| 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... | |
| |