Similia Similibus Curanter
This is the law of similars. It states that 'that which can cause can cure'. The onion, which produces tears in the eye and irritation (similar to a cold), can be used as a homeopathic medicine to cure colds which have irritating tears. The early Indians recognised this principle and states that Vishasya Vishamevam Aushadam and Samaha Samena Shantihi, but it was Dr. Hahnemann, who through his studies and experiments on the various medicines available in nature, practically proved the law.
Principle of Individualization
Treat the patient, not the disease. This is the most important doctrine of homeopathy. Not two human beings are alike and so the medicines used for their treatment need not be alike. Homeopathic medicines are prescribed based on the totality of symptoms of that individual. So, the name of the disease is not important to the doctor who tries to get a complete picture of the patient - his symptoms, the modalities of symptoms, his likes and disliked his environment, etc to arrive at the individualised remedy - which is the similimum.