Detroit's Latin motto, adopted after a 19th century fire, sums up the current hopeful mood in the city: "We hope for better things, it rises from the ashes."

There are still plenty of skeptics around who think the city boosters are really singing that blues refrain: "Been down so long, it looks like up to me."

But leading indicators suggest that the optimists are right - that Detroit hit bottom two or three years and is now modestly improving for the first time in at least 15 years.

Detroit lost more than 10 percent of its population and fully one-third of its jobs from the mid-1960s to the mid-1970s. The decline in the city's labor force was steady and ruinous during that decade, even when the auto industry was prospering.

In 1976, the decline stopped. The following year, whenthe Renaissance Center opened with its thousands of new jobs, the city's labor force grew modestly, for the first time in a decade, up 2 percent. This year, it is slightly larger still, while unemployment is down considerably. Detroit this March had a working population of 626,000 up 6 percent from the low point of 76.

Crime in Detroit, never quite as bad as the city's reputation as "murder city," peaked in 1975-76 and began dropping sharply. Last year, there were 24,000 reports of violent crimes - murder, rape, assault, robbery - down 20 percent from the previous year. The overall crime rate was still slightly above the 1973 level, the year before Coleman Young became mayor, but officials predict 1978 will show continued decline.

The property assessments for the downtown district increased in 1976 after a long decline. The improvement was modest, but assessment officials explain property assessments usually lag 18 months behind any increased business activity. The city's total property assessment continued to decline last year, but the assessor's office predicts that too will turn around next year.

The most convincing evidence of a turnaround is circumstantial. One developer has begun building 100 units of single-family houses near the downtown, the first private-market housing to be built in the inner city in a generation, according Chuck Davis, vice president of Detroit Renaissance.

The city's downtown development authority recently took bids on a 400-unit apartment project on Washington Boulevard, a faded avenue now being restored. The bid opening, according to Davis, was a good market test of whether private developers really believe that people want to return downtown to live. The Authority received four bids. "A very positive sign that the investment community has taken another look at Detroit," Davis said.

Furthermore, the Detroit News surveyed the housing market in residential neighborhoods and reported the first boom in sales and prices in 20 years. Mortgage companies reported that the city's long-depressed housing prices were beginning to appreciate in many neighborhoods, though not uniformly across the city.