The Elements of Euclid, with Many Additional Propositions and Explanatory Notes. ... Part II.1876 |
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Page 4
... four angles of the quadrilateral figure AKBM are together equal to four right angles ( ƒ ) , and the angles KAM and KBM are right angles ( d ) , the other two M and AKB are together equal to two right angles ; but the angles DEG and DEF ...
... four angles of the quadrilateral figure AKBM are together equal to four right angles ( ƒ ) , and the angles KAM and KBM are right angles ( d ) , the other two M and AKB are together equal to two right angles ; but the angles DEG and DEF ...
Page 5
... four circles may be described , touching them , one inscribed as above , and the other three touching each of the sides of the tri- angle externally , and the other sides produced . COROLLARY 1. The straight lines bisecting the three an ...
... four circles may be described , touching them , one inscribed as above , and the other three touching each of the sides of the tri- angle externally , and the other sides produced . COROLLARY 1. The straight lines bisecting the three an ...
Page 9
... four lines , AE , BE , CE , and DE , are equal , and therefore the circle described from the center E with the radius AE passes through the angular points , A , B , C , and D , and is circumscribed about the given square PROPOSITION X ...
... four lines , AE , BE , CE , and DE , are equal , and therefore the circle described from the center E with the radius AE passes through the angular points , A , B , C , and D , and is circumscribed about the given square PROPOSITION X ...
Page 11
... four - fifths of a right angle , and therefore the re- maining angle EBC equals one - fifth of the right angle ABC , and if the angle ABE be divided into four equal parts ( e ) by the lines BF , BG , and BH , the whole right angle ABC ...
... four - fifths of a right angle , and therefore the re- maining angle EBC equals one - fifth of the right angle ABC , and if the angle ABE be divided into four equal parts ( e ) by the lines BF , BG , and BH , the whole right angle ABC ...
Page 16
... four preceding books magnitudes have been compared simply as to their equality or inequality , but in the latter case no attempt has been made to determine how great or how small that inequality might be . The object , however , of the ...
... four preceding books magnitudes have been compared simply as to their equality or inequality , but in the latter case no attempt has been made to determine how great or how small that inequality might be . The object , however , of the ...
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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.