The Elements of Euclid, with Many Additional Propositions and Explanatory Notes. ... Part II.1876 |
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Page 21
... compounded of the ratios of A to B , B to C , and C to D. And if A has to B the same ratio which E has to F ; and B ... compounded of ratios which are the same with the ratios of E to F , G to H , and K to L : and the same thing is to be ...
... compounded of the ratios of A to B , B to C , and C to D. And if A has to B the same ratio which E has to F ; and B ... compounded of ratios which are the same with the ratios of E to F , G to H , and K to L : and the same thing is to be ...
Page 24
... compounded of the simple ratio and the subduplicate , and may be expressed algebraically , A : B :: A : C AXIOMS . 1. Equimultiples of the same , or of equal magnitudes , are equal to one another . Or if equals be multiplied by the same ...
... compounded of the simple ratio and the subduplicate , and may be expressed algebraically , A : B :: A : C AXIOMS . 1. Equimultiples of the same , or of equal magnitudes , are equal to one another . Or if equals be multiplied by the same ...
Page 63
... compounded of the same ratios , they are the same with one another . A B C DEMONSTRATION . Let A be to B , as D is to E ; and B to C , as E is to F : then the ratio which is compounded of the ratios of A to B , and B to C , which , by ...
... compounded of the same ratios , they are the same with one another . A B C DEMONSTRATION . Let A be to B , as D is to E ; and B to C , as E is to F : then the ratio which is compounded of the ratios of A to B , and B to C , which , by ...
Page 64
... compounded of the ratios of D to E , and E to F ; and in like manner the proposition may be demonstrated , whatever ... compounded of ratios which are the same with the first ratios , each to each , is the same with the ratio compounded ...
... compounded of the ratios of D to E , and E to F ; and in like manner the proposition may be demonstrated , whatever ... compounded of ratios which are the same with the first ratios , each to each , is the same with the ratio compounded ...
Page 65
... compounded of the ratios of N to O , and O to P , which are the same with the ratios of E to F , and G to H : and it ... compounded of several ratios be the same with a ratio compounded of any other ratios , and if one of the first ...
... compounded of the ratios of N to O , and O to P , which are the same with the ratios of E to F , and G to H : and it ... compounded of several ratios be the same with a ratio compounded of any other ratios , and if one of the first ...
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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 Edition equal and similar equal angles equi equiangular equimultiples Euclid ex æquali fore four magnitudes fourth given circle given straight line greater ratio HENRY LAW 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
Popular passages
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.