In the opening of this phrase Socrates compares the significance of a cook or cookery to a doctor and his/her knowledge of nutrition and medicine. Typically when children are asked who they think would know more about nutrition, a doctor or a cook, they would say a cook. The reason children would say a cook is because of the cook's experience with preparing food. The familiarity with cookery is not the same as or better than the knowledge of the nutrition from which the food that has been prepared. A doctor has the true knowledge of which kinds of foods have better sustenance than others. A doctor is feed information on medicine and obtains facts about what foods are healthier for us internally. A cook, however, is trained and condition with repetitive actions to ultimately create food that is tasteful. The notion that cookery and medicine coincide is flattery or common belief that one might have when the subject or question of nutrition comes about.
The second half of the phrase compares the use of artificial cosmetics or garments to gymnastics as a way to achieve true beauty. When one uses depilatories, makeup, and costumes to attain "true" beauty, they are merely giving away a false impression or an illusion of that beauty. Therefore, it is just a belief that a person with eye shadow and foundation on is one that has true beauty in his/her possession. When someone undergoes physical training and/or gymnastics, he/she will obtain true beauty. Being healthy and physically fit internally holds splendor but, using artificial items to attain beauty is a form of trickery.
The two divisions of the phrase mentioned above correspond with each other. Medicine and nutrition is something which is false knowledge to a cook like beauty if false appearance to a person using cosmetics. A doctor has true knowledge of medicine and nutrition like a trainer obtains true beauty.
