## Elements of Geometry |

### From inside the book

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Page xii

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**follows**that the other ratios of the same proportions are equal , and that , consequently , B + A : D + C :: BA : D― C , or , by changing the place of the means , BA : B - A :: D + C : D - C ; that is , the sum of the two first terms of ... Page xiii

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**follows**, that the sum of the antecedents is to their difference as the sum of the consequents is to their difference . If we have a series of equal ratios A : B :: CD :: E : F , by considering only the two first , which form the ... Page xiv

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**follows**, that the squares of four proportional quantities form a new proportion . by By multiplying the proportion we shall have A2 : B2 : C2 : De Ꭿ : B :: C : Ꭰ , A3 : B3 :: C3 : D3 ; that is , the cubes of four proportional ... Page 3

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**follows**from one or sev- eral propositions . A Scholium is a remark upon one or more propositions which have gone before , tending to show their connexion , their restric- tion , their extension , or the manner of their application . A ... Page 4

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**follows**that Fig . 17 . But and besides , by hypothesis , hence ACK KCB . ACK > ACD , KCB BCD ; ACD BCD ; ACK KCB ; and the line GH cannot fall upon a line CK different from CD ; consequently it falls upon CD , and the angle EGH upon ...### 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