1737


L A

PERSPECTIVE
CVRIEVSE.



17 3 7



THERE

PERSPECTIVE

CVRIEVSE

OV

MA G I E A R T I F IC I EL E

WONDERFUL EFFECTS.

F optics,
by direct vifion.

) The Catoptnque, by the reflection of the myrrh

Of

(e ) flat , Cylindrical & Conical.
the
The diopter, by the refraction 1: ion of Cryophiles.


<J > years which, moreover, VN abbreviates & method genm1le of the 1'er!Jefflue commU:.
in practice for regular bodies, EFT still in (eignee the way

to make I:: JJ conflict with any force of misshapen figures, which ejtant, want to •
their point! wall-to-wall ratio : the whole by pr11: s

Jifam, lieres, that 1ES less, veife'z, in the qeometry can feruir auer:

lejèul compa1 & la regle.

Kc: J A -;, U, > TD'l f..7dçûafw;

O. cuurc trcs-vtile for painters, architects, designers
, Sculptors, & in rousaucm
who are using Dolphin in their 0uurages.

By father F. IEAN FRANÇOIS NICERON Parifien de fOrdre des Minimes.


(1f.Q -:..;:·

"'r, - to

\t$:T..

A P A R I S,
rn,

Pierre BILLAINE, ruëS. Jacques;
to The Good Foy, deuant S. Yues.

M.
DC. XXXVIII.
<.WITH ..RIVILEGE. DV l{OY.


To

MR ONSEIGNEVR'

Lllufüioeme & Keuerendiffime,

M O N S .E I G N E V R.

GEORGES BOLOGNETTI

E V E S Q V E D' A S COL I

E T

N O N C E D E S A S A I N C T E,..'.

IN FRANCE.

ONSEIGNEVR,

This ouurage you eftant cbii=
er: facré des L'inftant De fa conception
,has not pluftoft veu the light, that it
go to your house take a seat, pouriouir
domefl:ique, & FRF..
clat de vofire nom, to paffer by everything,
despite the Zoiles & Amphiarchs, crazy
vo.ftreadueu, & at the heart of vofire proteehon.
I'm gonna flate myself in my perfumery.


dant, that he will not do discarded , & that willingly
you will grant this faueur:
but after so many times experienced

III iiij


E PIS T R E.

the effects of vofhe bene-Veilance in my
place; 1'ay believe that ie does not luy deuois
less efperer than vn fauorable home of
this mefme courtesies, which made you aymer
fon author, since he has the honor
of efrre known to you; & efhmer Fes ouurages,
when he has communicated them. If.
you agree, MoNs.EIGNEVR, iedo1s well
m'efj: imer happy to efrre hired by deuoir
to you prefer it, sniff this neceOEté
makes me renc69 - tter vne perfonne relay
dignity to protect him;&
aduantagee of all strong of rare
cognoilfances, to welcome.Siles terminals
prefcrits to vneEpifrreme the perinetoiet,
& howfrienemele defendifr: ie
could report icy vne part of the rare
quality you can say; new jobs
what you had, & beautiful seasons; " by
lef what"

you have reduced your recom-,
dable. the dirois, that after the night given in
this is the first time that we have been able to find a solution to this problem.
deep dotl: rine, we did not plufrofr you
veu paroifrre in the hierarchical Efrat,
that N. S. P. The Pope who wishes to prefer the
keys of St. Peter, admiring in you vne fageife
extraordinary & vne caution confommee
in the conduct of your afüons,
gave you the most honorable employees
who stood in the Court of Rome, & the main guuernemensdefon
Efrat. After
auoir paiféthe first honors; you fo


fl:e.,


EPIS T RE.

Florence, where you are
I have been able to identify the interefl: s of the
f?,m, et Siege, & so satisfied & con·
rç, qté the Prince & La Repu, bhque, que en re•
NGC.oiffance of v9s bell..s afüon5 you in
füftes Ieué at the end of d<:; 4, X years, & enuoy..
eij'fjance, for the wall.Q-re in mefme quafüé,
more a.ec all the more so dclat & de
fple.that the cfene, which is being prepared to
your Nertt1sefl: ILO plus folennelle & expofee,
..}I want everyone. The.. elloit-il
l:n..n fonnable rai, que vne Fi high mtelhgence
that vofl: re was not plu $ long-time
occupied at the TUI;: of vn lower Sky; ilf..lloit

