Elements of GeometryHilliard and Metcalf, 1825 - 224 pages |
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Page vi
... employing division may be simplified when the operation cannot be performed Division of compound quantities What is understood by arranging the terms of a quantity Rules for performing division Examples in division Method of arrangement ...
... employing division may be simplified when the operation cannot be performed Division of compound quantities What is understood by arranging the terms of a quantity Rules for performing division Examples in division Method of arrangement ...
Page vii
... employing only one un- known quantity 79 To resolve equations of the first degree , when there are two un- known quantities 81 Of the Resolution of any given number of Equations of the First Degree , containing an equal number of ...
... employing only one un- known quantity 79 To resolve equations of the first degree , when there are two un- known quantities 81 Of the Resolution of any given number of Equations of the First Degree , containing an equal number of ...
Page 3
... employ the letters of the alphabet , generally using the 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 ...
... employ the letters of the alphabet , generally using the 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 ...
Page 18
... employed by both the fountains running together in filling the vessel ? If the time were given we should verify it by calculating the quantities of water discharged by each fountain , and adding them together we should be certain , that ...
... employed by both the fountains running together in filling the vessel ? If the time were given we should verify it by calculating the quantities of water discharged by each fountain , and adding them together we should be certain , that ...
Page 19
... employ- ed by each fountain in filling the vessel , by the sum of these numbers ; the quotient expresses the time required by both the fountains run- ning together to fill the vessel . Applying this rule to the particular case under ...
... employ- ed by each fountain in filling the vessel , by the sum of these numbers ; the quotient expresses the time required by both the fountains run- ning together to fill the vessel . Applying this rule to the particular case under ...
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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.