Science is very much a logical progression through time. Progressing along a logical path of discovery is rather like following a path through the wilderness. Occasionally the path splits, presenting a choice; the correct logical interpretation leads to further progress, the wrong choice leads to confusion. By considering deeply the relevant science history, one might begin to recognize past faltering in the logical progression of observations and ideas and, perhaps then, to discover new, more precise understanding. The following specific examples of science faltering are described from a historical perspective: (1) Composition of the Earth's inner core; (2) Giant planet internal energy production; (3) Physical impossibility of Earth-core convection and Earth-mantle convection, and; (4) Thermonuclear ignition of stars. For each example, a revised logical progression is described, leading, respectively, to: (1) Understanding the endo-Earth's composition; (2) The concept of nuclear georeactor origin of geo- and planetary magnetic fields; (3) The invalidation and replacement of plate tectonics; and, (4) Understanding the basis for the observed distribution of luminous stars in galaxies. These revised logical progressions clearly show the inseparability of science history and discovery. A different and more fundamental approach to making scientific discoveries than the frequently discussed variants of the scientific method is this: An individual ponders and through tedious efforts arranges seemingly unrelated observations into a logical sequence in the mind so that causal relationships become evident and new understanding emerges, showing the path for new observations, for new experiments, for new theoretical considerations, and for new discoveries. Science history is rich in "seemingly unrelated observations" just waiting to be logically and causally related to reveal new discoveries.