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" The complements of the parallelograms which are about the diameter of any parallelogram, are equal to one another. Let ABCD be a parallelogram, of which the diameter is AC... "
Elements of geometry, containing books i. to vi.and portions of books xi ... - Page 69
by Euclides, James Hamblin Smith - 1872 - 349 pages
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A course of practical geometry for mechanics

William Pease - Geometry - 1843 - 80 pages
...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...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...described equal to the given triangle ABC, and having one of its angles CEF equal to the given angle DQKF PROPOSITION XLIII. THEOREM. The complements of the...parallelogram, are equal to one another. Let ABCD be a parallelogram, of which the diameter is AC: and EH, GF the parallelograms about AC, that is, through...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...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...parallelogram, are equal to one another. Let ABCD be a parallelogram, of which the diameter is AC, and EH, FG the parallelograms about AC, that is, through...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...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...parallelogram, are equal to one another. Let ABCD be a parallelogram of which the diameter is AC ; let EH, FG be the parallelograms about AC, that is, through...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...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...parallelogram, are equal to one another. Let ABCD be a parallelogram, of which the diameter is AC, and EH, FG the parallelograms about AC, that is, through...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...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...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...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...
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The London University Calendar

London univ - 1846 - 326 pages
...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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The first book of Euclid's Elements, simplified, explained and illustrated ...

Euclides - 1847 - 128 pages
...which = the gn. Dm ABCD, and having the L FCG = gn. L E. — QEF PROP. XLIII. THEOR. GEN. ENUN. — The complements of the parallelograms, which are about...diameter of any parallelogram, are equal to one another. PART. ENUN. — Let ABCD be aam, of which the diam. is AC ; EH, FG the AH » am8 about AC, ie through...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. PROP. XLIII. THEOREM. The complements of the parallelograms,...diameter of any parallelogram, are equal to one another. PROP. XLIV. PROBLEM. To a given straight line to apply a parallelogram, which shall be equal to a given...
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