 | Nathan Scholfield - 1845 - 894 pages
...formula, (a— 6)2=aa— 2ab+ b\ PROPOSITION III. THEOREM. The rectangle contained by the sum and the difference of two lines, is equivalent to the difference of the squares of those lines. Let AB, BC, be two lines ; then will CBK On AB and AC, describe the squares ABIF. ACDE : produce AB till the _ H produced... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...Scholium. This proposition is expressed algebraically thus: (a—by=a'—2ab+b\ Cor. (a+by—(a—V)'=<lab. PROPOSITION X. THEOREM. The rectangle contained by...the difference of the squares on AB and BC; that is, (AB+BC) X (AB—BC) = AB'—BC'. Upon AB describe the square ABKF, -p & K and upon AC describe the... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...formula, (a—6) 2 =a 2 —2ab+b*. PROPOSITION X. THEOREM. The rectangle contained by the sum and the difference of two lines, is equivalent to the difference of the squares of those lines. Let AB, BC, be two lines; then, will (AB+BC) x (AB—BC)=AB 2 —BC 2 . On AB and AC, describe the squares ABIF, ACDE;... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...100-120+36 = 16. PROPOSITION VII. THEOREM. The rectangle under the sum and difference of two lines, is equal to the difference of the squares of those lines. Let AB, BC be any two unequal FI : 1 ID lines ; then will the difference of the squares of AB, AC, be equal to a rectangle... | |
 | 582 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 squarea. SECTION II. 1. Angles in the same segment of a circle are... | |
 | 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... | |
 | 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...difference of the squares on AB and BC ; that is, (AB+BC) x (AB— BC) = AB"— BC'. Upon AB describe the square ABKF, p & K and upon AC describe the... | |
 | 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... | |
 | 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...difference of the squares on AB and BC ; that is, ( AB + BC ) x ( AB — BC) = AB' — BC'. Upon AB describe the square ABKF, jr G- K and upon AC describe... | |
 | 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... | |
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THEOREM. The rectangle contained by the sum and difference of two lines, is equivalent to the difference of the squares of those lines. 
