## Subtraction Sentence Examples

- It is evident that these laws all follow from the idea that a compound molecule can only alter through the addition or
**subtraction**of one or more complete atoms, together with the idea that all the molecules in a pure substance are alike. - 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. - Rather than a labour, for, by means of it, addition,
**subtraction**, multiplication, division and even the extraction of roots are accomplished simply by the motion of counters. - 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. - The deficiencies of the Greek symbolism were partially remedied;
**subtraction**was denoted by placing a dot over the subtrahend; multiplication, by placing bha (an abbreviation of bhavita, the product ") after the factors; division, by placing the divisor under the dividend; and square root, by inserting ka (an abbreviation of karana, irrational) before the quantity. - 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. - In Wright's translation of 1616 Napier has added the sentence - " But because the addition and
**subtraction**of these former numbers may seeme somewhat painfull, I intend (if it shall please God) in a second Edition, to set out such Logarithmes as shall make those numbers above written to fall upon decimal numbers, such as Ioo,000,000, 200,000,000, 300,000,000, &c., which are easie to be added or abated to or from any other number " (p. 19); and in the dedication of the Rabdologia (1617) he wrote " Quorum quidem Logarithmorum speciem aliam multo praestantiorem nunc etiam invenimus, & creandi methodum, una cum eorum usu (si Deus longiorem vitae & valetudinis usuram concesserit) evulgare statuimus; ipsam autem novi canonis supputationem, ob infirmam corporis nostri valetudinem, viris in hoc studii genere versatis relinquimus: imprimis vero doctissimo viro D. - 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. - The numerical relations existing between the trunk series and the branch series make it somewhat difficult to believe that they belong to different vibrating systems. But while we should undoubtedly hesitate on this ground to adopt Fredenhagen's 3 view that the two branch series belong to the element itself and the trunk series to a process of oxidation, we cannot press the argument against the view of Lenard, because the addition or
**subtraction**of an electron introduces two vibrating systems which are still connected with each other and some numerical relationship is probable. - 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.