## Elements of Geometry |

### From inside the book

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Page iv

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**theorem**for the solidi- ty of the triangular pyramid , by M. Queret of St. Malo , is sub- joined at the end . But the principal improvement in this edition consists in a new demonstration of the**theorem**relative to the three angles of a ... 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 , coin- cide 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 ... 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 BAC 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 angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence