The Elements of Euclid, with Many Additional Propositions and Explanatory Notes. ... Part II.1876 |
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Page 2
... diameter of the circle . SOLUTION . 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 ...
... diameter of the circle . SOLUTION . 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 ...
Page 8
... diameters AC , BD , at right angles to each other ; and join AB , BC , CD , and DA , then ABCD is the square required ... diameter , ABD is a semicircle , and therefore the angle BAD is a right angle ( b ) , and the quadrilateral figure ...
... diameters AC , BD , at right angles to each other ; and join AB , BC , CD , and DA , then ABCD is the square required ... diameter , ABD is a semicircle , and therefore the angle BAD is a right angle ( b ) , and the quadrilateral figure ...
Page 14
... diameter AD . From D as a center with the radius DG describe a circle GEHC , join EG and GC , and produce them to the points B and F. Join AF , FE , ED , DC , CB , BA , with straight lines , and they will form an equilateral and equian ...
... diameter AD . From D as a center with the radius DG describe a circle GEHC , join EG and GC , and produce them to the points B and F. Join AF , FE , ED , DC , CB , BA , with straight lines , and they will form an equilateral and equian ...
Page 98
... diameter . B K E D H F DEMONSTRATION . For , if not , let the parallelogram BD have its dia- meter AHC in a different straight line from AF the diameter of the parallelogram EG , and let GF meet AHC in H ; through H draw HK parallel to ...
... diameter . B K E D H F DEMONSTRATION . For , if not , let the parallelogram BD have its dia- meter AHC in a different straight line from AF the diameter of the parallelogram EG , and let GF meet AHC in H ; through H draw HK parallel to ...
Page 106
... the triangle ( BA , AC ) is equal to the rectangle under the perpendicular ( AD ) and the diameter of the circle described about the triangle . DEMONSTRATION . Describe the cir- cle ACB about the triangle 106 ELEMENTS OF GEOMETRY .
... the triangle ( BA , AC ) is equal to the rectangle under the perpendicular ( AD ) and the diameter of the circle described about the triangle . DEMONSTRATION . Describe the cir- cle ACB about the triangle 106 ELEMENTS OF GEOMETRY .
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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.
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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.
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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.