If A, B and C are connected in proportion, that is, a:b=b:c, then B is called the proportional mean of A and C, and the items in the proportion are relative to the equal proportion of items. Terms in numerical scale are different from those in geometry. It can be positive or negative.

The projective theorem was put forward by Euclid, a famous mathematician in ancient Greece and the author of The Elements of Geometry, so it is also called "Euclid Theorem". In a right triangle, the height on the hypotenuse is the median of the projection of two right-angled sides on the hypotenuse, and each right-angled side is the median of the projection of this right-angled side on the hypotenuse and the ratio of the hypotenuse. Projective theorem is an important theorem in mathematical graphic calculation.

Mathematical common sense

The so-called "golden section" principle is to divide a line segment into two parts, so that the length of the longer line segment is the middle value of the ratio of the length of the whole line segment to the length of another shorter line segment. The ratio is about 0.6 18. This proportion is recognized as the most aesthetic proportion, which is widely used in painting, sculpture and other fields.

At present, the name of projective theorem is not mentioned in junior high school mathematics textbooks (just like Vieta theorem is not mentioned), but the basic figures involved are often encountered in exercises and senior high school entrance examinations, and it is not difficult to learn. Therefore, it is undoubtedly necessary to master basic figures and conclusions, understand and digest the proof methods of conclusions, and learn to apply them.