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" Prove, geometrically, that the rectangle of the sum and the difference of two straight lines is equivalent to the difference of the squares of those lines. "
Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... - Page 60
by Sir John Leslie - 1809 - 493 pages
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Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - 1817 - 456 pages
...difference AC of the two lines AB and BC. B PROP. XVII. THEOR. The rectangle contained by the sum and difference of two straight lines, is equivalent to...having made AG equal to AC, draw GH parallel to AD (I. 23.), and CI, DH parallel to AE. Because GK is equal to KC or HD, and EG is equal -to CB or BD, the...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 380 pages
...described on the two lines minus twice their rectangle. 222. Prove, geometrically, that the rectangle of the sum and the difference of two straight lines is equivalent to the difference of the squares of those lines. 223. Prove, geometrically, that the sum of the squares on two lines is...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1872 - 382 pages
...described on the two lines minus twice their rectangle. 222. Prove, geometrically, that the rectangle of the sum and the difference of two straight lines is equivalent to the difference of the squares of those lines. 223. Prove, geometrically, that the sum of the squares on two lines is...
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Euclid simplified. Compiled from the most important French works, approved ...

John Reynell Morell - 1875 - 220 pages
...squares on each of the lines, increased by twice their rectangle. 179. The rectangle constructed on the sum and the difference of two straight lines is equivalent to the difference of the squares of those lines. 180. Make a square equal to the sum or the difference of two squares. 181....
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - 1887 - 331 pages
...rectangle of which the two lines are the adjacent sides. 20. Prove, geometrically, that the rectangle of the sum and the difference of two straight lines is equivalent to the difference of the squares of those lines. PROBLEMS. 21. To construct a triangle, given its angles and its area (equal...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - 1890 - 420 pages
...constructed on the lines, diminished by twice the rectangle of the lines. 46. Prove that the rectangle of the sum and the difference of two straight lines is equivalent to the difference of the squares constructed on the lines. 47. ABC is an isosceles triangle, CA, CB being the equal sides;...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - 1890 - 418 pages
...on the lines, diminished by twice the rectangle of the lines. 46. Prove that the rectangle of thesum and the difference of two straight lines is equivalent to the difference of the squares constructed on the lines. 47. ABC is an isosceles triangle, CA, CB being the equal sides;...
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A Text-book of Geometrical Deductions: Book I [-II] Corresponding to ..., Book 2

James Andrew Blaikie, William Thomson - 1892 - 74 pages
...angle is equal to the rectangle contained by the hypotenuse and its adjacent segment. §33, Ex. 1. The rectangle contained by the sum and the difference of two straight lines is equal to the difference between their squares. § 33, Ex. 4. The difference between the squares on...
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Elementary Geometry

William Chauvenet - 1893 - 340 pages
...rectangle of which the two lines are the adjacent sides. 30. Prove, geometrically, that the rectangle of the sum and the difference of two straight lines is equivalent to the difference of the squares of those lines. PROBLEMS. 21. To construct a triangle, given its angles and its area (equal...
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Elements of Geometry: Plane geometry

Andrew Wheeler Phillips, Irving Fisher - 1896 - 276 pages
...their rectangle. CB Hint.—Let AB and BC be the given lines. • 434. The rectangle whose sides are the sum and the difference of two straight lines is equivalent to the difference of the squares described upon the two lines. ABC Hint.—Let AB and BCbe the given lines. Question.—To...
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