PROPO RTI ONAL FO RM FURTHER STUDI ES I N THE SCI ENCE OF BEAUTY, BEI NG SUPPLE MENTAL TO THO SE SET FO RTH I N NATURE’ S HARMONI C UNI TY N SA MU E L O LMA N. A . Q , AND C . A RTH U R COA N, LL B . T O RS O NA T U R E' S HARMONI C U NIT AU H F Y , ETC TH RA N RREL N E R PT S A E BY MR LMA E D WINGS A D CO ATI G D SC I ION R . CO N TH E T AND M T HEM I S A E BY PT E T X A AT C R CA . COAN P TNA M ’ S SONS G . P . U NEW YO RK AND LONDON ‘ the lmtckerbocket press 1 920 Canno n . 1 9 30 u C AN SAMUEL COLMAN AND C . ARTHUR O u I l M J t he t ntchcrbochct pun, new Dork 00 ALL STUDENTS OF B EAUTY PAS T AND Pusan CONTE NTS — P AG E FOREWORD THE COAL SACK CHAPTE R — ’ I HEAVEN s FIRST LAW — II FORM AND PROPORTION S F E E E NU E I C E E UNIT O M ASUR M NT , M R AL UNITS , G OM TRIC M T TE F . F S THE O HE PE M . UNIT . TRAG N A ILY NTAGON A ILY L F M UMM SPIRA OR ATION . S ARY — III . THE TRIGON IN VISIB LE NATURE —THE IV . TRIGON IN FORCE N L H E TC . GRAVITY, SOU D , IG T , — ‘ V A E V E Y . A A E F E H B . SYMM TRY AND ARI T N NTIDOT OR SYMM TROP O IA E E E C E L AS YM CAT NARY CURV S , ELLIPS S , E C NTRICS , SPIRA S , ME TRICAL GROUPS — VI . THE GOLDE N SE RIE S IN NATURE — VII PROPORTIONAL FORM As APPLIED IN ART AND ARCHITE CTURE —T VIII . HE TAG APPE NDIX NOTE S INDE X Th s Cha t rs r tak en ro m The Gr e t M d A n I I e e e a e les C . Co a . p f a o u , , 9 4 I LLUSTRATI ONS AND D I AG RAMS Fo lio num bers inRom anr efer to th e page. uponwhich diagra m and mino r ino atratio na appear ; th oae in I talia refer to th e page. uponwhic h m aj o r illo atratioo a are de scrib e d inth e te xt. — I TETRAGON FAMI LY . — 2 . HE XAGON GROUP — 3. DIAGONAL OF THE CUB E — 4. EXTRE ME AND ME AN RATIO ' Fro m N t r e : H rm c t ( a u a oni Uni y. ) — E RE E I 5. PLAN OF EXT M AND ME AN PROPORT ON - E E AND 6. SOLID OF EXTR M ME AN PROPORTION — U A T E E AND E T 7. ANG L R EX R M M AN PROPOR ION — 8 . TII E PE NTAGRAM. PE RFE CT EXTRE ME AND ME AN PROPORTION — E 9 . PE RF CTION AMPLIFIE D o — I . PYRAMIDAL EXTRE ME AND ME AN PROPORTION . — I I . TII E IDEAL ANGLE AND TE E GOLDE N SE RIE S — OL D I 2 . P YE E RAL LIMITATIONS -I —SN w T I 3 6. o CRYS ALS ’ Fro m N t r e : H rm c t ( a u a oni Uni y.) — I 7 . SNo w CRYSTAL — P R I 8 . C U US URANITE Th e iliuatratio na are by Mr . Co lm anexce pt wher e o th erwise indicate d b elo w o r in the wor k i teell. Th e diagrama are by Capt. Coan. viii Illustrations P LATE — 1 9. DOLOMITE - — 20 2 I . TRIANGULAR DI ATOMs ' Fro m N t re s H rm c nt ( a u a oni U i y. ) 22— — 23. HE XAGONAL DIATOMS ' Fr m N t re H rm ne nt ( o a u : a o i U i y. ) - — 24 25 . OCTAGONAL DI ATOMS — AND 26. SE PALS SE ED VE SSE LS OF SYRINGA — 27 . ONAGRA BIE NNIS — 8 . TT 2 CO ON . — 29 . JONQUIL . 0 —T E L 3 . IG R ILY — 3L BUTTE RFLY AND TE E TRIGON — ’ 32 . WASP S NE ST — 33. HONE Y COMB — 34. JAPANE SE IRIS (TE E TRIANGLE . KORIN) — - 35 . DANISE C ROSS POPPY (TE E SQUARE ) — 36 . ANE MONE CORONARI A (HE XAGON) — 37 . SINGLE D AE LI A (OCTAGON) — B . 