..yç: 01R exercise fon aetmité en cduy_ de la
more flei1rHfante monarchy of the, Vniuers.
L) you are there, MoNSEIGN.Ev.to;
you auez ji Puilly attracted the affe ..
Qiqns of vn each ; you have treated the
FA Health-& FA Majefl Affairs:.1ec so much foing & diligence; auecvne
such caution & dexterity in times
the fafcheux, & the most
difficult: you have made those of the parties
auec so much courtesy & good•
watch, that all fülats & Kingdoms
dela Chrellienté enuient le Bonheur
of you poffeder, for-the recitations that we
in fact; & all those who are tefless
eyepieces will let you age in
this dignity, if your merits do not call you
elsewhere: but it Ell good to believe that e •
.Q-antd'vne fi noble & illu!three family, who has

E PI S T RE.

fourny at Eglife so many great perfonna.:
ges, prelates & Cardinals illufl: res in piety & e11.Doel: rine; between you and me
Paternal uncle Albert Bolognetti, who
pres a UOI R efl: NCE in Florence &
Vehize, & Legat in Poland, was made Cardiilal'lçrs
that ildl:ILO still in fa Legation: it
efr,I say, good to believe, when I had the mef.even more so than them, but far moreidentifiable, for those of you who have
eu deal; & you in efl: Ant acquitted auffi
at the very least,you will
bief honored with the dignity mefme, who you
dolmera fujet to produce outside, & do
i..?.1arqlfer, en vo..s of ..or..elles1: erfeél: I.., aqmferont cogno1fl: re to those QM rie the fçk..
uentpas,.may all that you have done be honorable in this life
p..s the least part of your merits, & that
the efclat of the highest dignities that you
baby, I'm not gonna let this one go.
your virtues & your perfeél:ions. On recognoifl:
by all the puiifance devofl: reGenie;
& that you dl: snore for some chofe of
large
, puif you make your diuertiifernens
of what others take for their busier occupations: in q uoy ie
you would gladly compare to Scipionl ' Afnquain,
which one, will have to deciceronen fon
Treaty of the Offices, after
paid, whichhe paid the charges, which he took in the Administrative Procedure.
laRepublique,trouuoit fon re.
pas & FA confolationin efl: Laphi ESU


lofophie


E PIS T R E.

lofophie: Ainfi, MoNsEIGNEVR, fi occupations,&
the foings of vofl: re charge, you
lai lfent a few hours in the woman, you
the confacrezaux Mufes;&, Horn this great
Captain, you're less feul.,
only when you efl: es fans Company; no y
I was less in authority than you were.
efl: business freedom; puifcanto in these times,
or you conuerf auec the dead, by the lelt: ure;
or auec the viuans, by the maintenance,
to continuously cultivate, & increase
all of the rare cogniifances, that
I had to tell you. C'efftcc: Quim'adonné.
the hardidfe of preferring you this Treaty of
the CvRI PERSPECTIVE.EVSE, doing well
moreover, you are particularly
this fcience: and stink my bonl1eur
it brought me such things, than to contribute
anything to your diuertiifemens,
by faifant veoir fes miracles, & you
I've heard that he's a good man.
will not make you defagreable to auoir
this drunk,the..uelforceiernetsauur,
fouz the proteebon devofrre name, & for
tef moignage de l'honneur& du refpeél: que
makes you

MONSEIGNEVR,

Poflre tres-hnmhle & trtr-oieyj[,.nt feruiteur.

F. hAN F .RAN..OIS N1CBRON. R. M.
De vofüc Conuent de 1A Placo
Royale cc 18, luillct 1611.


,î,,î,,î,,î,..,t,,î,:,!!,: .... /i!,: ,,i;,.l)f,..., U, .. ..Hey, r'!!, ..rtr,,,î,,,t..,'i', ri;,!; ,,t.
P E R.. MI S S I O N D V R. P. 'P R O VI N C I A L

I order minimums in la'!Prouinc, from France.

Do
Do
Ovs Fr. Gilles Co!fart Prouincial of !Order of Minima in
the Prouincc of France, having veuule report of the fathers by US
committed to !* Review of the book entitled, The p ER S P E C T I v E C vRI
EV SE, composed by the lcan Francois Niceron Religieux of
noll: redit order, auons entant que en nos EFT permis icelanduy. eftre
put in lu1hiere. In foy dequoy we have the prefente line, & in icelle
the cfeau of our office, in, 1of the Paris Conucnt, on the 15th.
April 1638.

