The Elements of Euclid, with Many Additional Propositions and Explanatory Notes. ... Part II.1876 |
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Page 25
... wherefore , as many magnitudes as are in AB equal to E , so many are there in AB and CD together equal to E and F together . Therefore , whatever multiple AB is of E , the same multiple are AB and CD together , of E and F together ; and ...
... wherefore , as many magnitudes as are in AB equal to E , so many are there in AB and CD together equal to E and F together . Therefore , whatever multiple AB is of E , the same multiple are AB and CD together , of E and F together ; and ...
Page 31
... wherefore EG is equal to AB ( c ) ; take from each of them the common magnitude AE ; and the remainder AG is equal to the remainder EB . Wherefore , since AE is the same multiple of CF that AG is of FD , and that AG is equal to EB ...
... wherefore EG is equal to AB ( c ) ; take from each of them the common magnitude AE ; and the remainder AG is equal to the remainder EB . Wherefore , since AE is the same multiple of CF that AG is of FD , and that AG is equal to EB ...
Page 32
... wherefore KH is equal to CD ( 6 ) ; take away the common magnitude CH , then the re- mainder CK is equal to the remainder HD ; but CK is equal to F ; therefore HD is equal to F. A G- B K C- H. Ꭰ E F ( a ) Hypoth . ( b ) V. Ax . 1 . A G ...
... wherefore KH is equal to CD ( 6 ) ; take away the common magnitude CH , then the re- mainder CK is equal to the remainder HD ; but CK is equal to F ; therefore HD is equal to F. A G- B K C- H. Ꭰ E F ( a ) Hypoth . ( b ) V. Ax . 1 . A G ...
Page 33
... wherefore , also , the double of the third is greater than the double of the fourth ; therefore the third is greater than the fourth ; in like manner , if the first be equal to the second , or less than it , the third can be proved to ...
... wherefore , also , the double of the third is greater than the double of the fourth ; therefore the third is greater than the fourth ; in like manner , if the first be equal to the second , or less than it , the third can be proved to ...
Page 35
... wherefore , by the as D is to C ; and to B as C is to D SCHOLIUM . The foregoing proposition , expressed algebraically , is as follows : - THEOREM . - Iƒ A = m . a , and B = m . b , or if a b then A a : B : b . m ' A = and B == m For ...
... wherefore , by the as D is to C ; and to B as C is to D SCHOLIUM . The foregoing proposition , expressed algebraically , is as follows : - THEOREM . - Iƒ A = m . a , and B = m . b , or if a b then A a : B : b . m ' A = and B == m For ...
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The Elements of Euclid, with Many Additional Propositions, and Explanatory ... Euclides No preview available - 2016 |
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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.
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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.
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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.
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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.