## Elements of Arithmetic, Algebra, and GeometryAdam Black and William Tait, 1826 |

### From inside the book

Results 6-10 of 11

Page 85

... × 35x ( 2x ) + x - 73 +35 × ( 2x ) 3 x - 7 + 21 x ( 2 ) 2 x 75+ 7x ( 2x ) X - 76-77-128x7-3136x + 32928x192080x + 672280x3 - 1411788x2 + 1647086x - 823543 . 51. By means of the

... × 35x ( 2x ) + x - 73 +35 × ( 2x ) 3 x - 7 + 21 x ( 2 ) 2 x 75+ 7x ( 2x ) X - 76-77-128x7-3136x + 32928x192080x + 672280x3 - 1411788x2 + 1647086x - 823543 . 51. By means of the

**binomial**theorem , a trinomial INVOLUTION AND EVOLUTION . 85. Page 86

George Lees. 51. By means of the

George Lees. 51. By means of the

**binomial**theorem , a trinomial , or even a quadrinomial quantity , may be raised to any power . Let it be required , for example , to find the fourth power of a + b + c . By considering a + b as one ... Page 96

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**Binomial**Theorem . For it may be demonstrated , that the general formula stated in No. 50 , is equally true , whether n be positive or negative , integral or fractional . The general formula may perhaps be most conveniently expressed in ... Page 99

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**Binomial**Theorem may be very conveniently em- ployed for extracting imperfect roots of numbers , more par- ticularly when the number exceeds the complete power , whose root is to be extracted by a very little . Ex . Required the cube ... Page 122

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**binomial**is equal to the squares of its two terms , together with twice their product , ( p . 82 , ) it follows , that if the square of either of the terms , and twice the product of the two , be given , 122 ALGEBRA .### Other editions - View all

### Common terms and phrases

algebraic quantities angle ABC angle ACB angle BAC angle CAB angle EBA annex Arithmetic binomial Binomial Theorem bisected Book centre ciphers circumference coefficient consequently continued fraction cube root denominator diameter difference divided dividend divisor drawn equation example expressed exterior angle figure find the values fore fourth given circle given number greater greatest common measure guinea Hence improper fraction join least common multiple less manner merator minuend multiplied number of terms opposite angles parallel parallelogram perpendicular preceding prefixed PROP Q. E. D. Cor quotient ratio Reduce remaining angle Required the sum right angles rule Scholium sides square root straight line subtracted subtrahend surd tangent THEOREM third Transp triangle ABC units unity unknown quantity vulgar fraction Wherefore whole angle whole number

### Popular passages

Page 174 - Similar triangles are to one another in the duplicate ratio of their homologous sides.

Page 132 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 172 - But by the hypothesis, it is less than a right angle ; which is absurd. Therefore the angles ABC, DEF are not unequal, that is, they are equal : And the angle at A is equal to the angle at D ; wherefore...

Page 171 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 129 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the base of the one greater than the base of the other ; the angle also contained by the sides of that which has the greater base, shall be greater than the angle contained by the sides equal to them of the other.

Page 171 - C to the remaining angle at F. For, if the angles ABC, DEF be not equal, one of them is greater than the other : Let ABC be the greater, and at the point B, in the straight line AB, make the angle ABG equal to the angle (23.

Page 164 - If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it, and if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square on GEOMETRY.

Page 142 - EK, because EH is less than EK ; therefore the square of BH is greater than the square of FK, and the straight line BH greater than FK, and therefore BC is greater than FG.

Page 109 - When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.

Page 148 - From this it is manifest, that if one angle of a triangle be equal to the other two, it is a right angle, because the angle adjacent to it is equal to the same two ; and when the adjacent angles are equal, they ate right angles.