I'. GILLES CosnsART, ProuinciAl.

,.,.

The Place du fceau. ,f<

.Approval of the Theologianr of !'Order.

Do
Do
Ous foubs!ignez religious 4th !'Ordre des Minimes, milionsnauoir veu & leu par com, mflion de nos R. P. Promncial vn
liureintirulé, the perspective CVRIEVSE ' compofed by the
Perc F. lean Francois Niceron Religious of nollredic order: to which theyans trouué routes chofes treated with dignity & conformemmcntàleur
fujer, fans no fufpicion d'erreut, or against the Foy, or against the
good morals, we believe that the public will not resort less
I: satisfaction & contentment. In
foy dcquoy we have fair & ligne La p1efenre en nofrre Conuent de
the ... the ... The Royal in Paris, nlc 13. April 1638.do

_do

Fr. MARIN MERSENNE.

Fr. Franc01s of the Novi:

SUMMARY


SUMMARY

OF THIS QYI IS CONTAINED IN

IN THIS REGARD, THE
CV R I E VS E,

PREFACE AND WARNING AV LECTEVR;

On thejfein, / 'infcription, jeujtt, fb' of this treaty; auec quelq•e.

adui.s nec1J4ires for re11x that / C 'lJoudront lrre aunft1tit & conttnument._
DEF.INITIONS NEC ESSA L R. ES, Tour L'inrell l,ence decette

Perjje{F; EU. page I

Problems, Ser11Ants to the conjlruelion of conttm1t's rs Bures figures

.

faù111, ns.. . 4

PREMIERE PRO POSITION. Avneligneâroiéle donnee menervne

·

·

another line is the para!lele J', vne dijlance, donnee. 4

About l T 1 0 n it. Right-handed Line; & D'vnpointdoné
in the case of a straight line perpendicular to the area, or far vne lig.ne droi11
, donnee, & d ' Vnpoineldonnehors d'rcelle, abbaijfer1me straight line perpendicular-

cu!air.. {

P R O P O S I T l O N Il1. Vom,er/e, mayen l. ecognoiflre, Ji 'Vneligne

efl perpendicular to vnt other. . . 1

ABOUT I T 1 0 N IV.Diuijêrvneligne droiéle given-entantdepar


ttes eY, ales, quel'onvoudr.t. • , i;

·

Proposal V, IUD, (ISR<t•ncercle en4,..,16, ' et:, c. P * rriesegales. 7
ABOUT l TI ON V 1. On'vneligne droiteet:.,to be given in

cellefairevn ..•glereélil..gne * eg * I to ' T'nanglereelilt, not given

7

J; ' R OP OS I TI ON VII. In ' lm c, rcledonné_infcrrevnpenrar, one,
. or VN Decagon regulier. 8
A PP END I EC. Of the communities/ionaU: Cerdeen 36o degreZ,_, or

* parties,bearing in mind the me(ure of N.A.,..( ' )
pofygones re_guliers, or figures to P!you guys. 9

THE FIRST BOOK OF PERSPECTIVE

CVRIE.VSE,

Contmdnt the principles of the gJ erfJ, eeliue & vnè general method, to
or put in per{peéliumutesforr!sde flat figures & folides;still tllu
do not touch the planqi in vnt li [, ne, or in VN point, verijie p. rexempl, è cin9.

;

you



Summary of proposals:

D E F I N I T I O N S.

Deslignrs (f) despoin{h, who {onten'vfa[/,in this m,T!,odede 'Per(pefliue, 13

A V 1 S NEC ESSA 1 RE,'!For the conjlruel, he took the ropofitifs.15

p REMI ERE about !Tl ON. Vnpo,..he / she is not given to the plan
Geometrtal, laheight de l'oeil@ / a dij / ance ejlantpareillemmt d,, nenw, hole•
the appearance of the Me{Me poinfiau plan per / pedtf, or in the table. 16

About !TI ON II. Give some About !TI ON II. Give some examples to the Greek
lafa.fiire merhode. 19

ABOUT I T 1 0 N 111 .Apply the age of cme regle, to the racoumf
{ment of circles f1: J other figures with curved lines. _ :.. ..

THE M ME 1. .A given two straight lines trouuer'vne m'dee..disproportionate.
l ,3

L E M M E I 1. * * * * * * * * * * •
right given, aitlamfmepr,, portion to which autrefimbl.given,
that this•ry, J: celltqu, fer4 tro11uet. .

