I,XV1 INTRODUCTORY 



mathematical law, was a philosophical solution of the problem reserved for the present 

 generation. 



The limits of this sketch do not admit of more than allusion to the artists, anato- 

 mists, mathematicians, or others, who, since the era of the renaissance, have made the 

 proportions of the human figure the subject of treatise or theory. Prominent among 

 them may be named, in Italy, Cimabue, Giotto, Ghiberti, Alberti, Leonardo da Vinci, 

 Raphael, Michael Angelo, the two Carracci, Cardan, Paggi ; in Germany, Albert Durer, 

 Holbein, Vesalius, Raphael Mengs, Winckelmann ; in France, Jean Cousin, Poussin, 

 the two Audrans, joubert, Buffon, Gerdy, Horace Vernet; in Belgium and Holland, the 

 Van.Eycks, Rubens, Vandyke, Rembrandt, Camper ; and in England, Sir Joshua Rey- 

 nolds, Flaxman, &c. For a more complete list of these authors and their works, reference 

 may be made to the bibliography of the subject, which will be found appended. 



A short notice of the more valuable of these theories of proportion is necessary, 

 in passing, to illustrate the progress of the investigation to the present day. In the 

 fifteenth century, the Florentine sculptor and mathematician Alberti devised his per- 

 fect human figure, being in its proportions the mean result of some measurements of 

 the best living models and classic sculpture. One-sixth of the entire height he assumed 

 for his modulus, calling it a foot; tliis foot he divided into ten degrees, and each degree - 

 into ten minutes.^ He appears to have followed the canon of Vitruvius in taking the 

 foot to be one-sixth of the entire height, and therein is the chief defect of liis scheme. 

 M. Quetelet has made a careful comparison of the proportions laid down by Alberti 

 with the table of mean dimensions, the result of his own observations of the living 

 subject, and is struck with the remarkable nearness to accuracy of the former.- 

 Two particulars of the Florentine's process are noteworthy : the use of the average or 

 mean, and of a decimal system of division. 



The work of the celebrated Albert Durer demands a short notice, as it became a 

 high authority in art. His treatise on proportion^ is divided into four books, in the first 

 of which he takes for his unit the entire height, which was an advance toward greater 

 accuracy ; this unit he divides into common fractional parts of thirds, fourths, fifths, 

 &c., marking the origins of the limbs. The measurements are so given as to present 

 his model under tlu-ee points of view — profile, front, and back. The second book is 

 mainly a repetition of the first, but with the foot for bis unit, and, still following 

 Vitruvius, he makes it one-sixth of the entire height. It is divided into one hundred 

 parts. The third and fourth books contain directions for applying his preceding cal- 

 culations to every possible ciu"ve and position of the human figure. Schadow is of 

 opinion that Dm'cr's model figure was the result of calculation, and not of actual 

 measurement of living subjects.^ 



Of Gerard Audran's work'' it has been admitted that his measurements of ancient 

 statues are the most accurate and valuable of all that had been previously given to the 



' VdJa architeotura di L. B. Albekii, libri x ; delta pittura, libri iii ; c della statiia, Hbro i ; tradolii in lingua italiaiia 

 da CosiMO liAUTOLi, 3 vols., folio, Loadra, 1726. 

 ^ Aulliropomctrir, p. 07. 



' llitrin sind hci/riffcn vicr hiichcr ron menschlicher proportion, &c., folio, Nuremberg, 1528. 

 * Poti/ctct, oil Ihiuric des mcsurcs de I'homme, p. 14. 

 '' Lii) proportions du corps humain mcsurdes eur les tieltes fujurcs de Vantiipntd, folio, Paris, 1683 



