## Elements of Geometry |

### From inside the book

Results 1-5 of 32

Page xi

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**difference**with the antecedent , this last will be contained once less than it was in the first consequent ; the new ratio will be equal to the primitive ratio diminished by unity . If the same operation be performed upon the two ratios ... Page xii

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**difference**of the two first terms is to the**difference**of the two last , as the first is to the third , or as the second is to the fourth . Moreover , the two ratios A : C , B : D , being common to the two proportions above obtained ... Page xiii

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**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 proportion A : B :: C : D , we obtain by what precedes A + C ... Page 2

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**difference**between the two angles DCE , BCE . Fig . 3 . Fig . 4 . Fig . 5 . Fig . 6 . Fig . 7 . Fig . 8 . Fig . 9 . 10. When a straight line AB ( fig . 3 ) meets another straight line CD in such a manner that the adjacent angles BAC ... Page 31

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**difference**of their radii CA , AD ( fig . 60 ) , these two circles will Fig . 60 . touch each other internally . Demonstration . In the first place , it is evident , that they will have the point A common ; and they can have no other ...### 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