Elements of GeometryHilliard and Metcalf, 1825 - 224 pages |
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Results 6-10 of 11
Page 35
... multiplicand by the second term - 4a3 b of the multiplier . This last having the sign , all the products which it gives must have the signs contrary to those of the corresponding terms of the multiplicand ; the coefficients , 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 signs contrary to those of the corresponding terms of the multiplicand ; the coefficients , the ...
Page 36
Adrien Marie Legendre. Multiplicand 5a1b2 + 7a3b3 — 15a5c + 23b2 d1 — 17bc3 d2 — 9abcdm3 Multiplier 11b3 8c35abc - 2bdm Several products . Result reduced . 55a4b5 + 77a3b6-165a5b3c + 253b5d4-187b4c3d2-99ab * cdm3 -40a4b3c3-56a3b3c3 + ...
Adrien Marie Legendre. Multiplicand 5a1b2 + 7a3b3 — 15a5c + 23b2 d1 — 17bc3 d2 — 9abcdm3 Multiplier 11b3 8c35abc - 2bdm Several products . Result reduced . 55a4b5 + 77a3b6-165a5b3c + 253b5d4-187b4c3d2-99ab * cdm3 -40a4b3c3-56a3b3c3 + ...
Page 37
... multiplicand are of the same degree ( 27 ) , and those of the multiplier are also of the same degree , all the terms ... multiplicand is of the fourth degree , the multiplier of the third ; and the product is of the seventh . In the ...
... multiplicand are of the same degree ( 27 ) , and those of the multiplier are also of the same degree , all the terms ... multiplicand is of the fourth degree , the multiplier of the third ; and the product is of the seventh . In the ...
Page 43
... multiplicand in the example of art . 32. This is called arranging the proposed quan- tities . When they are thus disposed , it is evident , that whatever be the factor by which it is necessary to multiply the second to ob- tain the ...
... multiplicand in the example of art . 32. This is called arranging the proposed quan- tities . When they are thus disposed , it is evident , that whatever be the factor by which it is necessary to multiply the second to ob- tain the ...
Page 44
... multiplicand 5 a1 , it follows that the multiplier must have the sign — . Divi- sion then being performed upon the ... multiplicand , the multiplier has the sign + , and , that when a product has the contrary sign to that of the ...
... multiplicand 5 a1 , it follows that the multiplier must have the sign — . Divi- sion then being performed upon the ... multiplicand , the multiplier has the sign + , and , that when a product has the contrary sign to that of 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.