 | Bhāskarācārya, Edward Strachey - Algebra - 1813 - 142 pages
...here then the differences of the two original numbers, " and of the two squares are both known ; and the difference of the squares of 'two "numbers is equal to the rectangle of the sum of the two numbers, into their " difference. Therefore when we divide the difference... | |
 | Euclides - 1840 - 192 pages
...possible to contrive any division of the scale which shall be capable of measuring both with exactness. The difference of the squares of two numbers is equal to the product of their sum and difference. Thus, take the two numbers 6 and 4, of which the sum is 10, the difference 2 ; then 6x6=36 4x4=H> 10x2=20... | |
 | William Desborough Cooley - Geometry - 1840 - 106 pages
...succeeding square, the remainders will be the series of odd numbers, 1,3,5, 7, 9, &c. The difference between the squares of two numbers is equal to the product of their sum and difference (App. c, p. i65), or to their sum, when their difference is only 1. Consequently, tbe difference of... | |
 | Frederic Augustus Adams - Arithmetic - 1847 - 46 pages
...necessary ; but let the pupil have no aid till he has overcome the difficulty, and is ready to proceed. P. The difference of the squares of two numbers is equal to the product of their sum and difference. T. Apply this to the triangle in hand, using the number given instead of the general term ab square.... | |
 | Thomas Lund - Geometry - 1854 - 520 pages
...can be proved both geometrically and algebraically, viz. that the difference of the squares of any two numbers is equal to the product of their sum and difference, the trouble of squaring large numbers may, in this instance and in some others, be avoided. Thus R'-r'... | |
 | W. H. Farrar - Mental arithmetic - 1860 - 180 pages
...triangle, and В С2 — А С2 = А B2 = 144 inches. The difference between B С and А С is 5 inches. As the difference of the squares of two numbers is equal to the product of the sum and difference, 144-=-5 = 28.8, 28 8-4-5 the sum of B С and А С ; therefore, — '-f- ,... | |
 | Education - 1863 - 406 pages
...of the base and hypothenuse. (80)^ = 6400 is the difference of the squares of the same quantities. The difference of the squares of two numbers is equal to the product of their sum into their difference. Hence,— — =32, or the difference, and ?2? + 3? = 116 or the hypotenuse,... | |
 | Richard Wormell - Geometry, Modern - 1868 - 286 pages
...(AC)2=(AB)2(BC)« ; (BC)•=(AB)2-(AC)". The following arithmetical facts may be applied at once to geometry. 1 st. The difference of the squares of two numbers is equal to the product of their sum and difference. and. The square of the sum of two numbers is equal to the sum of the squares together with twice the... | |
 | Richard Wormell - Geometry, Plane - 1870 - 304 pages
...(AB)2=(AC)2 + (BC)2; (AC)2 = (AB)2The following arithmetical facts may be applied at once to geometry. i st. The difference of the squares of two numbers is equal to the product of their sum and difference. znd. The square of the sum of two numbers is equal to the sum of the squares together with twice the... | |
 | James Smith - 1870 - 634 pages
...or two I shall favour you with a list of them, as also a new ' The difference of the squares of any two numbers is equal to the product of their sum and difference. This fact is of as much importance in practical Geometry, as in Algebra. JS t The square BBBB is an... | |
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The difference of the squares of two numbers is equal to the product of their sum and difference. 
