Elements of GeometryHilliard and Metcalf, 1825 - 224 pages |
From inside the book
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Page vii
... preceding questions by 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 ...
... preceding questions by 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 ...
Page 3
... preceding operations , will answer only for the particular example which is selected , while the course of reasoning considered by itself , by teaching us , that the less part is equal to half the number to Preliminary Remarks . 3 ...
... preceding operations , will answer only for the particular example which is selected , while the course of reasoning considered by itself , by teaching us , that the less part is equal to half the number to Preliminary Remarks . 3 ...
Page 6
... preceding result is deduced also from the following enunciation : Knowing the sum a of two numbers and their difference b , to find each of those numbers ; since , in other words , the number to be divided is the sum of the two numbers ...
... preceding result is deduced also from the following enunciation : Knowing the sum a of two numbers and their difference b , to find each of those numbers ; since , in other words , the number to be divided is the sum of the two numbers ...
Page 7
... preceding article , but we should be obliged to repeat all the reasonings and all the opera- tions , by which we have arrived at the number 30 , because there is nothing to show how this number is composed of 230 , 40 , and 60. To ...
... preceding article , but we should be obliged to repeat all the reasonings and all the opera- tions , by which we have arrived at the number 30 , because there is nothing to show how this number is composed of 230 , 40 , and 60. To ...
Page 8
... preceding article twice 40 , or 80 , and CO from 230 , there will remain 90 , of which the third part is 30 , as we have found already . If the number to be divided were 520 , one excess 50 , and the other 120 , we should subtract twice ...
... preceding article twice 40 , or 80 , and CO from 230 , there will remain 90 , of which the third part is 30 , as we have found already . If the number to be divided were 520 , one excess 50 , and the other 120 , we should subtract twice ...
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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.