Pennethorne, John; Robinson, John [Ill.]: The geometry and optics of ancient architecture: illustrated by examples from Thebes, Athens, and Rome (London [u.a.], 1878)

Part 11. Plate 11.

The Parthenon N? 2 . The South East angular Design shewing t*» Ude Heights trigonometric ally determined upon the Plane HOZ

¥i§. 1. The Plan of the Parthenon with the elevation

o

of the Portico and the return side traced upon
the three rectangular planes X Y, Y Z , XZ,
passing through the point of sight 0 .

rig. 2. Plan of the projections traced upon the Horizontal plane
X.Y. at the South East angle nearest to the point of sight O .

Z

T*E-



,ttos

The, sideB 0 of the oblique triangle' A B O

com he determined- from the Form

log.I = log a + lcg.sirv.23 - loq.suv.A.

\t(; IS /</ 13 12 II 10 ,

1 —if-------%-------*------$-------*-------^------f

if—If * *

6 5 4 3 ,p

& e

Kl___leu er step

11 lowest step

Si

4. The given heights of the Portico traced upon the plane H 0 Z
the perpendicular lineal magnitudes are all commensurable,

the angular magnitudes determined by the Form

log. tan. A — log. r + log. a — log. b, are incommensur

able

far/a above corona

U point, or' sight/ (cj- the- stm£k>\ east,
angular cLesixfrv 3 -2 belovy- the-
Tzpjper step. ^^l^^^

pavement 14 -.2 below the upper step

a:
6

vo a s

>------------------1------------------<r-

"J'

£*

V

&
^





^

^

•3



**tye a

"*° tiu

'Oreo,

"f/UU

Fi£. 3. The apparent length and breadth of the Middle step of the
South East angular design at the given height =9-2
above the horizon.

M

X

MM^

M

_Y

0

MOM" + MOM- M - I44-5G4"

this quantify regulate* the
whole apparent height

Fig. 5 The corrected perpendicular magnitudes upon the plane
HOZ, the visual angles are all made commensurable and
the true executed heights are determined by calculation irom
the Form. lofS . a — log. b + log . tan A — 10 .

I



5

So

HORIZON

158-77 thorn lowest step 15!) ■ I!) from tower step

162-91 ti-ein facta above, corona I63-O6thom pediment

165-537 thorn, abacus ..

\tv pcinl of sifjhb O

la

165-431 from upper step
166-117 thom architrave

■ -a

facia above- corona.

ft |

X)'

t^

j

s?

K

■S





5

"■^.

*4~--~^

3?
ft

s



~~¥~

1

!



§

;

1

•,'



i.

K.S> >

i





I



f* *

'



II 1 ■

1



e -,

"^



Ys *

*•









+ 1





q * "-'Me

«5

°0

J^mmmmmmm^^^^Mm^m_____________------------

if... 159-19 thorn lower step . ..— — .--

'f......____..... fg2- Sltf-om facia above corona

\___________163-06fhom pediment

'if------- .165-431 thorn upper step .. 165 ■ 537 thorn abacas.

______________ 166 ■ II' thorn, a i -chih 'owe

HORIZON

V ti pciiif af'.y/a/tf O.

61654

A,

" 40766

4* 14 CCS'

As

1410?. "

14-4564-

61654

4010,1

14-068

r

2

2-344 7 inccmmeioiuralile
.. nearest railc

f ■ SiZ

2 • 83

nearest ratio

nearest ratio

■ &98

j nearest ratio.

Corrections in the East Portico

first gival qua/lliiCes ■'i-ut clijucii.si.cii.i (idxiilicns and suhstradLonjB

obtained by pvtjjxirfcLow from, raitnlattCrt. /wufttna fftim correctunxs

Column.----------- 33- 7788...

£rdaMatare n ■ 2596

Styu4talc 5 ■ 0"'!)fi

Whole Iwic/M 50 ■ 6S8

Pediment 13 ■ 136

. 34 ■ Z460-
.11 ■ 1560
5 ■ 6786

51 ■ 074 ..
12 ■ 454 .

+ 0-462 fb. = 5-5uw.
-0-103 , = 1-2 ,
+ 0-048 „ = 0-6 „
+ 0 ■ 466 , = 'I ■ 8 ,
— 0- 681 , = 8-2 „

fix 144564" -=61956* — m-rected apparent height

7
(•,<>.-■ a" = 6884" — nutlnhi* of apparent height

Sfylqbate

Columns from, upper- \

step to the architrave I

Entablature

Peel iia cut

= 6884 " x I = 6884"

= 6884-' x 6 = 41304"

= 6884" x 2 = 13768'

= 6884" X 9 = 61956" + 172"= \qRparmt

= 6884" x. 2 «= 13768" { lati/ht-

whole

■..yC<?ai--f,JO'/t at/.

f,., '/. ,%2tf' /?///. /o.i//r<S/:. Av,,/iv, . /{. 7 '.