Elements of GeometryHilliard and Metcalf, 1825 - 224 pages |
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Page xi
... final equation 198 Of Commensurable Roots , and the equal Roots of Numerical Equations 199 ib . · ib . Every equation , the coefficients of which are entire numbers , that of the first term being 1 , can only have for roots en- tire ...
... final equation 198 Of Commensurable Roots , and the equal Roots of Numerical Equations 199 ib . · ib . Every equation , the coefficients of which are entire numbers , that of the first term being 1 , can only have for roots en- tire ...
Page 3
... last ; as in arithmetic we put x for the fourth term of a proportion , of which only the three first are known . It is from the use of these several signs that we derive the science of Algebra . I now proceed by means of them to ...
... last ; as in arithmetic we put x for the fourth term of a proportion , of which only the three first are known . It is from the use of these several signs that we derive the science of Algebra . I now proceed by means of them to ...
Page 25
... term + c , we have another part c to be add- ed , there will remain therefore to be subtracted only 4 c . The sum of the expressions proposed then , will be reduced to 6a16b- 4 c + 4 d e . The last operation exhibited above , by which ...
... term + c , we have another part c to be add- ed , there will remain therefore to be subtracted only 4 c . The sum of the expressions proposed then , will be reduced to 6a16b- 4 c + 4 d e . The last operation exhibited above , by which ...
Page 33
... term of the mul- tiplier , will be by the last example a cbc ; but by taking the whole of c for the multiplier instead of c diminished by d , we take the quantity ab so many times too much as is denoted by the number d ; so that the ...
... term of the mul- tiplier , will be by the last example a cbc ; but by taking the whole of c for the multiplier instead of c diminished by d , we take the quantity ab so many times too much as is denoted by the number d ; so that the ...
Page 35
... terms , we find it to be + 4 a5 b2 . The second line contains the products of all the terms of the multiplicand by the second term - 4a3 b of the multiplier . This last having the sign , all the products which it gives must have the ...
... terms , we find it to be + 4 a5 b2 . The second line contains the products of all the terms of the multiplicand by the second term - 4a3 b of the multiplier . This last having the sign , all the products which it gives must have the ...
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Common terms and phrases
a² b³ algebraic Algebraic Quantities Arith arithmetic becomes binomial changing the signs coefficient common divisor consequently contains courier cube root decimal deduce denominator denoted divided dividend division employed entire number enunciation equa evident example exponent expression extract the root figures follows formula fraction given in art given number gives greater greatest common divisor last term letters logarithm manner method multiplicand multiplied negative number of arrangements observed obtain operation perfect square polynomials preceding article proposed equation proposed number quan question quotient radical quantities radical sign reduced remainder represented resolve result rule given second degree second member second term simple quantities square root subtract suppose taken tens third tion tities units unity unknown quantity vulgar fractions whence whole numbers
Popular passages
Page 9 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 44 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 63 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 101 - Which proves that the square of a number composed of tens and units, contains the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 8 - Any side of a triangle is less than the sum of the other two sides...
Page 122 - ... is negative in the second member, and greater than the square of half the coefficient of the first power of the unknown quantity, this equation can have only imaginary roots.
Page 180 - CD, &c., taken together, make up the perimeter of the prism's base : hence the sum of these rectangles, or the convex surface of the prism, is equal to the perimeter of its base multiplied by its altitude.
Page 54 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Page 185 - The convex surface of a cone is equal to the circumference of the base multiplied by half the slant height.
Page 164 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.