Nexus Ne wo k Jou nal 10 (2008) 77-100 NEXUS NETWORK JOURNAL –VOL.10,NO. 1, 2008 77
1590-5896/08/010077-24 DOI 10.1007/ S00004-007-0057-7
© 2008 Kim Williams Books, Tu in
João Ped o Xa ie
Faculdade de A qui ec u a
da Uni e sidade do Po o
Rua do Gólgo a, 215
4150-755 Po o, PORTUGAL
[email p o ec ed]
Keywo ds: Leona do da
Vinci, ep esen a ional
echniques, bi d’s eye
pe spec i e, ca alie
pe spec i e, axonome y,
cen ally-planned
a chi ec u e
Resea ch
Leona do’s Rep esen a ional Technique o
Cen ally-Planned Temples
Abs ac . Leona do in en ed a new echnique o ep esen a ion
which combines he building plan and a bi d’s-eye pe spec i e o he
whole in o a single sys em. Bi d’s eye pe spec i e may ha e
de eloped ou o ca alie pe spec i e, and ins ances p e-da ing
Leona do can be ound, bu no used in he same way as he
employed i . Though no p e-axonome ic, Leona do ook ad an age
o axonome ic ep esen a ion’s capaci y o cons uc /decons uc an
objec in o i s componen pa s in o de o cla i y i ing and
unc ioning. This pape in es iga es he o iginali y o he echnique
and special ela ionship wi h his esea ch on cen ally-planned
chu ches, while examining i in he con ex o con empo a y
de elopmen s and a chi ec s.
I is ha d o deny ha Leona do, among many o he in en ions, should also be c edi ed
as he in en o o a new echnique o ep esen a ion, especially adap ed o his esea ch on
cen ally-planned chu ches, which combines, as a sys em, he building plan and a bi d’s-eye
pe spec i e o he whole, as in MS 2307, ol. 5 . ( ig. 1).
Fig. 1. Leona do da Vinci, plan and bi d’s-eye iew o a cen ally-planned chu ch (MS 2307, ol. 5 )
78 JOÃO PEDRO XAVIER –
Leona do’s Rep esen a ional Technique o Cen ally-Planned Temples
This was al eady poin ed ou by Mu ay, who w o e:
…in he g ea majo i y o he d awings in he a chi ec u al ea ise Leona do
p esen s a plan and a bi d’s-eye iew, so a anged ha he maximum amoun
o in o ma ion abou a building, bo h ex e nally and in e nally, is gi en in
wo d awings (…) [Mu ay 1978: 62].
P e iously, Lo z had connec ed he simul aneous use o hese wo kinds o d awings
wi h he ep esen a ion o cen ally planned emples [Lo z 1997: 94].
Fo bo h Mu ay and Lo z, he g ea inno a ion is he bi d’s eye- iew.
Mu ay ela es his ype o pe spec i e wi h Leona do’s ana omical d awings, asse ing
ha he use o he same echnique in a chi ec u e “opened a whole ield o new
possibili ies” and comple es his s a emen wi h his challenging commen a y:
… i is p obable ha B aman e inspi ed him o in en his new o m o
d augh smanship in connec ion wi h a chi ec u e and in u n, B aman e’s
whole cas o hough would ha e in luenced by he new echnique o
isualiza ion [Mu ay 1978: 62].
Lo z main ains ha he bi d’s-eye iew con ains he elemen s o a pe spec i e
cons uc ion ha will be known la e as “ca alie pe spec i e”, a ep esen a ional me hod
de eloped in he las qua e o 1400, acco ding o him.
In spi e o hese espec able opinions, I belie e Leona do’s genuine and p oduc i e
inno a ion was ac ually he sys ema ic combina ion o a bi d’s-eye iew and a plan in
a chi ec u al ep esen a ion. I is also possible o ind he single use o he i s kind o
d awing in F ancesco di Gio gio’s
T a a i di A chi e u a Ingene ia e A e Mili a e
(c.
1485), al hough no wi h he same cohe ence and quali y o Leona do’s ske ches, who was
undoub edly a gi ed d a sman.
We should speci y ha we a e no dealing wi h jus any kind o bi d’s eye- iew, which
could be simply de ined as a kind o pe spec i e p oduced when he objec he obse e is
looking a is abo e he ho izon line, HL.1 In ac , we a e dealing wi h cen al pe spec i e,
which means ha i we ake a cube as e e ence, we ha e wo aces pa allel o he pic u e
plane ha a e, consequen ly, in ue o m. Bu i is also a ac ha in hese d awings his
supposed cube is la e ally placed in ela ion o he cen al isual plane, which gi es us he
possibili y o see ano he o i s e ical aces, his one wi h he co esponden homological
ans o ma ion. The high posi ion o he obse e allows he iew o he op ace, also
ans o med by pe spec i e. As we see, he conjuga ion o all hese ac o s leads o he mos
usual o m o ca alie pe spec i e, and we migh hink ha his ela ionship would g ow
p opo ionally as he dis ance o obse a ion inc eases. Bu he e is he p oblem: he
exis ence o a poin o iew placed a a ini e dis ance om ano he one placed a he
in ini e is c ucial, as i is ac ually he di e ence be ween linea and pa allel pe spec i e, o
in o he wo ds, he di e ence be ween pe spec i e and axonome y.
