D. R. HAY. CONTENTS. PAGE INTRODUCTION 1 THE SCIENCE OF BEAUTY, EVOLVED FROM THE HARMONIC LAW OF NATURE, AGREEABLY TO THE PYTHAGOREAN SYSTEM OF NUMERICAL RATIO 15 THE SCIENCE OF BEAUTY, AS APPLIED TO SOUNDS 28 THE SCIENCE OF BEAUTY, AS APPLIED TO FORMS 34 THE SCIENCE OF BEAUTY, AS DEVELOPED IN THE FORM OF THE HUMAN HEAD AND COUNTENANCE 54 THE SCIENCE OF BEAUTY, AS DEVELOPED IN THE FORM OF THE HUMAN FIGURE 61 THE SCIENCE OF BEAUTY, AS DEVELOPED IN COLOURS 67 THE SCIENCE OF BEAUTY APPLIED TO THE FORMS AND PROPORTIONS OF ANCIENT GRECIAN VASES AND ORNAMENTS 82 APPENDIX, NO. I. 91 APPENDIX, NO. II. 99 APPENDIX, NO. III. 100 APPENDIX, NO. IV. 100 APPENDIX, NO. V. 104 APPENDIX, NO. VI. 105 ILLUSTRATIONS. PLATES [Illustration: I. Three Scales of the Elementary Rectilinear Figures, viz., the Scalene Triangle, the Isosceles Triangle, and the Rectangle, comprising twenty-seven varieties of each, according to the harmonic parts of the Right Angle from ¹⁄₂ to ¹⁄₁₆. _D. R. Hay delᵗ._ _G. Aikman sc._] [Illustration: II. Diagram of the Rectilinear Orthography of the Principal Front of the Parthenon of Athens, in which its Proportions are determined by harmonic parts of the Right Angle. _D. R. Hay delᵗ._ _G. Aikman sc._] [Illustration: III. Diagram of the Rectilinear Orthography of the Portico of the Temple of Theseus at Athens, in which its Proportions are determined by harmonic parts of the Right Angle. _D. R. Hay delᵗ._ _G. Aikman sc._] [Illustration: IV. Diagram of the Rectilinear Orthography of the East End of Lincoln Cathedral, in which its Proportions are determined by harmonic parts of the Right Angle. _D. R. Hay delᵗ._ _G. Aikman sc._] [Illustration: V. Four Ellipses described from Foci, determined by harmonic parts of the Right Angle, shewing in each the Scalene Triangle, the Isosceles Triangle, and the Rectangle to which it belongs. _D. R. Hay delᵗ._ _G. Aikman sc._] [Illustration: VI. The Composite Ellipse of ¹⁄₆ and ¹⁄₈ of the Right Angle, shewing its greater and lesser Axis, its various Foci, and the Isosceles Triangle in which they are placed. _D. R. Hay delᵗ._ _G. Aikman sc._]