2.3

PRO I ' 0 SIT ION III!. VN ejlantdonné circle rnvnplan, l..difl•nce
ej/ant parei/le,pent given, (JJ" l• {,El,it, where the table reroJânt perpendicular
make the plane; hole the height of the oe./ , fion which the circle
(OI aujji ' Vn * cercliparfa, t., 4

l' R OP OS I T 10 N V. Vn cmle ejlant given in ,,.m plane, height
from the oet! similarly given, & the ffl, on, or the table, ep,, (ar, t
perpendicular to the * plane; hole the dijlance, row• !, what the cer•
, the ejlant put in the erfj: fliu,, fon •pparenre done .,,.!Ji 1,•n circle by•

do{l., 5

PRO PO SIT 10 N VI. Efl, ntJ * nneel, natural height of line
ferpenrliru / air, fur ' VN plane, hole FA decrease, or F * Perfj-ec11ue, Fi Ion
place d.. /0114.!Jiete aud1tplan, or [on auancementdam Fe tll..b!eaw. 2. 0

PROPOSAL VII. Mettreeeenperjfefl,., 'VnCube repofant * U plan

steal r-1.m defls cofte': (, in fact he only touches it in'!Jne reads, ne. 18

PRO POSITION VIIl...; Jletter en Per (pef!I'll take you up.·
rami de perpendicularementfar L ' VN de FIS angfe;fa/ides, in farte that it does not
touches the plane, that in ' VN point {l,; o

.
PRO PO S I T I ON IX. vl - letter in perf}eelme ' Vn Otloëdre p, rpcn


Jicu1airem_ent J;r l"Vn d, fis angles [oli..s, strong that it does not touch the plane,
that in ' VN poinfl. ; ..
PRO po SI Tl ON X. Put, VN Cube enperl] ieEliuefur R ' Vn de

jès angles fali..s, enough that he does not touch the PL..n, que en'vn pain {{, @ que lafardia::,
onale ducubefoit perpendicular to the plane mefme. H
PRO PO and Tl ON. XI. Put it in rP, rffeR, EU'!Jn Dedecaëdre repofant
to planfur 1 'VN de fescofl '" < or arreft, s, in (orte that it does not touch said
pl, only in'vne line. · 37
PROPOSAL XII. .: Yetter en'!Perj}eel " tie, vnlcof;, drerepo


jantperpend,culairementfur L'vn de fis * ngltsJoli des, en Jor que, t touch the

'

3 9


Summary of Propofaions:

PROPOSAL XIII. Give '1Jnemethodefacile, for mttreen
perjpeEliue some corpmgulierscompofez. , or irregular

_

rule / impies. · • 41

PROPOSITION I (J N XIV. Pet Mellre/} etliue plowers body imgulim
d1f],of ez. round the clock, Boo-Boo! fol stones, Jembiable & equal,
each compr!ftof two oflogones, Jparallelograms & trapez.es. 4 5

PRO P-0 S I TI O N XV. In the form of a perforated cube;

or quamz cheuron compote.. 46

THE SECOND BOOK OF THE PÈRSP E CTIVE

C V RI EV S E.·

A uqucl font decl•rez. les m'!Yen to conflruire strong plujieurs of figures ap by•
lieutenants a /,. '1jijion droifle, lefque / / E, out of their poinfl fambleronr diffor


my & raifon fans, (b-wuës Dr their poinfl paroi_j / ront bien proportronne...

PRE MI ERE PROPOSAL. Do'unechaire enper_Jjefliueji

I mean, if she's out of town, she doesn't look like she's out of town. 51

PR O P O S I T I O N II. Give dt method defcti.re alljours dt
figures, images & tables, in/,.m, fme way that the chaim of/,. previouspropojition
in other words, what is the meaning of the word 'fparence'?
they are perfectly reprejent a propofl object.