Massimo Scola i, in an in e es ing essay abou he o igins o axonome y [1984],
con ex ualizing i s inhe en quali ies in philosophic e ms, alks abou a oyage ha begun
in “Plo inus’ in e io eye” and a i es o he “eye o he Sun”, o use Pie o Accol i’s
language,2 becoming a ew yea s la e he “poin a in ini y” in Desa gues’s p ojec i e
geome y. In any case, o Scola i, he de elopmen o axonome y coexis ed wi h ha o
NEXUS NETWORK JOURNAL  VOL.10,NO. 1, 2008 79
pe spec i e. This means we had a combina ion, om he i s a emp s o ep esen spa ial
dep h in a plane un il he sedimen a ion o bo h ep esen a ional sys ems in scien i ic
e ms, begun in he i een h cen u y, o wo ways o iew o ep esen he wo ld, o wo
ways o acing o hinking i : his in e io eye ision ound in axonome y and he
pe spec i e “body’s eye” a o me
mimesis
ins umen o ep oduce na u e. And, as Alan
Colquhoun explains,
[This] deba e be ween Euclid’s and Democ i us’s heo ies o ision, wi h
hei i al aes he ic implica ions was esol ed, in he cou se o 16 h and 17 h
cen u ies by di iding he ield o ep esen a ion wi h wo disc e e pa s.
Mimesis in gene al became abso bed by pe spec i e, while pa allel p ojec ion
and axonome y we e p e e ed whe e e he c i e ion o alue was
desc ip i e accu acy [Colquhoun 1992: 17].
As a as I know, he i s igo ous ca alie pe spec i es appea ed in Pie o Della
F ancesca’s manusc ip
Libellus de Quinque Co po ibus Regula ibus
. I is no su p ising
ha Luca Pacioli also u ilized his kind o pe spec i e in his own d awings o
Di ina
P opo ione
. An example could be Pie o’s d awing o an icosahed on insc ibed in a cube,
which Pacioli epea s in an eng a ing sui able o p in ing ( igs. 2 and 3). Cu iously,
Leona do’s d awings o Pacioli’s ea ise a e no ca alie bu bi d’s-eye pe spec i es ( ig. 4).
I will e u n o his u he on because I belie e his is a he signi ican .
Fig. 2. Pie o della F ancesca, icosahed on in a cube.
F om
Libellus De Quinque Co po ibus
Regula ibus
, ol. 40
Fig. 3. Luca Pacioli, icosahed on in a cube,
Di ina p opo ione
, Libellus, ol. 15
80 JOÃO PEDRO XAVIER –
Leona do’s Rep esen a ional Technique o Cen ally-Planned Temples
Fig. 4. Leona do da Vinci, Hexahed on (cube), om Luca Pacioli’s
Di ina p opo zione
(1509)
So, polyhed al ep esen a ion o , mo e widely, he ep esen a ion o spa ial geome y
will come o be p e e ed o ca alie pe spec i e d awings. I seems, hough, ha when he
objec s o pu e ma hema ics become objec s o a scien i ic app oach in he ield o
ep esen a ion we end mo e o axonome y han o pe spec i e in spi e o all he
as onishing pe spec i es o polyhed ons p esen ed in pe spec i e ea ises h ough he
six een h and se en een h cen u ies.
Fig. 5. F om O once Finé,
Libe de Geome ia
P a ica
, 1544
Bu his, I belie e, wi h a ew excep ions,
was mo e due o i uosi and a is ic
pu poses o pu e pedagogical easons, such
as he use o such shapes ha could
acili a e he lea ning o pe spec i e, han
o a ma hema ical app oach o geome y
i sel . Howe e , i is in e es ing o no e
ha Pie o was esponsible o he
beginning o a adi ion leading o ou
days, as ca alie pe spec i e is s ill he
main ool o isualiza ion in ma hema ics
li e a u e. One o he easons o his
longe i y could be i s connec ion wi h an
in ui i e p ocess o spa ial ep esen a ion,
i s simplici y and eadiness o use and, o
cou se, he possibili y o ob aining ue
measu emen s. I was O once Finé (1544)
who i s scaled he solids edges
legi ima ing he u u e designa ion (da ed
om he nine een h cen u y) o his
ep esen a ional sys em – axonome y
(axis measu emen s) ( ig. 5).
NEXUS NETWORK JOURNAL  VOL.10,NO. 1, 2008 81
Bu he main eason, in his case, could be pe haps he conside a ion o he objec as i sel as
axonome y gi es us a key o “ ead” i wi hou he subjec i i y inhe en in a pe sonal eye. So, in
axonome y, he e a e no eyes bu a con en ional one (ac ually, he e is mo e han one), placed a
in ini y, which allows a close app oach o he objec , o i s own cha ac e is ics and p ope ies, wi hou he
eil ha isual pe cep ion could impose in be ween.
