## Elements of Geometry |

### From inside the book

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Page iv

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**demonstration**of the 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 ... Page 3

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**demonstration**. A Problem is a question proposed which requires a solution . A Lemma is a subsidiary truth employed in the**demonstration**of a theorem , or in the solution of a problem . The common name of Proposition is given ... Page 4

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**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 , the distance AB will be ... Page 5

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**Demonstration**. Let the two points , which are common to the two lines , be A and B ( fig . 19 ) . In the first place , it is evident Fig . 19 . that they must coincide entirely between A and B ; otherwise , two straight lines could be ... Page 6

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**Demonstration**. For if CB is not the line AC produced , let CE be that line produced ; then , ACE being a straight line , the angles ACD , DCE , are together equal to two right angles ( 28 ) ; but , by hypothesis , the angles ACD , DCB ...### 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