## Elements of Geometry |

### From inside the book

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Page ix

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**multiplied**by the magnitude represented by B , or A**multiplied**by B. This product is also sometimes de- noted by writing the letters one after the other without any sign , thus AB signifies the same as Ax B. The expression A × ( B + C ... Page x

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**multiplied**by itself , the result is the second power , or square , of this number ; 5 × 5 , or 25 , is the second power , or square , of 5 . The second power therefore is the product of two equal fac- tors ; each of these factors is ... Page xiv

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**multiply**the proportion we shall have ( II ) A : B :: C : D A : B :: C. D Ꭿ e : Ba : : C : D , whence it follows ...**multiplied**by the number of linear units con- tained in B ; and we can easily conceive this product to be equal to ... Page 19

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**multiplied**by 4-2 , which makes four right angles ; therefore , if all the angles of a quadrilateral are equal , each of them will be a right angle , which justifies the definition of a square and rectangle ( 17 ) . 11 . 81. Corollary ... Page 63

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**multiplied**in order by the identical pre- portion . we shall have Hence AC : DF :: AC : DF , ABX AC : DEX DF :: AC : DF . -2 ABC : DEF :: AĈ : DF . Therefore two similar triangles ABC , DEF , are to each other as the squares of the ...### 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