multiplications Sentence Examples

• The method which Napier terms "Rabdologia" consists in the use of certain numerating rods for the performance of multiplications and divisions.

• The second method, which he calls the "Promptuarium Multiplicationis" on account of its being the most expeditious of all for the performance of multiplications, involves the use of a number of lamellae or little plates of metal disposed in a box.

• When algebra had advanced to the point where exponents were introduced, nothing would be more natural than that their utility as a means of performing multiplications and divisions should be remarked; but it is one of the surprises in the history of science that logarithms were invented as an arithmetical improvement years before their connexion with exponents was known.

• 1890, p. 490) that exp(mldl +m2d2+m3d3+...) = exp (Midi +M2d2+M3d3+...), where now the multiplications on the dexter denote successive operations, provided that pp t exp(MiE+M2 2+M3E3+...) +mlH+m2V+m3S3+..., being an undetermined algebraic quantity.

• where the multiplications on the leftand right-hand sides of the equation are symbolic and unsymbolic respectively, provided that m P4, M P4 are quantities which satisfy the relation exp (M14+Moir+...+Mp4EpnP+...) =1+mic -Fmoif+...+mp,eng+...; where E, n are undetermined algebraic quantities.

• (iii.) Multiplications, represented by X, are performed from right to left.

• This rule as to using brackets is not always observed, the convention sometimes adopted being that multiplications or divisions are to be performed before additions or subtractions.

• r we regard the multiplications as taking place from left to right; and similarly in r A product in which multiplications are taken in this order is called a continued product.

• by successive multiplications by Ada.

• In the course of reducing such expressions as (AB)C, (AB){C(DE)} and the like, where a chain of multiplications has to be performed in a certain order, the multiplications may be all progressive, or all regressive, or partly, one, partly the other.

• In 1617 he published a small work entitled Rabdologia relating to mechanical methods of performing multiplications and divisions, and in the same year he died.

• It is evident that Wittich's prosthaphaeresis could not be a good method of practically effecting multiplications unless the quantities to be multiplied were sines, on account of the labour of the interpolations.

• Involution is a direct process, consisting of successive multiplications; the other two are inverse processes.

• (v) Commutative Law for Multiplications and Divisions, that multiplications and divisions may be performed in any order: e.g.

• (vi) Distributive Law, that multiplications and divisions may be distributed over additions and subtractions, e.g.

• As the table of antilogarithms is formed by successive multiplications, so the logarithm of any given number is in theory found by successive divisions.

• The method which Napier terms "Rabdologia" consists in the use of certain numerating rods for the performance of multiplications and divisions.

• The second method, which he calls the "Promptuarium Multiplicationis" on account of its being the most expeditious of all for the performance of multiplications, involves the use of a number of lamellae or little plates of metal disposed in a box.

• When algebra had advanced to the point where exponents were introduced, nothing would be more natural than that their utility as a means of performing multiplications and divisions should be remarked; but it is one of the surprises in the history of science that logarithms were invented as an arithmetical improvement years before their connexion with exponents was known.

• Napier deliberately set himself to abbreviate multiplications and divisions - operations of so fundamental a character that it might well have been thought that they were in rerum natura incapable of abbreviation; and he succeeded in devising, by the help of arithmetic and geometry alone, the one 1 The title runs as follows: Arithmetica Logarithmica, sive Logarithmorum chiliades triginta....

• In multiplications or divisions of any length it is generally convenient to begin by forming a table of the first nine multiples of the multiplicand or divisor, and Napier's bones at best merely provide such a table, and in an incomplete form, for the additions of the two figures in the same parallelogram have to be performed each time the rods are used.

• 1890, p. 490) that exp(mldl +m2d2+m3d3+...) = exp (Midi +M2d2+M3d3+...), where now the multiplications on the dexter denote successive operations, provided that pp t exp(MiE+M2 2+M3E3+...) +mlH+m2V+m3S3+..., being an undetermined algebraic quantity.

• where the multiplications on the leftand right-hand sides of the equation are symbolic and unsymbolic respectively, provided that m P4, M P4 are quantities which satisfy the relation exp (M14+Moir+...+Mp4EpnP+...) =1+mic -Fmoif+...+mp,eng+...; where E, n are undetermined algebraic quantities.

• (iii.) Multiplications, represented by X, are performed from right to left.

• This rule as to using brackets is not always observed, the convention sometimes adopted being that multiplications or divisions are to be performed before additions or subtractions.

• - (i.) An expression such as a.2.a.a.b.c.3.a.a.c, denoting that a series of multiplications is to be performed, is called a monomial; the numbers (arithmetical or algebraical) which are multiplied together being its factors.

• r we regard the multiplications as taking place from left to right; and similarly in r A product in which multiplications are taken in this order is called a continued product.

• by successive multiplications by Ada.

• In the course of reducing such expressions as (AB)C, (AB){C(DE)} and the like, where a chain of multiplications has to be performed in a certain order, the multiplications may be all progressive, or all regressive, or partly, one, partly the other.

• In 1617 he published a small work entitled Rabdologia relating to mechanical methods of performing multiplications and divisions, and in the same year he died.

• It is evident that Wittich's prosthaphaeresis could not be a good method of practically effecting multiplications unless the quantities to be multiplied were sines, on account of the labour of the interpolations.

• If instead of commencing with I and making successive additions of 1 we commence with any number such as 3 and make successive multiplications by 3, we get a series 3, g, 27,.

• Involution is a direct process, consisting of successive multiplications; the other two are inverse processes.

• (v) Commutative Law for Multiplications and Divisions, that multiplications and divisions may be performed in any order: e.g.

• (vi) Distributive Law, that multiplications and divisions may be distributed over additions and subtractions, e.g.

• As the table of antilogarithms is formed by successive multiplications, so the logarithm of any given number is in theory found by successive divisions.