Arithmetical Spyglass and Teacher's Assistant: Intended as a Key and Supplement to the Different Works on Arithmetic, for the Use of Schools and Academies

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Waterhouse, 1842 - Arithmetic - 166 pages

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Page 74 - Compute the interest on the principle to the time of the first payment; if that be one year or more from the time the interest commenced, add it to the principal, and deduct the payment from the sum total. If there be after payments made, compute the interest on the balance due, to the next payment, and then deduct the payment as above ; and in like manner from one payment to another till all the payments are absorbed ; provided the time between one payment and another be one year or more.
Page 88 - ... 5, 7, 9, 11, 13, 15, &c. is an ascending series. ( 15, 13, 11, 9, 7, 5, 3, &c. is a descending series. The numbers which form the series are called the terms of the series. The first and last terms are the extremes, and the other terms are called the means. There are five things in arithmetical progression, any three of which being given, the other two may be found : — 1st.
Page 89 - Divide the difference of the extremes by the number of terms, less 1, and the quotient will be the common difference.
Page 48 - In a river, supposing two boats start at the same time from places 300 miles apart ; the one proceeding up stream is retarded by the current 2 miles per hour, while that moving down stream is accelerated the same ; if both be propelled by a steam engine, which would move them 8 miles per hour in still water, how far from each starting place will the boats meet ? Ans.
Page 34 - ... when the first is to the third, as the difference between the first and second is to the difference between the second and third, as the numbers 3, 4, 6.
Page 101 - The pulley is a small wheel, movable about its axis by means of a cord, which passes over it. When the axis of a pulley is fixed, the pulley only changes the direction of the power ; if movable pulleys are used, an equilibrium is produced when the power is to the weight as one to the number of ropes applied to them.
Page 75 - If any payments be made of a less sum than the interest arisen at the time of such payment, no interest is to...
Page 37 - There is a certain number which being divided by 7, the quotient resulting multiplied by 3, that product divided by 5, from the quotient 20 being subtracted, and 30 added to the remainder, the half sum shall make 65 ; can yon teli jnethe number?
Page 32 - Therefore, 54 measures b'oth 918 and 1998. It is also the greatest common measure; for, suppose there be a greater — then, since the greater measures 918 and 1998, it also measures the remainder, 162; and since it measures 162 and 918, it also measures the remainder 108; in the same manner it will be found to measure the remainder, 54; that is, the greater measures the less, which is absurd.
Page 45 - A hare starts 12 rods before a hound ; but is not perceived by him till she has been up 45 seconds ; she scuds away at the rate of 10 miles an hour ; and the dog, on view, makes after her at the rate of 16 miles an hour ; how long will the course hold, and what space will be run over, from the spot where the dog started ? Ans.

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