## Elements of Geometry |

### From inside the book

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**whence**or B : E :: D : F. IV . Other changes , besides the transposition of terms , may be made among proportionals without destroying the equality of the product of the extremes to that of the means . 1. If to the consequent of a ratio ... Page xiii

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**Whence**it follows , that the sum of the antecedents is to their dif- ference , as the sum of the consequents is to their difference . If we have a series of equal ratios A : B :: C : D :: E : F by considering only the two first , which ... Page xiv

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**whence**it follows , that the squares of four proportional quantities form a new proportion . By multiplying the proportion by we shall have A2 : B2 :: C2 D3 A B :: C : D , A3 : B 3 3 :: C3 : D3 , that is , the cubes of four proportional ... Page 5

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**whence**straight lines , which have two points common A and B , cannot separate the one from the other , when produced ; therefore they must form one and the same straight line . Fig . 19 . Fig . 20 . THEOREM . 33. If two adjacent Of ... Page 7

... be somewhere in CA ;

... be somewhere in CA ;

**whence**the point D , which must be at the same time in the lines BA and CA , can only be at their intersection A ; therefore the two triangles ABC , Fig . 23 . Fig . 24 . Fig . Of Perpendicular and Oblique Lines . 7.### 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