A Short View of the First Principles of the Differential Calculus

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J. Deighton, 1824 - 198 σελίδες
 

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Σελίδα xvii - Excudent alii spirantia mollius aera, Credo equidem, vivos ducent de marmore vultus, Orabunt causas melius, caelique meatus Describent radio et surgentia sidera dicent; Tu regere imperio populos, Romane, memento : Hae tibi erunt artes, pacisque imponere morem, Parcere subiectis, et debellare superbos.
Σελίδα xvii - Excudent alii spirantia mollius aera, credo equidem, vivos ducent de marmore vultus, orabunt causas melius, caelique meatus describent radio et surgentia sidera dicent : 850 tu regere imperio populos, Romane, memento (hae tibi erunt artes), pacisque imponere morem, parcere subiectis et debellare superbos.
Σελίδα 50 - The differential of the product of any number of functions is equal to the sum of the products which arise by multiplying the differential of each function by the product of all the others: d(uts) = tsdu + usdt -4- utds.
Σελίδα 5 - The area of a rectangle is equal to the product of the length by the breadth.
Σελίδα 44 - It was also shown in the same article, that the differential of the sum of any number of functions is equal to the sum of their...
Σελίδα 67 - Show how to divide a straight line into two parts so that the sum of the squares on the parts shall be equal to the square on a given line.
Σελίδα 74 - The sum of the logarithms of two numbers, is the logarithm of the product of those numbers; and the difference of the logarithms of two numbers, is the logarithm of the quotient of one of the numbers divided by the other. (Art. 2.) In Briggs' system, the logarithm of 10 is 1.
Σελίδα 133 - ... the angle which the tangent to the curve at that point makes with the axis of strain ; I will call this angle <f>.
Σελίδα 1 - If two sides and the included angle of a triangle are given, show how to solve the triangle. Ex. The two sides are 345, 174 feet respectively, and the included angle is 37° 20'; find the remaining angles of the triangle. log.,» 5'19 = -715167, log. tan. 71° 20/ = 10-471298. log.,0 1-71 = -232996, log. tan. 44° 17
Σελίδα 24 - If three magnitudes of the same kind are so related that the first is greater than the second, and the second greater than the third, then the first is greater than the third.

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