## Elements of Geometry |

### From inside the book

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**ratio**, it is evi- dent that the two other**ratios**may be put into a proportion , since they are each equal to that which is common . If , for ex- ample , we have then we shall have A : B :: C : Introduction . Page xi

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**ratio**then will be equal to the primitive**ratio**increased by unity . If the same operation be performed upon the two**ratios**of a proportion , there will evidently result from it two new**ratios**equal to each other , and consequently a ... Page xii

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**ratios**A : C , B : D , being common to the two proportions above obtained , it 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 ... Page xiii

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**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 : B + D :: A : B ; and , since the third**ratio**, E : F , is equal to the first , A : B , we ... Page xiv

Adrien Marie Legendre. tively the products of the primitive

Adrien Marie Legendre. tively the products of the primitive

**ratios**B F D and E ' C and H G which are equal . If we multiply the proportion Ꭿ : B :: C : Ꭰ D by we shall have ( II ) A : B :: C : D A2 : B2 :: C2 : D2 , whence it follows ...### 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