The Elements of Euclid, with Many Additional Propositions and Explanatory Notes. ... Part II.1876 |
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Page 21
... ratio of that which it has to the second . 11. When four magnitudes are continual proportionals , the first is said to have to the fourth the triplicate ratio of that which it has to the second , and so on , quadruplicate , & c ...
... ratio of that which it has to the second . 11. When four magnitudes are continual proportionals , the first is said to have to the fourth the triplicate ratio of that which it has to the second , and so on , quadruplicate , & c ...
Page 22
... ratio of A to B. Again , if A , B , C , D , be in continued proportion , and B 4X DIE X = A B C are all equal ; B'C ' D جزات therefore D = A3 Bai or A is to D in the triplicate ratio of A to B , and so on with any number of quantities ...
... ratio of A to B. Again , if A , B , C , D , be in continued proportion , and B 4X DIE X = A B C are all equal ; B'C ' D جزات therefore D = A3 Bai or A is to D in the triplicate ratio of A to B , and so on with any number of quantities ...
Page 147
... triplicate ratio of their homo- logous sides ( AE , CF ) . DEMONSTRATION . Pro- duce AE , GE , HE ; and in these produced , take EK equal to CF , EL equal to FN , and EM equal to FR ; and com- plete the parallelogram KL , and the solid ...
... triplicate ratio of their homo- logous sides ( AE , CF ) . DEMONSTRATION . Pro- duce AE , GE , HE ; and in these produced , take EK equal to CF , EL equal to FN , and EM equal to FR ; and com- plete the parallelogram KL , and the solid ...
Page 148
... triplicate ratio of that which it has to the second ( e ) ; therefore the solid AB has to the solid KO , the triplicate ratio of that which AB has to EX : but as AB is to EX , so is the parallelogram AG to the pa- rallelogram GK , and ...
... triplicate ratio of that which it has to the second ( e ) ; therefore the solid AB has to the solid KO , the triplicate ratio of that which AB has to EX : but as AB is to EX , so is the parallelogram AG to the pa- rallelogram GK , and ...
Page 171
... triplicate ratio of that of their homologous sides . DEMONSTRATION . Let the pyramids having the triangles ABC , DEF for their bases , and the points G , H for their vertices , be similar and similarly situated : the pyramid ABCG shall ...
... triplicate ratio of that of their homologous sides . DEMONSTRATION . Let the pyramids having the triangles ABC , DEF for their bases , and the points G , H for their vertices , be similar and similarly situated : the pyramid ABCG shall ...
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The Elements of Euclid, with Many Additional Propositions, and Explanatory ... Euclides No preview available - 2016 |
Common terms and phrases
altitude angle ABC angle BAC base ABC base DEF base EH bisected circle ABCD circle EFGH circumference common section cone Construction contained COROLLARY cylinder DEMONSTRATION duplicate ratio equal and similar equal angles equi equiangular equimultiples Euclid ex æquali fore four magnitudes fourth given circle given straight line greater ratio homologous homologous sides Hypoth inscribed join less LUDGATE HILL multiple opposite planes paral parallel parallelogram perpendicular polygon polyhedron prism PROPOSITION pyramid ABCG pyramid DEFH RALPH TATE reciprocally proportional rectangle rectilineal figure remaining angle right angles SCHOLIUM segments solid angle solid CD solid parallelopipeds sphere square on BD THEOREM THEOREM.-If third three plane angles three straight lines tiple triangle ABC triplicate ratio vertex vertex the point wherefore Woodcuts
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Page 10 - A KEY AND COMPANION to the above Book, forming an extensive repository of Solved Examples and Problems in Illustration of the various Expedients necessary in Algebraical Operations.
Page 111 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.
Page 14 - ... Practical Form. With a Course of Exercises. By ALFRED ELWES. is. 6d. 35. Spanish-English and English-Spanish Dictionary. Including a large number of Technical Terms used in Mining, Engineering, &c., with the proper Accents and the Gender of every Noun. By ALFRED ELWES.
Page 5 - SHIPBUILDING, NAVIGATION, MARINE ENGINEERING, ETC. 51. NAVAL ARCHITECTURE, the Rudiments of; or an Exposition of the Elementary Principles of the Science, and their Practical Application to Naval Construction. Compiled for the Use of Beginners. By JAMES PEAKE, School of Naval Architecture, HM Dockyard, Portsmouth.
Page 85 - ... have an angle of the one equal to an angle of the other, and the sides about those angles reciprocally proportional, are equal to une another.
Page 7 - Comprising Observations on the Materials from, and Processes by which, they are manufactured ; their Special Uses, Applications, Qualities, and Efficiency.
Page 18 - Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding...
Page 7 - By DIONYSIUS LARDNER, DCL, formerly Professor of Natural Philosophy and Astronomy in University College, London.