52. PRO PO SI TI ON . III. Geometrically Dif crere en la Jùrface <Xte•
1.m cone, ' tme figure, quoyque dt / form & confused
in appearance, there is no doubt that a certain amount of fine-grained repreflnte will be repreflnte.
'A p * opofé object. 16

PRO P O SI T I O N !III. Of the inner furf""
or concauc d'vn cone, vne figure, which, though y than Di / form & con4
fa (e rn app11,rence: eflant neantmoinsveuëd'vn certain poinfl, reprejènrep11, r4

·

fa1element'1jn objetdonnf.

rS

PROPOSAL V. Dejèrire p<rulemoyen numbers,inthe[urfaceuexterieure ilo co,:uexe A cane, A figure, which, quoy, that misshapen @·
confafè in appearance; ejlant neantmoim-vould'1.m certain poinEI, reprejènte
perfectly ' a propofe object. s 9

APPENDIX. Of the effageestablesof the Tangenresin theprevious Pro.

poftion (!) es_ (I, iuantes. 63

,

Purpose
WE SAW.

an inner face, or cone shape, of a figure, which forms

·

& conf,,fe in appearance; EJ / antneintontless '1game'd0' 1Jlf certain poinfl reproachsfairly
'An object 011 given image. · 6 6

PROPOSAL VII. I'll be in the outer furface of a pyramid.
quame, 'Une / igure, / quelqu'!Y q1,e difformeet:..confa (è in appearance: ejl, < nt
I had no idea of a certain point, reprefent by faiélementw objetpropo


fl 0

APPENDIX.


Summary of Propofitions.

THE TR, OISIESME BOOK OF PERSPECTIVE
CVR!EVSE,

.Auqu, 1il EJI traiElé des ..pparences: flat, cylindrical & conical mirrors;

.

(!!'ode the way to confirm figures that report & repr, jentent
by replexion any other chofi, that what they paroijftnt ejlant want to say:
estement.

A V AN T-P R o p 0 S. of the Catroptrics and:., mirror. 7 ,1,

FIRST PROPOSAL. Conflruire smefigure ou / mage en'un
this is not the case..exion en ' / Jn mirror
flat, and:., that the framework ej / antveu direelement en reprejènte ' / Jn other all

·

differenre. . . . 7 8'

PRO P O SI T I O N II. Explain what the ILO is dealing with the good;

, mirrors, which enters intocompojition, the ma-11.iere de les fandre, jettertn mou


* le & Le donner ' / Jn beau pofy. SR
PRO po SI TI on Ill. Ejlantdonné ' / Jn conuex cylindrical mirror,
perpendicular {ur '/Jnplan para/le/el fa bafe, defcrire in this plan '/Jne figure,
which quqy that misshapen @ confafe in appearance, will produce noantless
to the mirror by rejlexion ' IJne image well proportioned ,.& Fi mblable to which-,
what a propefe object. 8 J

PR OP OS I TI ON IV. (C) conuexa
perpendicular ' fur ' / Jn plane parallel Tofa bafe; defwrite G eometrically
as this plan '/Jne figure, which quqy that misshapen El/confa(e,
appearance,, confident neantless ' / Jeueoa 1m certain poinét, proJu, I by reflex / on

.

in the mirror ' / Jne image well proportioned, suitable for any object
propgfe. 88

.

P R O P O s I T I O N V. ejiant donnf "' n conue conical mirror..
uexefur ' / Jn plane parallel to fa bafe; the point of wue efl * nt set in 111 line
dt The AXIS, ejloigned from the plane & tip of the mirror of ijned, jlance propofee:
def crirt fur this plane around the mirror' / Jne figure, which qu'!) that dif
form & conf4; in appearance; ejl, mtneantless ' / Game of {on point per rrfle•
xion in the mirror, paroij) t well proportioned flJJèmbl.ble to any ob


jet propo{f, 94

APPENDIX. 99

The QyA TlUESME book of PERSPECTIVE
C V R f-J!.'S E,

To whom he EJ/ traieet! of this diopter meruille inuentée en nos iours, p; 1r

features of their proportions:

which fur the plan of IJN table, or will make rainy figures or porembiable
to

of all the connections that make to the table.u, aujfi well proportionee &f

Foreword on the subject & the order ofcellure.

100

PRE



Summary of propolis.

PREMIERE PRO positti ON. Explain the manner of ta; / ler
& Polish Polygon or faceted worms & cryftals, of which
we will. 103

PR O P O SI T I ON I 1. F xplicerefafon de dij}ofer the plan, to which

_

ondefcritordinarily these figures, & drejJer the bezel, by the ' lue / lee / le,
flront'veui!s. IOJ
P R O PO SI TI o n I i I. give the method of diuifer the plan D11 table,
& y plot I, Artificial plan of ID figure, or ier rfjaces, aufqu, ls must

,jlre reduced each defts parties.
PR O P O s I T 1 0 n I V. Cenjlruirele natural plan D, the image or figu


re, the defrire audit plan, & enfaire the redurl, on the plan artijictel; en forte

that, fiant ' IJeuë parla lunette, elle paroijfe Jembl./ , le & auJ!I well proportioned,
only naturally.

