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The rectangle contained by the sum and difference of two lines, is equivalent to the difference of the squares of those lines.
Elements of Geometry Upon the Inductive Method: To which is Added an ... - Page 62
by James Hayward - 1829 - 172 pages

## Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...and for altitudes BE = IK = IF. GEOMETRY. THEOREM XXXI. The rectangle constructed on the sum and the difference of two lines, is equivalent to the difference of the squares constructed on these two lines. Let AB be the greater line, BE = BE' the less, so that AE will represent...

## Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1857 - 242 pages
...proposition is expressed algebraically thus : Cor. (a+by— (a— b)'=4ab. PROPOSITION X. THEOREM. Hie rectangle contained by the sum and difference of two...lines, is equivalent to the difference of the squares of those lines Let AB, BC be any two lines ; the rectangle contained by the sum and difference of AB...

## National Society's Monthly Paper

1857 - 408 pages
...join equal and parallel straight lines towards the same parts are themselves equal and parallel. 3. The rectangle contained by the sum and difference of two lines is equal to the difference of their squares. SECT. II. — I. Angles in the same segment ofa circle are...

## Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...expressed algebraically thus : (a—by=a'—2ab+b\ Cor. (a+by—(a—b)'=4ab. PROPOSITION X. THEOREM. Fhe rectangle contained by the sum and difference of two...lines, is equivalent to the difference of the squares of those lines Let AB, BC be any two lines ; the rectangle contained by the sum and difference of AB...

## Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1860 - 246 pages
...expressed algebraically thus: (a—by=a t —2ab+b\ Cor. (a+by—(a—by=4ab. PROPOSITION X. THEOREM. fhe rectangle contained by the sum and difference of two lines, is equivalent to the difference of tlte squares of those lines Let AB, BC be any two lines ; the rectangle contained by the sum and difference...

## Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 472 pages
...rectangle AB xBE. * . -1 r- OO GEOMETRY. THEOREM XXXI. The rectangle constructed on the sum and the difference of two lines, is equivalent to the difference of the squares constructed on these two lines. Let AB be the greater line, BE = BE' the less, so that AE will represent...

## A Treatise on Special Or Elementary Geometry: In Four Parts ..., Part 3

Edward Olney - Geometry - 1872 - 96 pages
...the sum of the squares on the lines, minus twice the rectangle of the lines. 66 Y. The rectangle of the sum and difference of two lines is equivalent to the difference of the squares described on the lines. Sen.— The three preceding propositions are but geometrical conceptions and demonstrations...

## A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 562 pages
...the sum of the squares on the lines, minus twice the rectangle of the lines. 667. The rectangle of the sum and difference of two lines is equivalent to the difference of the squares described on the lines. OJ Fio. 370. oS Fio. 871. Fio. 873. VARIOUS DEMONSTRATIONS OF THE PYTHAGOREAN PROPOSITION....