 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...the square of AC : hence, A AC* = AB* + which was to be proved. - 2AB x BC ; PROPOSITION X. THEOREM. .The rectangle contained by the sum and difference of two lines, is equal to the difference of their squares. Let AB and BC be two lines, of which AB is the greater :... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...AC=AD + EF—BD — CF. (a — b)2 = a2 + b2 — 2ab. 208. Proposition X. — Theorem. The rectangle of the sum and difference of two lines is equivalent to the difference of their squares. Let each side of the square AB be a, Er 1 — --s each side of the square CB be b, the... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...Scholium, This proposition is expressed algebraically thus : (ab)2=a"— 2ab+b2. PROPOSITION X. THEOREM. The rectangle contained by the sum and difference...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... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...square HF; that is, HF = AE + CK-(AK+CE), or AC l = AB* + BC*-'2AB. BC. Proposition 6. Tlieorem. — The rectangle contained by the sum and difference of two lines is equal to the difference of their squares. Let AB, BC be two lines; then (AB + BC) (AB-BC) From BA cut... | |
 | Vermont. Dept. of Education - 1880 - 216 pages
...line perpendicular to u diameter at its extremity is a tangent to tlie circumference." 6. Prove, " The rectangle contained by the sum and difference of two lines is equivalent to the diflerence between the squares of those lines." Prove, " The diagonal and side of a square have no... | |
 | Bombay city, univ - 1880 - 754 pages
...square on the line Ijetween the points of section, is equal to the square on half the line. Deduce that the rectangle contained by the sum and difference of two lines is equal to the difference of their squares. 3. The opposite angles of any quadrilateral figure, inscribed... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...the two lines minus twice the rectangle of the lines. 4. Prove geometrically that the rectangle of the sum and difference of two lines is equivalent to the difference of the squares described on the lines. 5. If a straight line is drawn from the vertex of an isosceles triangle to any point... | |
 | F. B. Stevens - Examinations - 1884 - 202 pages
...equivalent) to the squares of the two parts, together with twice the rectangle contained by the parts. 6. The rectangle contained by the sum and difference...lines is equivalent to the difference of the squares of those lines. 1880. 1. If a straight line fall on two parallel straight lines, it makes the alternate... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...square of AC : hence, AC2 = AB2 + BC3 - 2AB x BC ; which was to be proved. PROPOSITION X. THEOREM. The rectangle contained by the sum and difference of two lines, is equal fo the difference of their 8quares. • Let AB and BC be two lines, of which AB is the greater... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...contained by the lines. SCHOLIUM. Compare (a — b)* = a* — 2 ab + P. Proposition X. A Theorem. 245. The rectangle contained by the sum and difference of two lines is equal to the difference of their squares. SCHOLIUM. Compare (a + b) (a — b) = a* — P. Proposition... | |
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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. 