These d awings, unequi ocally igo ous and as hus pe ec axonome ic p ojec ions,
achie ed a long ime be o e he heo iza ion o his ep esen a ional sys em (bu his
happened wi h all sys ems o ep esen a ion), cohabi wi h he kind o bi d’s-eye iews,
used by Leona do and F ancesco di Gio gio, which a e usually conside ed as p e-ca alie
d awings, and hus p e-axonome ic ones, as ac ually hey a e no a om geome ic
ca alie pe spec i e. O cou se, he e is he lack o pa allelism o he pe pendicula lines o
he pic u e plane, as hey con e ge o he cen al anishing poin ( he
pun o cen ico
as
Albe i bap ized i ). The e is also he impossibili y o picking up ue measu es. Anyway,
he conside able dis ance o he obse e , placed a a poin whe e bi ds usually a e, in a
middle s age be ween man’s iew in a s anding posi ion – ha is, wi h ee on he loo –
and he in ini e dis ance o he eye o God, gi es a comple e h ee-dimensional iew o he
objec and he possibili y o desc ibing i in a syn he ic way, a quali y ypical o
axonome y.
In he speci ic case o Leona do, I hink he delibe a ely p osc ibed pa allel o ca alie
pe spec i e. He wan ed o do exac ly wha he did: no hing o he han bi d’s-eye
pe spec i es!
Wha gi es me pe mission o s a e his? Fundamen ally, wo hings. Fi s o all,
Leona do li ed in he wo ld o pe spec i e, which he p oclaimed se e al imes as he unique
ins umen ha makes i possible o ge knowledge o na u e and all he en i onmen
(including all he a i ac s i is possibly o ind in i o in en o i ). E en in he ield o
pe spec i e i is possible o e i y ha Leona do ne e o ge s ha he poin o iew is
ac ually he human eye, in con as o Pie o della F ancesca’s ma hema ical app oach,
whe e he conside ed i mo e a single geome ic poin (c . [Cabezas 2002: 147]), al hough
his p e e ence o bi d’s-eye iews could lie behind he image o he winged eye, shown in
he e so o Ma eo de Pas i's po ai medallion o Leon Ba is a Albe i, i we accep ha
his emblem, a symbol o pe spec i e, inspi ed he kind o imagina i e ision which came
o encompass all his aes he ic ideas in i s gaze, as no ed by Gadol [1969: 69]. Secondly, as I
ema ked be o e, and I belie e his is de e minan , his d awings o polyhed a o Luca
Pacioli we e pe spec i es and no ca alie , as Luca Pacioli’s own d awings we e in he
oo s eps o Pie o. So, he knew pe ec ly ha kind o pe spec i e, whe e lines he ac ually
saw as con e gen s angely emained pa allel agains he e idence o his senses. And his,
o a man who had an absolu e ai h in expe ience, could ne e be ole a ed!
Thus I belie e ha , wi h Leona do, we a e no dealing wi h a d awing p oduc ion
classi iable as p e-axonome ic in he sense o a p imi i e s age o ha kind o
ep esen a ional sys em. Such conside a ion is alid o he p io adi ion as in Taccola’s
p e-ca alie pe spec i es o mechanisms ( ig. 6), which bo h F ancesco di Gio gio and
Leona do ollowed ( ig. 7). Bu i in he enginee ing d awings made by Taccola and
F ancesco di Gio gio some de ec able inconsis ency can be a ibu ed o hei incapaci y o
con ol h ee-dimensional ep esen a ion,3 which does no comp omise a all i s comple e
e icacy o displaying hei unc ional and cons uc i e aspec s, I hink ha wi h Leona do
hings a e comple ely di e en .

82 JOÃO PEDRO XAVIER –
Leona do’s Rep esen a ional Technique o Cen ally-Planned Temples
Fig. 6. Ma iano di Jacopo (il Taccola), Sailing-ca ,
Libe Te ius de Ingenis ac Edi i iis non
usi a is
, 1433
Fig. 7. Leona do da Vinci, c ane o li hea y weigh s,
Codex A lan icus
ols. 30 /8 -b
NEXUS NETWORK JOURNAL  VOL.10,NO. 1, 2008 83
Once again, wi hou lea ing his belo ed pe spec i e in his o m o bi d’s-eye iews (a
echnique he mas e ed as no one e e be o e), he ook ad an age o ano he quali y o
axonome ic ep esen a ion: he capaci y o cons uc /decons uc an objec in o i s
componen pa s in o de o cla i y i ing and unc ioning, which was ano he main eason
o keep axonome ic d awings nea o enginee ing p oduc ion o a chi ec u al cons uc ion
de ails.4 I we look ca e ully a he bi d’s-eye pe spec i es he used o explo e all he ields he
was in e es ed in, which we e many, we can de ec ha he poin o iew he usually chose
was no as high as i is now in con en ional ca alie pe spec i e.
