The Elements of Euclid, with Many Additional Propositions and Explanatory Notes. ... Part II.1876 |
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Page 111
... CYLINDER is a solid figure described by the revolution of a right - angled parallelogram ( ABC ) about one of its sides ( AB ) , which remains fixed . 20. The AXIS OF A CYLINDER is the fixed straight line ( AB ) about which the ...
... CYLINDER is a solid figure described by the revolution of a right - angled parallelogram ( ABC ) about one of its sides ( AB ) , which remains fixed . 20. The AXIS OF A CYLINDER is the fixed straight line ( AB ) about which the ...
Page 112
Euclid Henry Law. 22. SIMILAR CONES AND CYLINDERS are those which have their axes and the diameters of their bases proportionals . 23. A PARALLELOPIPED is a solid figure contained by six quadrilateral figures , whereof every opposite two ...
Euclid Henry Law. 22. SIMILAR CONES AND CYLINDERS are those which have their axes and the diameters of their bases proportionals . 23. A PARALLELOPIPED is a solid figure contained by six quadrilateral figures , whereof every opposite two ...
Page 174
... cylinder ; this prism shall be greater than half of the cylinder : for let a square be described about the circle , and let a prism be erected upon the square , of the same altitude with the cylinder ; then the inscribed square is half ...
... cylinder ; this prism shall be greater than half of the cylinder : for let a square be described about the circle , and let a prism be erected upon the square , of the same altitude with the cylinder ; then the inscribed square is half ...
Page 175
... cylinder which to- gether are less than the excess of the cylin- der above the triple of the cone ( d ) : let them be those upon the segments of the circle , AE , EB , BF , FC , CG , GD , DH , HA ; therefore the rest of the cylinder ...
... cylinder which to- gether are less than the excess of the cylin- der above the triple of the cone ( d ) : let them be those upon the segments of the circle , AE , EB , BF , FC , CG , GD , DH , HA ; therefore the rest of the cylinder ...
Page 176
... cylinder : but this pyramid is the third part of the prism upon the same base AEBFCGDH , and of the same altitude with the cylinder ; therefore this prism is greater than the cylinder of which the base is the circle ABCD : but it is ...
... cylinder : but this pyramid is the third part of the prism upon the same base AEBFCGDH , and of the same altitude with the cylinder ; therefore this prism is greater than the cylinder of which the base is the circle ABCD : but it is ...
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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.