The Elements of Euclid, with Many Additional Propositions and Explanatory Notes. ... Part II.1876 |
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Page 8
... base AB is equal to AD ( a ) ; and in the same manner it may be shown that each of the other sides , DC and BC are equal to AB , and therefore that the quadrilateral figure ABCD is equilateral . But the straight line BD being a diameter ...
... base AB is equal to AD ( a ) ; and in the same manner it may be shown that each of the other sides , DC and BC are equal to AB , and therefore that the quadrilateral figure ABCD is equilateral . But the straight line BD being a diameter ...
Page 10
... base shall be double of the angle opposite to the same . SOLUTION . Take any straight line AB , and divide it in C ... base , B and BCD , double of the vertical angle BDC . COROLLARY 2. The triangle ACD is isosceles , and each of the ...
... base shall be double of the angle opposite to the same . SOLUTION . Take any straight line AB , and divide it in C ... base , B and BCD , double of the vertical angle BDC . COROLLARY 2. The triangle ACD is isosceles , and each of the ...
Page 11
... base , ADC and ACD , by the straight lines BD and EC ( c ) , and join CB , BA , AE , and ED ; then ABCDE is the pentagon required . G F H ( a ) IV . 10 . IV . 2 . ( c ) I. 9 . ( d ) Solution . III . 26 . ( f ) III . 29 . ( g ) Ax . 2 ...
... base , ADC and ACD , by the straight lines BD and EC ( c ) , and join CB , BA , AE , and ED ; then ABCDE is the pentagon required . G F H ( a ) IV . 10 . IV . 2 . ( c ) I. 9 . ( d ) Solution . III . 26 . ( f ) III . 29 . ( g ) Ax . 2 ...
Page 12
... base are each double its vertical angle ; and in like manner any other equilateral figure of any number of sides may be inscribed in a circle , by the aid of an isos- celes triangle , in which each of the angles at its base is to its ...
... base are each double its vertical angle ; and in like manner any other equilateral figure of any number of sides may be inscribed in a circle , by the aid of an isos- celes triangle , in which each of the angles at its base is to its ...
Page 71
... bases . CONSTRUCTION . Produce BD both ways to the points H , L , and take any number of straight lines BG , GH , each equal to the base BC ; and DK , KL , any number of them , each equal to the base CD ; and join AG , AH , AK , AL . EA ...
... bases . CONSTRUCTION . Produce BD both ways to the points H , L , and take any number of straight lines BG , GH , each equal to the base BC ; and DK , KL , any number of them , each equal to the base CD ; and join AG , AH , AK , AL . EA ...
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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.