Alzheimer's disease (AD) is a fatal degenerative disease of the brain for which there is no cure. AD causes brain cells to die. AD is thought to be caused by an excess of beta-amyloid (β-amyloid), a sticky protein in the brain that forms amyloid plaques. At autopsy, AD patients are required to have these amyloid plaques in the brain in order to have a definitive diagnosis of AD. Inhibiting the enzyme gamma-secretase (γ-secretase) lowers the production of β-amyloid. Semagacestat (LY450139) is a functional γ-secretase inhibitor and was shown to lower β-amyloid in blood and spinal fluid in humans tested thus far and in blood, spinal fluid, and brain in animals tested thus far. This study used several different tests to measure the effect of semagacestat on both β-amyloid and amyloid plaques for some participants. The build-up of amyloid plaques was measured by a brain scan that takes a picture of amyloid plaques in the brain. Other tests measured the overall function of the brain and brain size in some participants. In this trial, participants who initially received placebo (inactive sugar pill) were, at a certain point in the study, switched over to active drug, semagacestat. In other words, all participants could eventually receive active drug. Participation could last approximately 2 years. Participants taking approved AD medications were permitted to participate in this study and continue taking these medications during the study. All participants who completed this study had the option to continue receiving semagacestat by participating in an open-label study.