The Elements of Euclid, with Many Additional Propositions and Explanatory Notes. ... Part II.1876 |
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Page 9
... parallelograms ( d ) , their opposite sides are equal ( e ) ; therefore , EG , FG , HG , and GK are all equal , and the circle described from the center G with the radius EG will pass through the points F , H , and K , and because the ...
... parallelograms ( d ) , their opposite sides are equal ( e ) ; therefore , EG , FG , HG , and GK are all equal , and the circle described from the center G with the radius EG will pass through the points F , H , and K , and because the ...
Page 71
... parallelograms ( EC , CF ) which have the same altitude , are to one another as their 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 ...
... parallelograms ( EC , CF ) which have the same altitude , are to one another as their 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 ...
Page 72
... parallelogram CE is double of the triangle ABC ( c ) , and the parallelogram CF double of the triangle ACD ( c ) , and that magnitudes have the same ratio which their equimul- tiples have ( d ) ; as the triangle ABC is to the triangle ...
... parallelogram CE is double of the triangle ABC ( c ) , and the parallelogram CF double of the triangle ACD ( c ) , and that magnitudes have the same ratio which their equimul- tiples have ( d ) ; as the triangle ABC is to the triangle ...
Page 73
... parallelogram GB is to the parallelogram BH , so is the base GC to the base CH ( a ) ; but the parallelogram BG is double of the triangle ABC , and the parallelogram BH is double of the triangle DBC , and magnitudes have the same ratio ...
... parallelogram GB is to the parallelogram BH , so is the base GC to the base CH ( a ) ; but the parallelogram BG is double of the triangle ABC , and the parallelogram BH is double of the triangle DBC , and magnitudes have the same ratio ...
Page 75
... parallelograms FI , MC , the opposite sides are equal ( a ) , therefore , FM equal GI , and ML equal IC ; and in the triangles AFG and FBL , AD is to DF , as AE is to EG ( b ) ; and FH is to HB , as FM is to ML ( b ) , that is , as GI ...
... parallelograms FI , MC , the opposite sides are equal ( a ) , therefore , FM equal GI , and ML equal IC ; and in the triangles AFG and FBL , AD is to DF , as AE is to EG ( b ) ; and FH is to HB , as FM is to ML ( b ) , that is , as GI ...
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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.
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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.
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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.