38 . OR ITS OF TE E SUPE RI OR PLANETS — T E 39. ORB ITS OF E E INFE RIOR PLANE TS WIT MARS — — B M 40. FORCE S COMPARED A SYM OLIC DIAGRA m T tM d (Fro he Grea o ule s . ) — 4I . PYTE AGOREAN LAWS — 42 . OVE RTONE VIB RATIONS — M E 43. HAR ONY MADE VISIB L Fro m T t ( he Grea Modules . ) Illustrations PLATE — E M E 44. GEOM TRIC DIAGRA OF PITCH INT RVALS — ’ N E . 45 . CE LAD I S EXP RIME NTS — E E 46. SAM CONTINUE D (PATT RNS WITE A ROUND DISK) — B E 47. VI RATIONS OF A B LL — 48 . CATE NARY CURVE S FROM NATURE — ° 49. ME TE OD OF DELINEATING A CATE NARY CURVE OF 1 5/75 B Y VE RSE D SINE S — ’ 50 . AN ENGINE E R S DRAFTE D DE LINE ATION OF A CATE NARY CURVE ° F 60 B Y VE E E O RS D SIN S . — 5 L DIVE R — E 52 . V INS — 53. EDGE S — E . LD TI E TE E 54. JAVE LIN THROW RS AN O ME EQUIVAL NT OF MOVING PICTURE — ' 55 . SPIDE R S WE B (C . V. H. C . ) — 56. TE E FLI GE T OF TE E GOLDFINCH — E 57 . TE GREAT WAVE OF KANAZAWA (HOKUSAI) — T 58 . MOUNTAINS OF E E GILA RIVE R COUNTRY — M AND E 59. SYM ETRICAL ASYMM TRICAL ELLIPSE S (ROSS) — 6o . A E E E LO T E ALL E E NCI NT GR K U ROPHOROS, SYMM TRIC Y D SIGN D ON AN ELLIPSE — E 6 I . SYMM TRICAL AND ECCE NTRI C CIRCLE S — 62 . FLAT SPIRALS . — ARI M D R 63. LOG TE MI C SPIRAL E TE O (FROM CE U CE ) — 64. SUNFLOWE R CAPITULUM Illustrations — ME OD 65 . FIG. A. TE OF DRAWI NG IONIC VOLUTE (DORE R) LOGARI E FI G . B . TE MI C SPIRAL (DUR R) — E E E 66 . WE IT PIN CON 6 —YE L P E E 7 . L OW IN CON — E — N 68 . SPIRAL OF WE ITE PIN PLA —T MAXI MUs— O P M T PE 69. ROCHUS L OKING DOWN RO EE A X —TROCE US MAxmus— DE IDE F 70. UN R S O SPIRAL — 7 I COMMON SNAI L — E E 72 . ORE GON PIN CON — I 73. DOL UM — ALI OTU U A 74. H S CORR G TA —XE NOPE ORA I S 75. SOLAR — 76. NAUTE .US — 77 . MURE X — C A P RETI OSA 78 . S AL RIA — L EL E AND E T 79 . SPIRA H IC S ECC N RICS —E E 80 . Y LLOW CLOV R I —T C U M S . RO H S MAXI US — 82 . FACELARI A — A 83. ASP RAGUS — LB OP TE E (NP RE S S 84. E OW MON R Y —B E NI A 85 . GO —FUsus—A LE T C L 86. O ROPI SPIRA ’ t (Fro m Natur e s Harmonic Uni y. ) — RYS0DOMUS ANTI UUS A E C L 87 . CE Q ( D XIOTROPI SPIRA ) Illustrations — R URA 88. SAN PAOLO FUO I LE M — E E M N URE 89 . GR K OUPPLO (FROM NAT ) — 9I WALLACE I AN SE E E P — E 92 . KOODOO (HOOK R) — E 93. AQUIL GIA — I 94. PLAN OP A CRINO D — 95. C RINOI D — E 96. ANT DON — 97 . ECHI NODE RM — - 98 . STAR FISE — NE 99. O OP TE E ASTE ROIDE — - I oo . PLAN OP WOOD SORREL I — OI . PYROLA . — I o z . LOOS E STRI P E — I O3. P I TCE E R PLANT I — O4. PARNASSIA I O — R 5 . PA NASSIA I — o6 . HE NB ANE — I 0 . 7 JAPANE SE BE LL FLOWE R . 1 0 — E 8. PIPSISS WA I 0 — 9. SPIRE A VAN HOUTI — I I o . WILD ROSE I —W B I I . OOD INE — I I 2 . FOOT OP A HOUND xn Illustrations P LATE — I I 3. ANATOMY OP TE E HUMAN HAND — T I I 4. BONE S OP E E HAND AND ARM — 1 1 5 . BONE S OP TE E LE G AND FOOT — I I 6 . EGYPTIAN CANON As ACCE PTED B Y POLYCLITUS — T E E I I 7 . RE LATION OP E E GRE E K CANON To A S RI S IN EXTRE ME ME AN PROPORTION ’ on (Fro m Natur e s Har m ic Unity. ) — T I 1 8 . PARTHE NON AND E E SQUARE rre latio ns Mr H i (Co by . amb dge . ) — R I I g. DE SI GN FO A FOUNTAIN — ! 2 . E I O SAN GIOVANNI , SI NA — I z I . A E OP A RC UGUSTUS , SUSA — I 22 . A E OP T R E RC ITUS , OM — 1 2 .