Key to Davies' Bourdon: With Many Additional Examples, Illustrating the Algebraic Analysis |
Other editions - View all
Common terms and phrases
2d rem 3d quotient 6abc a²+b² a²b² a²x² adding arithmetical progression cask Clearing of fractions co-efficient combining and eliminating denote the number dividing both members equal example extracting the square factor find the values find x formula fractions and reducing given equation Given to find greatest common divisor hence least common multiple Let x denote member from member member to member Multiplying both members Multiplying both terms number of days number of dollars number of gallons number of miles number of shillings performing indicated operations problem real roots rule SECOND DEGREE SECOND OPERATION second polynomial SIMULTANEOUS EQUATIONS square root squaring both members Substituting and reducing subtracting taking the upper THIRD OPERATION three numbers transposing and reducing travelled upper sign variations whence x²y xy² Зах ха
Popular passages
Page 105 - A man and his wife usually drank out a cask of beer in 12 days ; but when the man was from home, it lasted the woman 30 days : how many days would the man alone be in drinking it ? Ans. 20 days.
Page 105 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...
Page 169 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the lesser, is equal to 12 ? Ans.
Page 254 - ... the first cask was filled with the mixture. It now appears that if 6| gallons of the mixture be drawn off from the first into the second cask, there will be equal quantities of brandy in each. Required the quantity of brandy first drawn off.
Page 103 - 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 104 - A footman agreed to serve his master for £8 a year and a livery, but was turned away at the end of 7 months, and received only £2 13s.
Page 146 - What number is that, which, being divided by the product of its digits, the quotient is 3 ; and if 18 be added to it, the digits will be inverted ? Ans.
Page 172 - Ans. 24. 14. A regiment, in garrison, consisting of a certain number of companies, receives orders to send 216 men on duty, each company to furnish an equal number. Before the order was executed, three of the companies were sent on another service, and it was then found that each company that remained would have to send 12 men additional, in order to make up the complement, 216. How many companies were in the regiment, and what number of men did each of the remaining companies send?
Page 109 - A number is expressed by three figures ; the sum of these figures is 11 ; the figure in the place of units is double that in the place of hundreds ; and when 297 is added to this number, the sum obtained is expressed by the figures of this number reversed. What is the number ? Ans. 326. 24. A person who possessed 100,000 dollars, placed the greater part of it out at 5 per cent, interest, and the other part at 4 per cent.
Page 265 - To find three numbers in arithmetical progression, so that the sum of their squares shall be 93 ; also if the first be multiplied by 3, the second by 4, and the third by 5, the sum of the products may be 66. Ans 2, 5, 8.