons , and on the regular poly- edrons , are inserted in this at the end of the fourth section of the second part . Also an improved demonstration of the

... spherical isoperimetrical polygons , and on the regular poly- edrons , are inserted in this at the end of the fourth section of the second part . Also an improved demonstration of the

**theorem**for the solidity retation Presented to. Page 3

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**theorem**, or in the solution of a problem . The common name of Proposition is given indifferently to**theorems**, problems , and lemmas . A Corollary is a consequence which follows from one or sev- eral propositions . A Scholium is a ... Page 4

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**THEOREM**. 27. ALL 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 ... Page 5

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**THEOREM**. 32. Two straight lines , which have two points common , coincide throughout , and form one and the same straight line . Demonstration . Let the two points , which are common to the two lines , be A and B ( fig . 19 ) . In the ... Page 6

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**THEOREM**. 34. Whenever two straight lines AB , DE ( fig . 21 ) , cut each other , the angles opposite † to each other at the vertex are equal . Demonstration . Since DE is a straight line , the sum of the angles ACD , ACE , 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