Table of quarter-squares of all integer numbers up to 100,000, by which the product of two factors may be found by the aid of addition and subtraction alone

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C. and E. Layton, 1856 - Mathematics - 214 pages
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Page 207 - Ans. 56.64+ feet. 5. A line 81 feet long, will exactly reach from the top of a fort, on the opposite bank of a river, known to be 69 feet broad ; the height of the wall is required. Ans. 42.42 6 feet. 6. Two ships sail from the same port, one goes due east 150 miles, the other due north 252 miles; how far are they asunder ? Ans. 293.26 miles. 269. To find a mean proportional between two numbers. RULE. — Multiply...
Page iv - ... quoted by Prof. Carey Foster (p. 593) is given in full in the preface to Mr. Blater's table. It seems to me that the words in question — "This application of a table of quarter squares, as it is derived from the simplest principles, might have readily occurred to a mathematician ; yet I have nowhere seen it brought into practical use till, last summer, I met with, at Paris, a small book by Antoine Voisin, printed in 1817...
Page xxvii - Given in numbers any two sides of a right angled triangle, the third side can be found, for it is the square root of the sum or difference of the squares of the given lines, according as the given sides contain the right angle or not. Cor. 2. To find a square equal to the sum of two F<g.
Page 208 - ... area. PROBLEM III. To find the area of a triangle. RULE. Multiply one of its sides as a base by a perpendicular let fall from the opposite angle, and take half the product for the area. Or, from half the sum of the three sides subtract each side separately, and multiply the three remainders so obtained and the half sum together, and the square root of the product will be the area. EXAMPLE 1. Required the area of a triangle ABC, whose busa AB =; 16-5, and perpendicular DC = 10-25.
Page iv - ... added, besides other valuable matter ; and, in the preface to this second edition, I pray you to observe what he himself says of it. He says, " In this edition I have introduced considerable improvements, and other useful tables are inserted in the folding sheet ; but the most valuable addition that I have made consists in the table of quarter-squares, near the end of the volume, which, to a certain extent, perform the multiplication of numbers more expeditiously than even logarithms themselves.
Page 214 - Ans. 9.05952 feet. 5. The diameter of a well is 3 feet 9 inches, and its depth 45 feet ; what did it cost sinking at 7s.
Page 210 - X 17.75 =. 2183.25; and = 1091.625 feet = 1091 fi. 7 in. 6 pa. the area required. 2. What is the area of a -court-yard in the form of a regular pentagon, whose side measures 92 feet 6 inches, and perpendicular 63 feet 8 inches ? Am.
Page iv - The frequency of division into four parts has caused the word to be used sometimes in the sense of a part or portion allotted. Thus the portion of a camp or barrack allotted to one soldier is called his quarters. QUARTER-SQUARES. A table of the fourth part of the squares of numbers may be substituted for one of logarithms in multiplication. For since (a+6)8 (a-6...
Page iv - It would be a great service, however, in facilitating many calculations, to have the whole Table reprinted, or perhaps even extended to 200,000, which might be condensed into a moderate sized volume.
Page vi - Edit-, 1836, intended as a supplement to the second edition of his Mathematical and Astronomical Tables, in which, at p.

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