## Subtraction Sentence Examples

- The size of the boiler may be increased or diminished by the addition or
**subtraction**of one or more sections; these, being simple in design, are easily fitted together, and should a section become defective it is a simple matter to insert a new one in its place. - A master could not enter into a contract with his slave, nor could he accuse him of theft before the law; for, if the slave took anything, this was not a
**subtraction**, but only a displacement, of property. - - To find a square number which remains a square after the addition and
**subtraction**of 5, put to our mathematician in presence of the emperor by John of Palermo, who, perhaps, was quite enough Leonardo's friend to set him such problems only as he had himself asked for. - (i.) In the case of
**subtraction**the second of these two questions is perhaps the simpler. - It is true that we obtain this result by subtracting 3 from io by means of a
**subtractiontable**(concrete or ideal); but this table merely gives the generalized results of a number of operations of addition or**subtraction**performed with concrete units. - This is due to the fact that there are really two kinds of
**subtraction**, respectively involving counting forwards (complementary addition) and counting backwards (ordinary**subtraction**); and it suggests that it may be wise not to use the one symbol - to represent the result of both operations until the commutative law for addition has been fully grasped. - The five processes of deduction then reduce to four, which may be described as (i.)
**subtraction**, (ii.) division, (iii.) (a) taking a root, (iii.) (b) taking logarithms. It will be found that these (and particularly the first three) cover practically all the processes legitimately adopted in the elementary theory of the solution of equations; other processes being sometimes liable to introduce roots which do not satisfy the original equation. - (c) The fundamental properties of
**subtraction**and of division are that A - B +B = A and m X m of A = A, since in each case the second operation restores the original quantity with which we started. - - (i.) The results of the addition,
**subtraction**and multiplication of multinomials (including monomials as a particular case) are subject to certain laws which correspond with the laws of arithmetic (ï¿½ 26 (i.)) but differ from them in relating, not to arithmetical value, but to algebraic form. - The unknown he terms arithmos, the number, and in solutions he marks it by the final s; he explains the generation of powers, the rules for multiplication and division of simple quantities, but he does not treat of the addition,
**subtraction**, multiplication and division of compound quantities. - Stifel introduced the sign (+) for addition or a positive quantity, which was previously denoted by plus, pia, or the letter p.
**Subtraction**, previously written as minus, mene or the letter m, was symbolized by the sign (-) which is still in use. - Girard is inconsistent in his notation, sometimes following Vieta, sometimes Stevin; he introduced the new symbols ff for greater than and ï¿½ for less than; he follows Vieta in using the plus (+) for addition, he denotes
**subtraction**by Recorde's symbol for equality (=), and he had no sign for equality but wrote the word out. - (b2V2 + n2) (a2 - b 2) = - z It will now be convenient to introduce the quantities a l, a 2', 7731 which express the rotations of the elements of the medium round axes parallel to those of co-ordinates, in accordance with the equations Ty - 1 = dz ' 3= - dy 2 = dx - In terms of these we obtain from (7), by differentiation and
**subtraction**, (b 2 v 2 + n 2) 7,3 = 0 (b 2 0 2 +n 2) .r i = dZ/dy (b 2 v 2 +n 2)', , 2 = - dZ/dx The first of equations (9) gives 3 = 0 (10) For al we have ?1= 47rb2, f dy e Y tkr dx dy dz - The change of the intrinsic energy in passing from one state to another, as from B to C is represented by the addition of the heat-area H= Bczz', and the
**subtraction**of the work-area W = BCcb. - A marine force was raised to stop smuggling; and the
**subtraction**of coal during coaling operations was stopped by drastic legislation. - The most instructive is to regard the prismoid as built up (by addition or
**subtraction**) of simpler figures, which are particular cases of it. - It is found that the alteration of the tangent elevation is almost insensible, but the quadrant elevation requires the addition or
**subtraction**of the angle of sight. - Logarithms were originally invented for the sake of abbreviating arithmetical calculations, as by their means the operations of multiplication and division may be replaced by those of addition and
**subtraction**, and the operations of raising to powers and extraction of roots by those of multiplication and division. - The explanation of this property of the base io is evident, for a change in the position of the decimal points amounts to multiplication or division by some power of 10, and this corresponds to the addition or
**subtraction**of some integer in the case of the logarithm, the mantissa therefore remaining intact. - 2 The method consists in the use of the formula sin a sin b=2 {cos(a-b)-cos(a+b)l, by means of which the multiplication of two sines is reduced to the addition or
**subtraction**of two tabular results taken from a table of sines; and, as such products occur in the solution of spherical triangles, the method affords the solution of spherical triangles in certain cases by addition and**subtraction**only. - Logistic or Proportional Logarithms. - The old name for what are now called ratios or fractions