Elements of Geometry |
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Page xii
... follows that the other ratios of the same proportions are equal , and that consequently B + A : D + C :: B - A : D - C , or , by changing the place of the means , BA : BA :: D + C : D - C ; that is , the sum of the two first terms of a ...
... follows that the other ratios of the same proportions are equal , and that consequently B + A : D + C :: B - A : D - C , or , by changing the place of the means , BA : BA :: D + C : D - C ; that is , the sum of the two first terms of a ...
Page xiii
... 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 form the ...
... 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 form the ...
Page xiv
... 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 ...
... 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 3
... 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 ...
... 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
... 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 ...
... 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 ...
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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