Why are indifference curves in economics slope downward?

Samuelson and Nordhaus define indifference curve as:

A curve drawn on a graph whose two axes measure amounts of different goods consumed. Each point on such a curve, indicating different combinations of the two goods, yields exactly the same level of satisfaction to a given consumer.

It is quite true that law of diminishing marginal utility ensures that indifference curves are downward sloping. Further it also ensures that the indifference curves are convex to the origin. But downward sloping curve is possible also when the marginal utility is constant rather than diminishing with the total quantity consumed.

To ensure a downward sloping curve it is enough that reduction in quantity of one of the two goods represented on indifference curve must be accompanied by some increase in the quantity of the other good represented. Similarly increase in quantity of first good mus be accompanied by decrease in quantity of the other good. It is not possible for quantity for both the goods to increase or decrease simultaneously and still have the same combined utility of the two. If it was possible for combined utility of two goods to behave in this way than the indifference curve would have been an upward sloping curve.

When marginal utility of both the goods on indifference curves is constant then the indifference curve is a downward sloping straight line. When one of the two good has constant marginal utility and the other has diminishing marginal utility the indifference vurve is a curved line concave to the origin. When both the goods have diminishing marginal utility, the indifference curve is a curved line convex to the origin.

Source:

Samuelson P.A. and Nordhaus W.D., Economics, Eighteenth Edition, 2005, Tata McGraw-Hill, New Delhi