Proposal V. lts parts of thejigureor thejlantreduites
Es, J}aces of the artificial plan,/, sd,fi, uiflr of strong than hiding the artifice of/a
conjlrurlion, on faJ!I think it's a good idea to do this,but I think it's a good idea to do this.

·

anything other than what is contained in the bezel. ..r.


tiij

\


PREFACE,

And A. D Green ISSE ME NT
to the Leeteur.

SVR, ..... Design, inscription, SVJET


0 v T Es the ra1cics of mathematics have at the

vcrite rare inucntions & fobti!itez, who the

have made dl: itncr & culciuer by 1 -: s more beautiful efprits

of antiquity , & who still make them today * huy

search by the most curious of noll: rc ciacle:

but it is necessary to auoier auec the best fenfez, that cel


That's prifer & rechmherparde!other people;

lefquelles outrck,bdlcsveritez they demon!l: (ent, & of which elksfatisfy
& perfcéhonncnt understand us; no\) s fourm!FRNT again
a thousand conveniences in the exccution of our entrcprif, diucm!ftnt &
recreate our fens, exercising the indulgence of those who fecontcntans
our steps of useless & infrueèucufes fperulations, take advantage of
they have been medicated by
vn lono-efiude. Ain / I I ' Architefü1ret: Mt cimlc that military us prefcriuan
..building order & structure, & giving
the way to fortify, deftèndrc & arquer the squares; de Dre!iron in full
campaign of battalions of all forts, fuiuanc places & meetings;
the mechanics provided us / Eme in Fes demonfications the fa,:
you're a dre!ferdes Machines,for foulleuer of maifons cntiercs:these fciéces,
I say, we pre-writing these rules & giving us these iriuencionS"
Garlic:rolabes , pinnules , & .other millet: rurnens qm .dmgent I. e vifuel Ray.
L11 Philophophie nacurellc veri / Ile plus part of the experiences of
middle fon: the Archiceel: ure takes order from her for the fymmecrie & the
grace * de fesouurages, quinefont ell: imcz beau:< ,Qu'antant que les do
pleasing to the eye in their proportions: Breflla paint, that ,we called
the Princelfedes bows, that ell: - this ..utre chofr-que vnepurc pr; iel: ique
decerrefcience,enfomqueiama_is it:no ell: veu good painter, who is
fur fçauant, Encoreamourd h, ouyfinousen auons, qudques-vns,iidans
Paris we see who rcü!Iilfent in excellence, like Monficur
Voüet first painter of the Roy, Moficur DCLA Hyre & a few others':
their ouurages nousfonralfez cog1'oiil: re that they (uiucm all the maxi a

in the conduct of their de(faiths, & the application of
their color.

T oute & the faults on the contrary & the impertinences that the common
painters incourses, source of ignorance of these principles,
where does that come from if they want to make paroill: re VN flowerpot, or someone else·
chofe femblable, planc.F droic in the middle of vne cab le, they put it fur
the.edge : ....make figures in eiloignemcnt, they afoiblilfent the ca



PREFACE.

loris, & in no way diminish the perfectconfiguration of their parts;
Still quclaforme & the figure of objects Fe defrobe in our eyes well
plu!loll: that coul..ur, as we see that vne round quarreetoussparoill round in! it will be possible to use the same colour as our own.
eyes: cc that makes me say that'o ptiquea so much aduantage by de!fus
rell: and desfriences, comele Fens dela veuë parde!fus the others: and about it
ledoetc V illalpandus en Fes comments fur Ezekiel says that the
Fcience of Perfpeetiue must Ell: Rea bontroitcenfce la prima endignée,
& the Most Excellent of all, then she takes care of confidercr
the effects & propnetez of the lwniere, that e!the beauty of all
es fen!ibles: but what is more admirable, he says, Ell: that by
fonmoyen we learn to trace the linesnvnplans, fiaabout,
that she expresses body & figuresfolid, which deceive not only
the eyes: but still somehow the iugemmt &
the horseradish: indeed all the artifice & the. beauty of painting,
perdelaforte, & make paroillre of rdiefcwhich only it configured in flat.
It's why the hills make us so cll: at this ouurage of
Zeuxis, which finaifuely Paints The Grapes of AIFM, than the oyfcaux the
but it is more than the play of Parrhafius, who Trop
the Mefine Zcuxis, by the means of VN feultideau, which he could reprefenter
fi arri!L: emenr, that fon antagonille begged him to laugh, to see her painted.
rcqu'1I penfoit ellre cacheeddfous , & if appcrceuantdelatromperie fc
confe!fa defeated, by what he auoic deceived only oyfeaux, & Parrha-:
fius vn Painter.