are logistic numbers, so that a table of log (a/x) where x is the argument and a a constant is called a table of logistic or proportional logarithms; and since log (a/x) =log a-log x it is clear that the tabular results differ from those given in an ordinary table of logarithms only by the
**subtraction**of a constant and a change of sign. - Gaussian logarithms are intended to facilitate the finding of the logarithms of the sum and difference of two numbers whose logarithms are known, the numbers themselves being unknown; and on this account they are frequently called addition and
**subtraction**logarithms. The object of the table is in fact to give log (a =b) by only one entry when log a and log b are given. - In Order, Therefore, To Render The
**Subtraction**Possible, L Must Be Increased By Some Multiple Of 7, As 7M, And The Formula Then Becomes 7M L X. - Combination of this doctrine with a tendency to think chiefly of experiment, of the controlled addition or
**subtraction**of these elements one at a time, that we owe the theoretically premature linking of a as effect to A as cause. - GP) = o, for we should have, by
**subtraction**, ~(m(~+P~)1=0, or ~(m).GG o; (4) - Possessed opposite electricities, so that in charging the jar as much positive electricity is added to one side as negative to the other, led Franklin about 1750 to suggest a modification called the single fluid theory, in which the two states of electrification were regarded as not the results of two entirely different fluids but of the addition or
**subtraction**of one electric fluid from matter, so that positive electrification was to be looked upon as the result of increase or addition of something to ordinary matter and negative as a**subtraction**. - 3 For this conception of the gospel and of the officially organized church, our nearest analogy is in Matthew, or rather in the blocks of precepts of the Lord which after
**subtraction**of the Markan narrative framework are found to underlie our first gospel. - As an illustration, we may take the elementary processes of addition,
**subtraction**, multiplication and division. - (i) If we consider that we are dealing with numerical quantities, we must recognize the fact that, while addition and
**subtraction**might in the first instance be limited to such quantities, multiplication and division necessarily introduce the idea of pure number. - Or we might say that, since multiplication is a form of addition, and division a form of
**subtraction**, there are really only two fundamental processes, viz. - (iii) The inclusion of the four processes under one general head fails to indicate the essential difference between addition and multiplication, as direct processes, on the one hand, and
**subtraction**and division, as inverse processes, on the other (§ 59). - Addition and
**Subtraction**3.2.2 32. **Subtraction**11.1.4 98.- The principle of
**subtraction**from a higher number, which appeared in notation, also appeared in numeration, but not for exactly the same numbers or in exactly the same way; thus XVIII was two-from-twenty, and the next number was onefrom-twenty, but it was written XIX, not IXX. - Addition is the process of expressing (in numeration or notation) a whole, the parts of which have already been expressed; while, if a whole has been expressed and also a part or parts,
**subtraction**is the process of expressing the remainder. - Except with very small numbers, addition and
**subtraction**, on the grouping system, involve analysis and rearrangement. - - The above method of dealing with addition and
**subtraction**is synthetic, and is appropriate to the grouping method of dealing with number. - The
**subtraction**of 4 from 9 may mean either " What has to be added to 4 in order to make up a total of 9," or " To what has 4 to be added in order to make up a total of 9." - This is a more advanced method, which leads easily to the idea of negative quantities, if the
**subtraction**is such that we have to go behind the o of the standard series. - Thus multiplication and division in the power-series correspond to addition and
**subtraction**in the index-series, and vice versa. - Comparison, Addition and
**Subtraction**of Fractions.-The quantities 4 of A and 7 of A are expressed in terms of different units. - But, in attempting the inverse processes of
**subtraction**, division, and either evolution or determination of index, the data may be such that a process cannot be performed. - This cannot be done; but the result of the
**subtraction**, if it could be done, is something which, when 6 is added to it, becomes 3 - 7+6 = 3+6 - 7 = 2. - - In order to deal, by way of comparison or addition or
**subtraction**, with fractions which have different denominators, it is necessary to reduce them to a common denominator. - Addition and
**Subtraction**of Percentages. - Addition or
**subtraction**of two numbers or quantities, and multiplication by some small numbers - are with a little practice performed more quickly and more accurately from left to right. - There is no difference in principle between addition (or
**subtraction**) of numbers and addition (or**subtraction**) of numerical quantities. **Subtraction**by counting forward is called complementary addition.- If We Count Forwards, Working From The Left, Or Backwards, Working From The Right; While, If We Count Backwards, Working From The Left, Or Forwards, Working From The Right, The
**Subtraction**Is Of 6S. - In long division the divisor is put on the left of the dividend, and the quotient on the right; and each partial product, with the remainder after its
**subtraction**, is shown in full.