The key term in your question is "new method/new idea".

Developing new methods is a mainstream in science development.

To verify newly developed method the results of former methods are required (regardless whether it are your results or someone's else).

But the questions are:

- are the results obtained by the new method correct/better?

- is the new method better (faster, simpler, more accurate)?

- is the new method different from existing one to be considered as new one?

A good question

If reference of previous result is given only, it is O.K. But if previous data, table etc. are used again in another article, it is one type of malpractice. Many students/ researchers perform this to increase the number of publication by publishing such articles in different predatory journals.

I think it is under plagiarism issue.

Certainly cite the original. Assuming you are offering an improvement in the new article, highlight the improvement. That is the point after all.

Acknowledging that certain material has been borrowed and providing the information necessary to find that source. Generally speaking, we rely on the work of others to advance knowledge. Many of us did literature search in preparation for graduate level research and citations at the end of each publication is required. However, there are exceptions such as

• Copying sentences and structures of a paragraph(s).
• Copying too many ideas from others that fundamental represent the majority of your work, whether you give credit or not.
• In the case of poetry, you must seek permission.
• Publishing someone else's work as your own!

I just found out that a well-know researcher used a mathematical model that I developed to describe organic soils settlement behavior did not give proper credit or provide any reference. This person works for a major research 1 university in the USA.