Elements of Arithmetic, Algebra, and GeometryAdam Black and William Tait, 1826 |
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Página 55
... algebraic quantities , it indicates that they are to be taken collectively , or as one whole quantity . Thus a + bx c + d , means that the sum of a and b is to be multiplied by the sum of c and d If the quantities stood thus , a + bx c ...
... algebraic quantities , it indicates that they are to be taken collectively , or as one whole quantity . Thus a + bx c + d , means that the sum of a and b is to be multiplied by the sum of c and d If the quantities stood thus , a + bx c ...
Página 56
... more extended sense than it has in Arithmetic ; for here , both Ad- dition and Subtraction , strictly so called , are employed in finding the sum . From the division of algebraic quantities into positive and negative 56 ALGEBRA . 17.
... more extended sense than it has in Arithmetic ; for here , both Ad- dition and Subtraction , strictly so called , are employed in finding the sum . From the division of algebraic quantities into positive and negative 56 ALGEBRA . 17.
Página 57
George Lees. From the division of algebraic quantities into positive and negative , like and unlike , then arise three cases of addition . CASE I. To add like quantities with like signs . 18. RULE . Add together the coefficients of the ...
George Lees. From the division of algebraic quantities into positive and negative , like and unlike , then arise three cases of addition . CASE I. To add like quantities with like signs . 18. RULE . Add together the coefficients of the ...
Página 60
... algebraic quantities , is commonly divided into three cases , in each of which , it must be observed , that if the signs of the factors be like , that is , either both positive + , or both negative , the sign of the product will be + ...
... algebraic quantities , is commonly divided into three cases , in each of which , it must be observed , that if the signs of the factors be like , that is , either both positive + , or both negative , the sign of the product will be + ...
Página 68
... Algebraic quantities , may sometimes be carried on ad infinitum , like a recurring decimal . A few terms , however , of the quotient , will be sufficient to indicate the rest ; and , therefore , supersede the necessity of actually going ...
... Algebraic quantities , may sometimes be carried on ad infinitum , like a recurring decimal . A few terms , however , of the quotient , will be sufficient to indicate the rest ; and , therefore , supersede the necessity of actually going ...
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Términos y frases comunes
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
Pasajes populares
Página 174 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Página 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.
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.