5 As ega ds his
a chi ec u al d awings, we e i y no lack o ealism, since he iews o a single building o
an en i e ci y a e ob ained as i he we e looking a hem om he op o a hill, as in he i s
landscape we know o his ( ig. 8).
Fig. 8. Leona do da Vinci, landscape, 1473. Flo ence, U izi Galle y
Pa icula ly, i we hink o his cen ally-planned chu ches c owned by a dome, we can
easily pe cei e ha he has d awn hem as i he we e iewing he dome o San a Ma ia del
Fio e om he neighbo ing campanile by Gio o, o he chu ch o San a Ma ia degli
Angioli om he lan e n o San a Ma ia del Fio e, which we e de e minan e e en ial
models o his esea ch on cen ally-planned space. Ca lo Ped e i goes e en so a as o
sugges ha his iew om a high poin o h ee-qua e s o he Tempio degli Angioli,
simila o a iew o an ac ual wooden model o he chu ch placed on a able, mus be
ela ed o Leona do’s use o his kind o pe spec i e in a chi ec u al d awings [1981: 14].
E en in his d awings o ci ies, Leona do emained loyal o bi d’s-eye pe spec i e ( ig. 9),
while F ancesco di Gio gio was de eloping o his o i ica ions a kind o d awing whe e
he on iew and he plan end o appea , simul aneously, in ue o m ( ig. 10). Faced
wi h he need o display clea ly he geome y o his plans o o i ied ci ies, F ancesco di
84 JOÃO PEDRO XAVIER –
Leona do’s Rep esen a ional Technique o Cen ally-Planned Temples
Gio gio in ui i ely disco e ed a d awing me hod which p o ed o be pe ec o
ep esen ing mili a y a chi ec u e and, la e on, a chi ec u e in gene al. Tha is why he
igo ous o m o his kind o pe spec i e, oday called “planome ic p ojec ion”, was i s
known as “mili a y pe spec i e”, o
p ospe i a solda esca
as Gi olamo Maggi and Jacomo
Cas io o called i s i . Acco ding o Scola i, pa allel pe spec i e as an al e na i e o
Renaissance pe spec i e was clea ly p esen ed, o he i s ime, in hei wo k
Della
o i icazione delle ci à
(Venice, 1564).6
Fig. 9. Leona do da Vinci, bi d’s-eye iew o a
o ess (c. 1504). Manusc ip 8936, ol. 79 ,
Mad id, Biblio eca Nacional
Fig. 10. F ancesco di Gio gio, Pen agonal s a
o ess,
T a a i di A chi e u a Ingene ia e A e
Mili a e
, c. 1485
Re u ning o he new echnique b ough in o a chi ec u al ep esen a ion by Leona do,
we should now y o unde s and i s no el y and special ela ionship wi h his esea ch on
cen ally-planned chu ches, while examining i s con ex ualiza ion.
In a way we may conside Leona do’s sys em – plan plus bi d’s eye pe spec i e – as a
pe sonal syn hesis o Vi u ian ideas on a chi ec u al ep esen a ion, since o him i was
enough o use only wo kinds o
disposi io
, as Vi u ius says: he so-called
ichonog aphia
(g ound plan) and
scenog aphia
(pe spec i e). I seems e iden ha he missing elemen o
he iad, he
o og aphia
(ele a ion), could be dispensed wi h, as i was implici ly included
in he on al bi d’s-eye iews he used. In any case, as a as he posi ion o he obse e is
conce ned, Vi u ius’s
scenog aphia
seems o be a bi di e en . The e is no doub ha he is
e e ing o cen al pe spec i e, ce ainly in i s p e-s age ( he e we e no means, a ha ime,
o es ablish co ec ly he diminu ion o dis ances in dep h), when he says, “…pe spec i e is
he me hod o ske ching a on wi h he sides wi hd awing in o he backg ound, he lines
all mee ing in he cen e o a ci cle” [Vi u ius 1970: I, ii, 15]. Bu as he only e e s o he
NEXUS NETWORK JOURNAL  VOL.10,NO. 1, 2008 85
possibili y o seeing he sides o he building and no he oo , we can in e ha he
obse e was no a he high le el whe e Leona do always p e e ed o place him in o de o
con ol h ee-dimensionali y in a single d awing. And, as we know, he was pa icula ly
in e es ed in he design o he oo , since he shape, size and disposi ion o he domes, apa
om hei cons uc ional aspec s, we e ques ions o main impo ance in ecclesias ic
a chi ec u e. Fu he , acco ding o Rich e , i seems ha hese chu ch d awings we e
exp essly designed o a “T a a o delle Cupole” ha he en isioned w i ing [Rich e 1970:
38].
