| John Playfair - 1842 - 317 páginas
...will apply to the problem : to make a triangle equivalent to a given rectangle. PROP. XLIII. THEOR. . **The complements of the parallelograms which are about...parallelograms about AC, that is, through which AC** passes, and let BK, KD be the other parallelograms, which make up the whole figure ABCD, and are therefore... | |
| Euclides - 1842
...equivalent to the sum of the two triangles ; that is, to the trapezoid ABC r>. QED PROP. XLIII. THEOR. **THE complements of the parallelograms, which are about the diameter of any parallelogram, are equal** or equivalent to one another. Let ABC D be a parallelogram, of which the diameter is AC; and EH, FG,... | |
| William Chambers, Robert Chambers - 1842
...explanation with the annexed figure. Let ABCD be a parallele- . ,. „ gram, of which the diagonal **is AC ; let EH, FG, be the parallelograms about AC, that is, through which AC** passes, and BK, KD, the other parallelograms which make up the whole figure ABCD, which are therefore... | |
| William Pease - 1843 - 68 páginas
...parallel to AE, cutting AD in H, and EF in I ; when AHIE shall be the rectangle required. Reason : because **the complements of the parallelograms which are about...diameter of any parallelogram, are equal to one another.** Vide Prop. XLIII, Bk. I. Euclid ; («. e. AF being the diameter,) the complement BEIG is equal to the... | |
| Euclid - 1845 - 199 páginas
...one of its angles CEF equal to the given angle D. Which was to be done. PROPOSITION XLIII. THEOB. — **The complements of the parallelograms, which are about...ABCD be a parallelogram, of which the diameter is AC,** and EH, FG the parallelograms about AC, that is, through which AC passes ; and BK, KD the other parallelograms... | |
| Euclides - 1845
...triangle ABC, and having one of its angles CEF equal to the given angle DQKF PROPOSITION XLIII. THEOREM. **The complements of the parallelograms which are about...ABCD be a parallelogram, of which the diameter is AC:** and EH, GF the parallelograms about AC, that is, through mhich AC passes: also BK, KD the other parallelograms... | |
| Euclides - 1846
...given triangle ABC, and having one of its angles CEF equal to the given angle DQEF PROP. XLIII. THEOR. **The complements of the parallelograms, which are about...ABCD be a parallelogram, of which the diameter is AC,** and EH, FG the parallelograms about AC, that is, through which AC passes, and BK, KD the other parallelograms... | |
| Great Britain. Admiralty - 1846
...equal bases and to-wards the same parts, are between the same parallels PROP. XXXVII. THEOR. 43.1 Eu. **The complements of the parallelograms which are about the diameter of any parallelo-gram, are equal to** each other. Let ABCD be a /—7 m , AC its diam.; and EAHK, GKFC, /—T" about AC, that is, through... | |
| Great Britain. Admiralty - 1846
...equal bases and towards the same parts, are between the same parallels PROP. XXXVII. THEOR. 43. lEu. **The complements of the parallelograms which are about the diameter of any parallelogram, are equal to** each other. Let ABCD be a /—7 m , AC its diam.; and EAHK, GKFC, /—7°" about AC, that is, through... | |
| London univ - 1846
...Parallelograms upon the same base and between the same parallels are equal to one another. 7. Show that **the complements of the parallelograms which are about the diameter of any .parallelogram are equal.** 8. In any right-angled triangle, prove that the square which is described upon the side subtending... | |
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