## Elements of Geometry |

### From inside the book

Page ix

...

...

**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 A × B. The expression A × ( B + ... Page x

...

...

**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 xiii

...

...

**multiply**them in order , that is , term by term , the products will form a proportion ; thus AXE : BxF :: CxG : D x H , BXF DXH This is evident , since the new ratios , AXE CXG ' are respec- tively the products of the primitive ratios ... Page xiv

...

...

**multiply**the proportion we shall have ( П ) A : B :: C : D A : B :: C : D A2 : B2 : : C2 : D2 , whence it ...**multiplied**by the number of linear units con- tained in B ; and we can easily conceive this product to be equal to ... Page 16

...

...

**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 ) . 66. Corollary 1. The ...### 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 convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent 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 pyramid S-ABC 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