I ha e al eady p esen ed an ensemble o possibili ies de i ed om such bi d’s-eye
posi ioning in gene al: i s h ee-dimensional abili y o gi e a syn he ic o e iew o he
whole, he ocusing on he objec in i sel , con ibu ing o he possibili y o unde lining i s
geome ic p o ile and showing i s pa s and he way hey a e spa ially assembled and
combined in o de o compose he whole. And, conce ning he measu emen s, we should
also add, a leas , he possibili y o ge ing p opo ional measu emen s in he on al iews,
since i s o m emains unal e ed.
On he o he hand, a plan d awing (
ichonog aphia
),7 in addi ion o i s main ole in
unc ional aspec s o accessibili y, ci cula ion and in e connec ion, which a e ela ed o
men’s ho izon al mo emen s h ough space, is like an eng a ing on he g ound o he
building’s geome ical ma ix – a pe ec mi o o i s ma hema ics. And, ac ually, i is also
om he g ound up ha i will g ow.
In combining a plan – some imes a me e diag am o jus a scheme – wi h he 3D
possibili ies o bi d’s-eye pe spec i e, Leona do ound an e icien ins umen o sculp ing
a building in space, a way o con ol i s g ow h h ough i s inal s age, ensu ing i s
geome ical in eg i y om he loo o he oo . Wi h hese wo d awings he could also gi e
he maximum amoun o in o ma ion abou i , as Mu ay unde lined. Bu i is easy o
p o e ha his is especially ue in he case o cen ally-planned emples, and e en he e we
shall ha e oppo uni y o poin o some inde e mina ions and unsol ed ques ions.
I is e iden ha wha makes his in o ma ion “almos enough” is ac ually he cen al
symme y o he building.
Bi d’s-eye pe spec i e, simul aneously p esen ing he on ele a ion and a la e al one, is
implici ly elling us wha he con o ma ion o he o he wo sides no shown is. I any
doub emains, i is su icien o look a he plan o con i m his. The ele a ion in on al
iew also indica es he p opo ional ela ionship be ween ho izon al and e ical measu es
o he açade, which is ex ensible o hem all.
One o he açades, o en he one in on al iew, is sub ly di e en om he o he s
because i is whe e Leona do loca es he en ance. E en so, i is di icul o speak abou he
exis ence o a main açade, since Leona do’s conce n o emphasizing cen ally-planned
space o ces him o a oid dis inguishing any kind o di ec ion. The doo is he e, bu only
o connec ex e io and in e io . I is no by chance ha he some imes e en omi s i .
Fu he , some imes we don’ e en know whe e i could possibly be placed, as in he plan
o an oc agonal chu ch wi h ound chapels in each side ( ig. 11, uppe igh ). To
con adic his, he e is also a mo e elabo a ed oc agonal plan wi h G eek-c oss chapels on
each side (see ig. 1), wi h an excep ionally de eloped na hex. Bu he e, as i does no
appea in he bi d’s-eye iew, i seems ha i was added only in plan, as a possible solu ion
o sol ing he di icul ies inhe en in he p e ious plan scheme. So, he p e ailing eeling is
92 JOÃO PEDRO XAVIER –
Leona do’s Rep esen a ional Technique o Cen ally-Planned Temples
The e is also ano he amily o plans gene a ed om a egula oc agon o which
co espond, once again, a p isma ic space co e ed by an oc agonal dome. The chu ch
p esen ed in MS B, ol. 22 is an example o his kind o plan. He e again he e is no any
possibili y o misunde s anding ( ig. 19). Conside ing he oc agon as he esul o he
in e sec ion o wo concen ic squa es o a ed 45º, we a i e o he whole plan wi h an
ad
quad a um
g ow h o each squa e. Along he way, co esponding o he co ne s o each
squa e, we will ind ou chapels and ou apses. One o he ex e io limi ing squa es, which
cu s he apses a he middle, co esponds o he dominan quad angula p isma ic mass o
he building om which he main dome and he ou domes o he chapels a e de ached. In
he example selec ed, he chapels a e quad angula p isms c owned wi h hemisphe ical
domes pe ched on cylind ical d ums; he hal -de ached side apses a e cylinde s wi h
hemisphe ical domes.
Fig. 19. Leona do da Vinci, plan gene a ed om a cen al oc agon wi h an
ad quad a um
s uc u e
MS B, ol. 22 ., Pa is, Ins i u de F ance. Geome ic o e lay by he au ho
Bu he p oblems a i e wi h he squa ed plan, which is ac ually ela ed o he G eek-
c oss plan, o which co esponds in mos cases a hemisphe ical dome wi h a cylind ical
d um, al hough i can also be oc agonal.10 I is no by chance ha all he in e io
pe spec i es we ha e a e in ela ion o his plan, bu e en so, no e e y hing can be
disclosed.
