The Elements of Euclid, with Many Additional Propositions and Explanatory Notes. ... Part II.1876 |
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Page 4
... remaining angle L is equal to the remaining angle D ( k ) ; and therefore the triangle LMN circumscribed about the circle ABC is equiangular to the given triangle . SCHOLIUM . The demonstration of this proposition has been somewhat ...
... remaining angle L is equal to the remaining angle D ( k ) ; and therefore the triangle LMN circumscribed about the circle ABC is equiangular to the given triangle . SCHOLIUM . The demonstration of this proposition has been somewhat ...
Page 19
... remaining magnitude we should then increase , say 10 times , and again sub- tract B until another remainder less than B was obtained , which should be again increased by 10 , and the process continued until a sufficiently accurate ...
... remaining magnitude we should then increase , say 10 times , and again sub- tract B until another remainder less than B was obtained , which should be again increased by 10 , and the process continued until a sufficiently accurate ...
Page 48
... proportionals when taken separately ; that is , if two magnitudes together have to one of them the same ratio which two others have to one of these , the remaining one of the first two shall have to the other the 48 ELEMENTS OF GEOMETRY .
... proportionals when taken separately ; that is , if two magnitudes together have to one of them the same ratio which two others have to one of these , the remaining one of the first two shall have to the other the 48 ELEMENTS OF GEOMETRY .
Page 49
... remaining one of the last two has to the other of these . Let AB , BE , CD , DF be the magnitudes taken jointly which are proportionals ; that is , as AB is to BE so is CD to DF ; they shall also be proportionals taken separately , viz ...
... remaining one of the last two has to the other of these . Let AB , BE , CD , DF be the magnitudes taken jointly which are proportionals ; that is , as AB is to BE so is CD to DF ; they shall also be proportionals taken separately , viz ...
Page 66
... remaining ratios of the first , or the remaining ratio of the first , if but one remain , is the same with the ratio com- pounded of those remaining of the last , or with the remain- ing ratio of the last . A B C D E F G H K L M ...
... remaining ratios of the first , or the remaining ratio of the first , if but one remain , is the same with the ratio com- pounded of those remaining of the last , or with the remain- ing ratio of the last . A B C D E F G H K L M ...
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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
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.