Elements of Algebra: To which is Prefixed, a Choice Collection of Arithmetical Questions, with Their Solutions, Including Some New Improvements Worthy the Attention of Arithmeticians. The Principles of Algebra are Clearly Demonstrated, and Applied in the Resolution of a Great Variety of Problems on Different Parts of the Mathematicks and Natural Philosophy |
From inside the book
Results 1-5 of 43
Page 10
... Extracting the Roots of Surd Binomials Problems producing Equations whofe Solutions exercise the preceding Rules The Solution of unlimited Problems To find a Number , which being divided by givenDivisors , fhall leave given Remainders ...
... Extracting the Roots of Surd Binomials Problems producing Equations whofe Solutions exercise the preceding Rules The Solution of unlimited Problems To find a Number , which being divided by givenDivisors , fhall leave given Remainders ...
Page 50
... extracting Roots of given Numbers by Logarithms , yet it may fuffice to give a Learner fome Notion of Ex- ponential Quantities ; and how to folve various Equations containing fuch Quantities fhall be fhown in the Course of this Work . I ...
... extracting Roots of given Numbers by Logarithms , yet it may fuffice to give a Learner fome Notion of Ex- ponential Quantities ; and how to folve various Equations containing fuch Quantities fhall be fhown in the Course of this Work . I ...
Page 100
... extracting the Roots of all Powers , there is another by which the Square Root of a Quantity may be more readily ob- tained ; which is thus : Find the Square Root of the first Term a2 , which gives a for the first Term of the Root ...
... extracting the Roots of all Powers , there is another by which the Square Root of a Quantity may be more readily ob- tained ; which is thus : Find the Square Root of the first Term a2 , which gives a for the first Term of the Root ...
Page 104
... extracting the Square Root of a2x2 , becomes ax x . In like Manner 18a2 + 9a2x ) = 3a√2 + x und √ öa2 + 4a2x = 2a√2 + x . This kind of Reduction is alfo ufeful in Addition and Subtraction of Surd Quantities , where the Quotients ( un ...
... extracting the Square Root of a2x2 , becomes ax x . In like Manner 18a2 + 9a2x ) = 3a√2 + x und √ öa2 + 4a2x = 2a√2 + x . This kind of Reduction is alfo ufeful in Addition and Subtraction of Surd Quantities , where the Quotients ( un ...
Page 113
... or other Power , then will the Value of the unknown Quantity be obtained by extracting the proper Root from both Sides of the Equa- I tion ; tion ; for if two Quantities are equal their Roots ELEMENTS OF ALGEBRA . 113.
... or other Power , then will the Value of the unknown Quantity be obtained by extracting the proper Root from both Sides of the Equa- I tion ; tion ; for if two Quantities are equal their Roots ELEMENTS OF ALGEBRA . 113.
Other editions - View all
Elements of Algebra: To Which Is Prefixed, a Choice Collection of ... John Mole No preview available - 2016 |
Common terms and phrases
Acres added affumed alfo Algebraic Quantities Anſwer arifing becauſe Biquadratic Cafe Cent Co-efficient completing the Square confequently Cube Root Cubic Cubic Equation Denominator denotes Difference Diſtance divided Dividend Divifion Divifor Equa equal EXAMPLE Exponent expreffed fame Manner fecond Equation fecond Term Feet fhall fhews fifth Power fignifies fimple fince firft Equation firft Term firſt folved fome fourth fquare Fraction fubtracted fuch fuppofe given Equation gives hence Inches Increaſe Intereft itſelf laft Term laſt Latitude leaft lefs likewife Logarithm meaſure merator Miles muft multiplied muſt negative nth Root Number fought obferve pofitive Pound Product Progreffion propofed Queſtion Quotient refpectively Remainder repreſented ſhall Sides Square Root Surd thefe theſe third Term thofe thoſe tion Triangle unknown Quantity uſed Value vulgar Fraction Weight whence whofe whole Numbers writing Yards
Popular passages
Page 13 - If the sun moves every day one degree, and the moon thirteen degrees, and at a certain time the sun be at the beginning of Cancer, and in...
Page 21 - The workmen thought that substituting part silver was only a proper perquisite ; which taking air, Archimedes was appointed to examine it ; who on putting it into a vessel of water, found it raised the fluid 8-2245 cubic inches : and having discovered that the inch of gold more critically weighed 10-36 ounces, and that of silver but 5-85 ounces, he found by calculation what part of the king's gold had been changed. And you are desired to repeat the process. Ans.
Page 81 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 23 - ... in 9 weeks, how many oxen will eat 24 acres in 18 weeks, the grass being at first equal on every acre, and growing uniformly ? This example is taken from Newton's Universal Arithmetic.
Page 113 - RULE. 1. Observe which of all your unknown Quantities is the least involved, and let the Value of that Quantity be found in each Equation by the Rules already given), looking upon all the Rest as known : let the Values thus found be put equal to each other (for they are equal...
Page 21 - Vespasian weighed,, suppose 10OOOOlb. and was moved, let us admit, with such a Velocity, by Strength of Hands, as to pass through 20 Feet in one Second of Time ; and this was found suffic:ent to demolish the Walls of Jerusalem.
Page 179 - The coefficient of the third term is the fum of all the products that can be made by multiplying any two of the roots together. The coefficient of the fourth term is the fum of all the products which can be made by multiplying together any three of the roots with their figns changed ; and fo of others.
Page 78 - Jhall give the numerator of the quotient. Then multiply the denominator of the dividend by the numerator of the divifor, and their produft Jhall give the denominator.
Page 181 - and there are three changes ^ from the firft to the fécond, from the third to the fourth, and from the fourth to the fifth term : therefore there are three affirmative roots.
Page 114 - ... for that quantity and its respective powers in the other equation; and with the new equations thus arising repeat the operation, till you have only one unknown quantity and one equation. Thus x being the...