The author advances a unified account of aesthetic harmony grounded in numerical and geometric ratios, adapting Pythagorean ideas to explain beauty in sound, form, color, and ornament. The text demonstrates how rectilinear constructions, ellipses, and harmonic parts of the right angle produce pleasing proportions in architecture, vases, and the human head and figure, and includes plates and diagrams that illustrate stepwise constructions and variations. Appendices supply technical elaboration, while practical commentary indicates how artists and designers might apply these mathematical principles to achieve balanced forms and color relationships.