The Elements of Euclid, with Many Additional Propositions and Explanatory Notes. ... Part II.1876 |
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Page 2
... Draw a diameter BC of the circle ; and if this be equal to the given line D , the problem is solved ; but if it is not , take in it the segment CE equal to D ( a ) , and from C as a center , with the radius CE , describe the circle AEF ...
... Draw a diameter BC of the circle ; and if this be equal to the given line D , the problem is solved ; but if it is not , take in it the segment CE equal to D ( a ) , and from C as a center , with the radius CE , describe the circle AEF ...
Page 3
... draw the straight line KB ; at the point K in the straight line KB form the angle BKA equal to the angle DEG ( b ) , and from the same point , and on the other side of the same L B N E T ( a ) III . 1 . ( b ) I. 23 . H straight line ...
... draw the straight line KB ; at the point K in the straight line KB form the angle BKA equal to the angle DEG ( b ) , and from the same point , and on the other side of the same L B N E T ( a ) III . 1 . ( b ) I. 23 . H straight line ...
Page 4
... draw the straight lines ML , MN , and NL , touch- ing the circle ABC ( c ) , then shall they meet in the points M , N , and I , and form the triangle required . DEMONSTRATION . Join A and B , then because KAM and KBM are right angles ...
... draw the straight lines ML , MN , and NL , touch- ing the circle ABC ( c ) , then shall they meet in the points M , N , and I , and form the triangle required . DEMONSTRATION . Join A and B , then because KAM and KBM are right angles ...
Page 5
... draw DE and DG perpendicular to AB and AC . Then the angle ABC being bisected by DB ( e ) , the angles EBD and FBD are equal , and the angles DEB and DFB being both right angles ( f ) are also equal , therefore the triangles ÉBD and FBD ...
... draw DE and DG perpendicular to AB and AC . Then the angle ABC being bisected by DB ( e ) , the angles EBD and FBD are equal , and the angles DEB and DFB being both right angles ( f ) are also equal , therefore the triangles ÉBD and FBD ...
Page 7
... draw GF and HF respectively B perpendicular to BC and CD ( c ) . H ( b ) Theor . attached to I. 29 . DEMONSTRATION ... drawn from F to the other sides AB , AE , and DE are all equal to HF , and therefore that a circle described from F as ...
... draw GF and HF respectively B perpendicular to BC and CD ( c ) . H ( b ) Theor . attached to I. 29 . DEMONSTRATION ... drawn from F to the other sides AB , AE , and DE are all equal to HF , and therefore that a circle described from F as ...
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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.