How did leonardo da vinci show proportion when drawing this human head?

eonardo drew this self portrait in red chalk on paper in 1512, when he was about 60 years old and living in France. The original drawing measures 33.3 x 21.3 cm (13 1/8 x 8 3/8 in) and now is a part of the magnificent collection of the Biblioteca Reale, Turin. In it we can see the head of an elderly man in three-quarter view, slightly turned towards the viewer’s right. Leonardo distinguishes himself by his long hair and waving beard which overflows over his shoulders and chest. The length of the hair and beard is uncommon in Renaissance portraits and suggests, a person of maturity. His face has an aquiline nose and is marked by the deep lines on the brow and baggy pouches below the eyes. It appears as if he has has lost his upper front teeth, causing deepening of the grooves from the nostrils to his upper lips. His deep solemn eyes do not engage the viewer but gaze ahead, shielded by the long eyebrows, give a sense of solemnity and a somber feel to the entire drawing.

for many centuries, the catholic church has been a patron of the arts. the church has used various scientific methods to maintain its power.

not 100% sure though!