Elements of GeometryHilliard and Metcalf, 1825 - 224 pages |
From inside the book
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Page 39
... divisor and those of the quotient ; whence , by suppressing in the dividend all the factors which compose the divisor , the result will be the quotient sought . Let there be , for example , the simple quantity 72 a3 b3 c2 d to be ...
... divisor and those of the quotient ; whence , by suppressing in the dividend all the factors which compose the divisor , the result will be the quotient sought . Let there be , for example , the simple quantity 72 a3 b3 c2 d to be ...
Page 40
... divisor . We see by this , that the proposition , every quantity which has zero for its exponent , is equal to 1 ... divisor should have no letter which is not found in the dividend ; 2. that the exponent of any letter in the divisor ...
... divisor . We see by this , that the proposition , every quantity which has zero for its exponent , is equal to 1 ... divisor should have no letter which is not found in the dividend ; 2. that the exponent of any letter in the divisor ...
Page 41
... divisor , and may consequently be suppressed . To find the number of factors b common to the two terms of the fraction , we must divide the higher b by the lower b3 , ac- cording to the rule above given , and the quotient ba shows ...
... divisor , and may consequently be suppressed . To find the number of factors b common to the two terms of the fraction , we must divide the higher b by the lower b3 , ac- cording to the rule above given , and the quotient ba shows ...
Page 42
... divisor is or is not a factor of the dividend . As the divisor multiplied by the quotient must produce the dividend , it is necessary that this last should contain all the sev- eral products of each term of the divisor by each term of ...
... divisor is or is not a factor of the dividend . As the divisor multiplied by the quotient must produce the dividend , it is necessary that this last should contain all the sev- eral products of each term of the divisor by each term of ...
Page 43
... divisor in the order of the expo- nents of the power of the same letter , beginning with the highest and proceeding from left to right , as may be seen with reference to the letter a in the quantities 5 a7 — 22 a® b + 12 a5 b2 6 ab3 ...
... divisor in the order of the expo- nents of the power of the same letter , beginning with the highest and proceeding from left to right , as may be seen with reference to the letter a in the quantities 5 a7 — 22 a® b + 12 a5 b2 6 ab3 ...
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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.