I is su icien o look a he se e al plans p esen ed in MS 2037, ol. 3 o ind he i s
di icul ies (see ig. 18). The la ge plan o which he la ge bi d’s-eye iew abo e
p esumably co esponds does no in ac ma ch. Compa ing he dimensions o he dome o
he isible hal -domes o he apses, we conclude ha i should co e he whole space, which

NEXUS NETWORK JOURNAL  VOL.10,NO. 1, 2008 93
is incompa ible wi h he p esence o he pie s in he plan. The e is a mo e schema ic plan a
le , and ano he , e en mo e schema ic one a he igh o he la ge bi d’s-eye iew, in
which he pie s do no appea , bu we canno be su e i his is a consequence o he
simplici y o he ske ches. Wha is ce ain is ha he plan ha ma ches he bi d’s-eye
pe spec i e canno ha e pie s. Bu he e canno be any kind o connec ion in he co ne s
ei he , as is also shown in he plan, sugges ing he de ini ion o a semi- egula oc agon
insc ibed in he squa e. Anyhow, he e is also ma ked in he same plan (uppe le co ne ) a
sho a c o a ci cle ha could co espond o pa o he p ojec ion o he dome shown in
pe spec i e. I , on he con a y, we s ay wi h he ou pie s, he dome necessa ily has o be
sho e and should be insc ibed in he squa e de ined by hese pie s. Bu i i is he semi-
egula oc agon ha emains, hen he dome can be maximized again and he e we ha e he
in e es ing ques ion posed by he spa ial ansi ion be ween a semi- egula oc agon and a
ci cle, a p oblem p esen ed and pe ec ly sol ed in B aman e’s p ojec o San Pie o in
Rome.
Conside ing all hese possibili ies, and o he s no ye men ioned, we begin o belie e
ha om ha plan i is possible o ex ac di e en plans, o mo e exac ly, di e en
a ia ions o he same ype o building, which is a clea indica ion ha Leona do was awa e
o such implica ions and was ying o ind solu ions o he p oblems posed by each. So,
he e again we see his mind in ac ion.
Table 1. Types o cen ally-planned chu ches de i ed om MS BN.2037, ol 3 .
Pa is, Ins i u de F ance
I ha e ied o econs i u e hese possibili ies diag amma ically, whe e each ype (o sub-
ype) is p esen ed in Leona do’s p e e ed sys em – plan plus bi d’s-eye pe spec i e – o
which I added a sec ion and an ele a ion (Table 1). Because I could u ilize CAD so wa e
o make hese d awings, I also cons uc ed i ual 3D models which we can ( i ually)
94 JOÃO PEDRO XAVIER –
Leona do’s Rep esen a ional Technique o Cen ally-Planned Temples
en e . Wi h his ins umen , he emaining doub s abou he in e io space become mo e
e iden .
All ypes ake as hei poin o depa u e a squa ed plan. By subdi iding each side in o
ou uni s we ge a ne o six een squa es, which unde lies he dimensions o all he spa ial
elemen s p esen in all he ypes. I seemed o me ha his g id i , mo e o less, in he
majo i y o he ske ches, pa icula ly he la ge plan o MS 2307, ol. 3 ( ig. 20).
Fig. 20. Squa ed plan g id. Geome ic o e lay by he au ho
Fig. 21. Leona do da Vinci, G eek-c oss chu ch.
Codex A lan icus
, ol. 362 -b, -b
Type A co esponds o a nea squa ed plan wi h one semici cula apse on each side. The
main space is almos cubic and a hemisphe ical dome pe ched on a cylind ical d um co e s
i . The apses a e cylind ical and c owned by hal -hemisphe es. In he ex e io he e a e ou
pinnacles in he co ne s o he cubic p ism, which a e ac ually small
empie os
, as in he
p ojec o he Ca hed al o Pa ia. The ansi ion be ween he squa e plan and he ci cula
base o he cylind ical d um could be ce ainly sol ed wi h sphe ical iangles. The building
NEXUS NETWORK JOURNAL  VOL.10,NO. 1, 2008 95
ha is mos simila o his ype o scheme is B aman e’s San a Ma ia delle G azie in Milan.
Bo h eali ies mus be aken in conside a ion in o de o explain San a Ma ia della
Consolazione in Todi. He e, howe e , he apses a e wide , which b ings he plan close o a
G eek c oss.
Type Aƍ is con igu ed as a clea G eek-c oss plan, bu he ex e io appea ance o he
aul s o he de ached a ms o he c oss is no con incing ( ig. 21). Pe haps i could be
co e ed wi h a saddle- oo wi h a pedimen a he end, as is shown in a pe spec i e in he
Codex A lan icus
, ol. 37 -a (second om igh a he bo om o he page) (see ig. 16).
The mos simila examples in ac ual buildings a e Giuliano da Sangallo’s San a Ma ia delle
Ca ce i in P a o (1485-95), al hough apses a e absen he e, and San Biagio in
Mon epulciano (1518-1545) by An onio da Sangallo he Elde , which p esen s wo
de ached bell- owe s in he co ne s and a lowe semi-ci cula body, he sac is y, joined o
he a m whe e he al a is.
