## Elements of Geometry |

### From inside the book

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**pyramid is**a solid formed by several triangular planes proceeding from the same point and terminating in the sides ...**ABC**, are two symmetrical polyedrons . " 381. Two triangular**pyramids**are similar when they have two faces similar ... Page 139

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**pyramid S**- ABCDE ( fig . 214 )**is**cut by a plane a b d , Fig , 214 , parallel to the base , 1. The sides SA , SB ...**ABC**,**abc**, being parallel , their intersections AB , ab , by a third plane SAB , will be parallel ( 340 ) ... Page 140

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**S**- ABCDE ,**S**- XYZ , be two**pyramids**that have a common vertex , and whose altitudes are the same , or whose bases ...**abc**de , being similar , their sur- faces are as the squares of their homologous sides AB , ab ; but AB : ab :: SA ... Page 141

... pyramids will coincide throughout ( 384 ) . Therefore the entire

... pyramids will coincide throughout ( 384 ) . Therefore the entire

**pyramid S - ABC**is composed of two tri- angular prisms AGF , GIF , equivalent to each other , and two equal pyramids S - DEF , E - GBI . 411. Corollary 1. From the vertex S ... Page 142

... pyramid D - AGH equal to the pyramid S - DEF ; for the base DEF may be placed upon its equal AGH , and then , the ... ABC + M ) . If we make the same construction as in the preceding proposi- tion , the

... pyramid D - AGH equal to the pyramid S - DEF ; for the base DEF may be placed upon its equal AGH , and then , the ... ABC + M ) . If we make the same construction as in the preceding proposi- tion , the

**pyramid S - ABC**will be divided ...### 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