In his review of Ronald Reagan's autobiography "An American Life" {Book World, Nov. 4}, Jonathan Yardley expresses surprise that the former president's declared intention in rebuilding U.S. defense strength was to ultimately achieve arms reduction. Mr. Yardley writes, "That's how it worked out, but to claim as Reagan does that it was all planned this way is either disingenuous or self-deluding."

Evidently Mr. Yardley was not paying very close attention for several years. As the author of the 1983 book "The Reagans: A Political Portrait," I know that dating back well before his presidency, Mr. Reagan made clear his belief that, in negotiating arms, the Soviets would respect strength and exploit weakness. From the earliest days of his presidency this was summarized in the phrase "peace through strength."

The massive Soviet arms buildup of the '70s (continuing into the '80s) was bankrupting the economy of the U.S.S.R. Mr. Reagan knew it. Soviet leaders Andropov and Gorbachev knew it. At their first meeting, in Geneva, Mr. Reagan told Mr. Gorbachev that if there were an all-out arms race there was no doubt that a determined United States would come out ahead and the Soviet economy would be ruined. (By then the Strategic Defense Initiative was well underway, another factor contributing to Mr. Gorbachev's decision to bring on glasnost and perestroika.)

That a long-term peaceful relationship with the Soviet Union was Mr. Reagan's goal was stated by him many times. One example is found in his address to the World Affairs Council of Los Angeles on March 31, 1983: "To the leaders and people of the Soviet Union, I say, join us in the path to a more peaceful, secure world. Let us vie in the realm of ideas, on the field of peaceful competition... . And let us practice restraint in our international conduct, so that the present climate of mistrust can some day give way to mutual confidence and a secure peace." So it is coming to pass, and it's no accident. PETER D. HANNAFORD Washington The writer was an aid to Gov. Reagan in California and later was with a firm that did public relations work for him there.