Type B could be a pe ec building
in se
, bu we de ec i s p esence mo e as a spa ial
uni ha is pa o a mo e complex composi ion, such as he plan o an oc agonal chu ch
p esen ed in MS 2307, ol. 5 (see ig. 1). I is also e y simila o he chu ch o San
Sepolc o, on which Leona do and B aman e p obably wo ked, pu ing o h a p oposal o
i s eno a ion ( ig. 22).
Fig. 22. Leona do da Vinci, plan o San Sepolc o in Milan. Manusc ip B, Ins i u de F ance, Pa is
Wi h he aid o an in e io pe spec i e d awing (see ig. 15), i is possible o make a su e
in e p e a ion o he con igu a ion o his space. I is clea ha he ound dome is now
ci cumsc ibed by he squa e de ined by he ou pie s and i s a icula ion is iden ical o ype
A. O e he smalle squa es he si ua ion is p obably epea ed, as we can see lan e ns ha
appea on he oo . Tha is con i med in he plans and in e io pe spec i es o
Codex
A lan icus
ol. 37 -a (see ig. 16). Bu i is in e es ing o no e he wo solu ions ad anced by
Leona do o de ine he limi s o hese co ne s: wi h en abla u es ( he op ion o ype B),
and wi h a ches.
96 JOÃO PEDRO XAVIER –
Leona do’s Rep esen a ional Technique o Cen ally-Planned Temples
Type Bƍ appea s in he same shee . He e he space co esponding o he squa es in he
co ne is lowe and hus he a ched aul in be ween become appa en . Consequen ly, he
a icula ion o he olumes unde lines he subjacen G eek-c oss s uc u e o he plan.
Type C and Cƍ bo h ha e a semi- egula oc agon insc ibed in he squa e. Taking ou
g id as e e ence, i s la ge sides measu es wo uni s, he same as he diame e o he semi-
ci cula apses, and he smalle sides 2. Once again, bo h ypes could be ei he independen
buildings o spa ial uni s, bu we can de ec hei p esence in he Ca hed al o Pa ia as well
as in he Chu ch o San Lo enzo in Milan. The impo ance o his Ea ly Ch is ian emple is
well documen ed in Leona do’s esea ch on cen ally-planned chu ches. The e is e en a
d awing o a chu ch ha is a clea de elopmen o San Lo enzo’s plan ha was execu ed a
he Ca hed al o Pa ia ( ig. 23).
Fig. 23. Leona do da Vinci, plan o a chu ch based in San Lo enzo in Milan.
Manusc ip B, Ins i u de F ance, Pa is
Type Cƍ wi h an oc agonal dome is he adi ional solu ion, de i ed om he Go hic
pe iod, o co e ing a p isma ic oc agonal space, and his is he solu ion ha was employed
in Pa ia (see ig. 14). He e we can e i y ha he heigh o he dome has been educed in
compa ison o many o Leona do’s d awings, whe e he comple e ene a ion o
B unelleschi and he in luence o he dome o San a Ma ia del Fio e a e e iden .
Type C, wi h a hemisphe ical dome, is he mode n esponse. We know how B aman e
sol ed he ansi ion om he oc agon o he ci cle whe e he cylind ical dome si s. I is in
his p ojec o San Pie o and i is clea ly desc ibed in a d awing by one o his collabo a o s
( ig. 24). A ew yea s la e , Raphael did he same hing on a much smalle scale in he Chigi
NEXUS NETWORK JOURNAL  VOL.10,NO. 1, 2008 97
Chapel o San a Ma ia del Popolo in Rome. We canno be su e i Leona do was he i s o
concei e his solu ion. His inno a i e ep esen a ional sys em is no su icien o allow us o
be su e, o pe haps he p oblem is ha insu icien in o ma ion is gi en in he plan. In his
pa icula case, since we do no ha e a wooden model, an o hog aphic sec ion o an
in e io pe spec i e would be welcome.
Fig. 24. Design o San Pie o in Rome (1505). Plan by B aman e. Plan and sec ion
o he p ojec o he sphe ical pendi i es by An onio di Pelleg ino ( o B aman e).
Axonome y o he sys em by he au ho
Pe uzzi sol ed he p oblem h ough an o iginal syn hesis o bo h p ocedu es (see ig.
13). Bu he could no know ha his app oach was leading him away om he wo ld o
pe spec i e and opening he doo s o he de ini i e en ance o axonome y in he ield o
a chi ec u al ep esen a ion.
Acknowledgmen
The au ho wishes o hank A chi ec Domingos Ta a es, His o y o Mode n
A chi ec u e Lec u e and P o esso a FAUP, o his ad ice on his pape , A chi ec Ana
Fe ei a, who cons uc ed he i ual 3D models, and A chi ec Kim Williams, who so
ca e ully e ised he ex . I am also g a e ul o A chi ec Syl ie Du e noy, gues edi o o
his issue o he
Nexus Ne wo k Jou nal
.

98 JOÃO PEDRO XAVIER –
Leona do’s Rep esen a ional Technique o Cen ally-Planned Temples
No es
1. Pe haps we should add “conside able” abo e HL p esuming an obse a ion om a high poin
o iew.
