# An Elementary Treatise on Algebra, in Theory and Practice: With Attempts to Simplify ... that Science ... With Notes and Illustrations ... To which is Added an Appendix, on the Application of Algebra to Geometry

Hilliard, Gray, & Company, 1840 - Algebra - 605 pages

### Contents

 Addition three Cases 5 Multiplication three Cases 12 Division 19 do 25 Addition of 41 Multiplication 47 Square Root Case 2 53 Simple Equations 59
 First general Method 133 125 164 142 272 Figurate and Polygonal Numbers 311 Vanishing Fractions and other par 319 Solutions 448 Deophantine Questions and Solu 478 Question on page 273 See 498

### Popular passages

Page 126 - In one of the given equations obtain the value of one of the unknown quantities in terms of the other unknown quantity; Substitute this value in the other equation and solve.
Page 544 - Two travellers, A and B, set out to meet each other, A leaving the town C at the same time that B left D.
Page 94 - A person has two horses, and a saddle worth £50 ; now, if the saddle be put on the back of the first horse, it will make his value double that of the second ; but if it be put on the back of the second, it will make his value triple that of the first ; what is the value of each horse ? Ans.
Page 258 - Then, as the difference of these results is to the difference of the two assumed numbers, so is the difference between the true result, and either of the former, to the correction of the number belonging to the result used ; which correction being added to that number when it is too little, or subtracted from it when it is too great, will give the root required, nearly.
Page 492 - There is a rectangular field, whose length is to its breadth in the proportion of 6 to 5. A part of this, equal to -£ of the whole, being planted, there remain for ploughing 625 square yards. What are the dimensions of the field ? 1 3.
Page 97 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Page 435 - At the 50th mile stone from London, A overtook a drove of geese which were proceeding at the rate of three miles in two hours ; and two hours afterwards met a stage waggon, which was moving at the rate of 9 miles in 4 hours.
Page 439 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means, as 7 to 3. What are the numbers ? Ans.
Page 497 - Is. ; for each of which I paid as many shillings per yard as there were yards in its side. Now had each of them cost as many shillings per yard as there were yards in a side of the other, I should have paid 17s.
Page 96 - Divide the number 90 into 4 such parts, that the . first increased by 2, the second diminished by 2, the third multiplied by 2, and the fourth divided by 2, shall all be equal.