The Elements of Euclid, with Many Additional Propositions and Explanatory Notes. ... Part II.1876 |
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Page 2
... PROPOSITION I. PROBLEM . In a given circle ( ABC ) to inscribe a straight line , equal to a given straight line ( D ) , which is not greater than the diameter of the circle . SOLUTION . Draw a diameter BC of the circle ; and if this be ...
... PROPOSITION I. PROBLEM . In a given circle ( ABC ) to inscribe a straight line , equal to a given straight line ( D ) , which is not greater than the diameter of the circle . SOLUTION . Draw a diameter BC of the circle ; and if this be ...
Page 4
... proposition has been somewhat altered from that of Euclid , who omits to prove that the lines MN , LM , and LN must necessarily meet when produced . PROPOSITION IV . PROBLEM . - To inscribe a circle in a given triangle ( ABC ) ...
... proposition has been somewhat altered from that of Euclid , who omits to prove that the lines MN , LM , and LN must necessarily meet when produced . PROPOSITION IV . PROBLEM . - To inscribe a circle in a given triangle ( ABC ) ...
Page 5
... proposition is only a particular case of the more gene- ral problem , " To describe a circle touch- ing three given straight lines . " 1 ° . If the three given lines are parallel to each other ; or 2o . If they intersect at the same ...
... proposition is only a particular case of the more gene- ral problem , " To describe a circle touch- ing three given straight lines . " 1 ° . If the three given lines are parallel to each other ; or 2o . If they intersect at the same ...
Page 6
... PROPOSITION V. 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 , therefore a circle may be described passing ...
... PROPOSITION V. 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 , therefore a circle may be described passing ...
Page 7
... PROPOSITION V. B. THEOREM . - If any equilateral and equiangular rectilineal figure ( ABCDE ) be inscribed in a circle , tangents to the circle , drawn through the angular points , will form an equilateral and equiangular figure of the ...
... PROPOSITION V. B. THEOREM . - If any equilateral and equiangular rectilineal figure ( ABCDE ) be inscribed in a circle , tangents to the circle , drawn through the angular points , will form an equilateral and equiangular figure of the ...
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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.
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.
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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.
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.