2. Pie o Accol i,
Lo inganno degli occhi
(1625) ela es pa allel p ojec ion wi h he shadow
p ojec ed by he Sun. Di ec ing his a en ion o p ac icing pain e s he s a es:
insegnandoci il es imonio del senso isi o (al quale unicamen e so opos a la
pi u a) manda l’omb e sue, pa allele sul piano… con la in ini a dis anza del
luminoso degli opachi… così es iamo capaci po e si all’occhio nos o, in
disegna a app esen azione di quella p ecisa edu a di qualsi oglia da o
co po, espos o all’occhio (pe così di e) del Sole quale ad esso Sole gli si
app esen a in edu a: onde si come speculando in endiamo il Sole non
ede e giammai alcuna omb a degl’opachi, e supe icie, ch’egli imi i e
illus i, cosi u e quelle, che engono in sua edu a, in endiamo es a e
lumeggia e e pe con a io u e le al e a lui ascose es a e omb eggia e...
Così in endiamo do e esse e il sudde o disegno, pe app esen azione di
edu a del Sole, e mina o con linee, e la i pa alleli, non occo en i a pun o
alcuno di P ospe i a
[Scola i 1984: 46].
3. I wouldn’ be ai no o poin o F ancesco di Gio gio’s e y in elligen way o d awing. In
ac , his pe spec i es ha e a g ea lexibili y in o de o show a once wha has o be shown.
Thus he has no p oblem wi h in en ionally dis o ing hem on behal o immedia e legibili y.
4. Among he d awings o
Codice Cone
i is possible o ind some p e-ca alie pe spec i es,
especially some a chi ec u al de ails seen om a low poin o iew ( he so-called wo m’s-eye
iews, in con as o he high posi ion o he obse e in he bi d’s-eye iew).
5. In he mos usual o m o ca alie pe spec i e he anishing angle o he
y
-axis is 45º; he
educ ion coe icien along he
y
-axis is ½.
6.
Non pensi alcuno in ques e mie ope a ede e mode o egole di p ospe i a, l’ una pe non
esse e p o essione di solda o non le sap ei a e; l’al a pe ché li sco ci che i and ebbono,
l’huomo le e ebbe oppo dalle pian e; pe ò in esse pian e, e p o ili consis e à il u o di
ques e ope a e ques a si di à p ospe i a solda esca
[Maggi and Cas io o 1564], ci ed in
[Scola i 1984: 43].
7.
A g oundplan is made by he p ope successi e use o compasses and ule, h ough which we
ge ou lines o he plane su aces o buildings
[Vi u ius 1960: I, ii, 15].
8. Ca lo Ped e i speaks abou a enewal p og am o possible B aman esque inspi a ion. C .
[Ped e i 1981: 24].
9. I am e e ing o pe spec i e whe e he cen al anishing poin ac s as he unique anishing
poin . So, he
y
-axis is pe pendicula o he pic u e plane.
10. The La in-c oss plan does no aise any new ques ion, since in his si ua ion he na e wo ks as
an an echambe o a cen ally-planned emple.
Re e ences
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CABEZAS, Lino. 2002. Las máquinas de dibuja . En e el mi o de la isión obje i a y la ciencia de la
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Máquinas y he amien as de Dibujo
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Leona do A chi e o
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RICHTER, Jean Paul. 1970.
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VELTMAN, Kim H. 1986.
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The Ten Books on A chi ec u e
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WITTKOWER, Rudol . 1971.
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No on.
XAVIER, João Ped o. 1997.
Pe spec i a, pe spec i a acele ada e con ape spec i a
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Publicações.
Abou he au ho
João Ped o Xa ie is an a chi ec and geome y eache . He ecei ed his deg ee in A chi ec u e om
he Facul y o A chi ec u e o he Uni e si y o Po o (FAUP), a Ph.D. in A chi ec u e in 2005, and
has been licensed as an a chi ec a he College o A chi ec s in Po o since 1986. He has won
academic p izes, including he P émio Flo êncio de Ca alho and P émio Engº An ónio de Almeida.
He wo ked in Ál a o Siza's o ice om 1986 o 1999. A he same ime, he es ablished his own
p ac ice as an a chi ec . He has been eaching geome y since 1985 a he A chi ec u e School o
Coope a i a Á o e in Po o, he Fine A s School o Po o and a FAUP om 1991 o he p esen .
He is he au ho o
Pe spec i a, pe spec i a acele ada e con ape spec i a
(FAUP Publicações, 1997)
and
Sob e as o igens da pe spec i a em Po ugal
(FAUP Publicações, 2006). Xa ie has always been
in e es ed in he ela ionship be ween a chi ec u e and ma hema ics, especially geome y. He
published se e al wo ks and pape s on he subjec , p esen ed con e ences and lec u es and augh
cou ses o high school eache s. He p esen ed “An ónio Rod igues, a Po uguese a chi ec wi h a
scien i ic inclina ion” a he Nexus 2002 con e ence in Óbidos, Po ugal.