The Elements of Euclid, with Many Additional Propositions and Explanatory Notes. ... Part II.1876 |
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Page 5
... A triangle is equal in area to the rec- tangle under the radius of the inscribed circle , and half the sum of the three sides or perimeter of the triangle . A C F E B For the area of the whole triangle ABC is equal ELEMENTS OF GEOMETRY . 5.
... A triangle is equal in area to the rec- tangle under the radius of the inscribed circle , and half the sum of the three sides or perimeter of the triangle . A C F E B For the area of the whole triangle ABC is equal ELEMENTS OF GEOMETRY . 5.
Page 6
... half the sides AB , BC , and AC . PROPOSITION V. B PROBLEM . To circumscribe a circle about a given triangle ( ABC ) . SOLUTION . The three angular points , A , B , and C , of the trian- gle , are not in the same straight line ...
... half the sides AB , BC , and AC . PROPOSITION V. B PROBLEM . To circumscribe a circle about a given triangle ( ABC ) . SOLUTION . The three angular points , A , B , and C , of the trian- gle , are not in the same straight line ...
Page 9
... half a right angle ( a ) , and in the same manner it may be shown that each of the angles into which the angles of the square are divided by the diagonals is half a right angle ; and , therefore , that they are all equal . Then in the ...
... half a right angle ( a ) , and in the same manner it may be shown that each of the angles into which the angles of the square are divided by the diagonals is half a right angle ; and , therefore , that they are all equal . Then in the ...
Page 12
... half the number of its sides minus half , is to unity ; thus a square may be inscribed by the aid of an isosceles triangle having the ratio between each of the angles at its base and its vertical angle as ( 1 − 1 = ) 11 : 1 ; a ...
... half the number of its sides minus half , is to unity ; thus a square may be inscribed by the aid of an isosceles triangle having the ratio between each of the angles at its base and its vertical angle as ( 1 − 1 = ) 11 : 1 ; a ...
Page 13
Euclid Henry Law. H G A M E L ABF is half of ABC ( d ) , AEF is half of AED ; and in the same manner it may be shown that the other angles BCD and CDE are bisected by the lines FC and FD . Therefore in the triangles FBH and FBG the ...
Euclid Henry Law. H G A M E L ABF is half of ABC ( d ) , AEF is half of AED ; and in the same manner it may be shown that the other angles BCD and CDE are bisected by the lines FC and FD . Therefore in the triangles FBH and FBG the ...
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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 Edition equal and similar equal angles equi equiangular equimultiples Euclid ex æquali fore four magnitudes fourth given circle given straight line greater ratio HENRY LAW 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.