This is the perfection that we would define in the workings of our CPIN=
very; mris there is little ink plulieurs, who arrive there, especially as they neglect
plufpmlacognoilfanceoftheperipeel:
in addition, they do not contribute to their financing.
because there are many good authors,who have dre!Fe
methods & donnc:examples.We mean that of Viator in Latin&
enFran..ois imprime bien fix twenty years ago: Albm Durer en a
put some chofe in the practical geometry; like lean Baptill: eAlbercau
the reason he did the painting: lean Coufm, du Cerceau,
Salomon de Caus & !vlarolois have dealt with it expre!fement, & since cu, c
again Monfieurde Vaulezard, MonfieurHe.rigone & Monfieur Defargues,
who amisau iourvnemechode general & Fort expeditiue,
it ainuétee,auec yet longer linkers other wonderful fecrets to the Architeél:ee
& the Perfpeetiue, so he will make public pattau when illuy pleases. The
Italians & Germans enontencorevne quantity of others, .commeSebafüen
Serlio, Sirigati, Vignole auecthe comments of R. P. Egnatio

Danti, guide Vbatde, DanielBarbaro; Fernando Di Diana, LcnKerus,
lamicferus, Fortius, ilferoitlong to search & nomrner all
speak menu: what will do maybe: re that ons'llonnera, that aftervnfigridnobre of Authcurs, who have efcrit delaperfpeetiue, ie me once wanted mefkr,
come fi ..hcr:i_clacognoifance,I don't want to

* fansEtires


PREFACE.

to satisfy plainly their curiosity, in these ouurages.

Laveri.. what concerns the common Perfpeeeiue, what is it?
plans & the eleuation of figures fo!ides,a e!L: Hey!fez bié deduced by ers
Authors; deforremefme que Il fembre, que no puilferiendefirer: Entre
other films like Iean Coulin & Vignole and onra!fez bicnreüili, &fe
make familiar & intelligible to all, each in fa hngue: aulli n'e11: ILO-
this is not my first deikin, to say nothing of these principles in this treaty;
but feulement of. propofer genrillelfes De H Perfpeél:iuecurieufecomprifes
the last three lessons of this ouuragc, meperfuadat que apresm'y ell:
employed for some time; after dark or war a few weeks, &
faahtéles merhodes & practices of what ell: ILO defo inuenré, for my
vfugeparciculier, & to diumir me some of the dl: udes more ferielL')
in theology, where my profdlion engages me more parricularly; I do not
ferois not chofe defagreable to the curious of their prefenter the fruit of my
fpeculations, de monrauail & Des experiences que'ay faiél: es fur cefujet,

I want them to be content with what they have acquired with pain.

the European Parliament and the council
more recommendable, & La metrte dauant en ell: ime among those, to whom it
what matters most is the cognoilfance , which,in this way, have neglected it to prefer, for the sake of the children: the preuoyois, I say,
that because Way in leurpropofantcesnewyou & these genrillelfcs, Horn
the most beautiful attractions of this fcience)e la]euran you search
auec ardeur & s'en in!l: run to the due diligence, to take at least lcurrententemeat
in similar cases, the need for
fesprecepcesordinary, not their ell: not VN Alfez pui!slant pattern, for them shoot
dela parelfe & leurfaireembr.ilferle tr.iuail: was this maxim that die

Omne t * lit punfium, qui mifcuit ' Vtile du / ci.

that the good vrile & L'agricable joinrsenfemble in vn mefmefujct; we at


* shoot much more puifamenr. FA looking , only if it's not!l: oir auanrag.f
that of the vn or the other feparement.
..'e_!l: oitdon..my prize..delfein in the ronceptoof this painting: r

. .

ma1Scome 1 C lifo1s sometimes authors, who have Efcnr of Perfpe1bud,
& parriculierement those who have dealt with the five regular bodies; ieremarquay
let those who hear it be written in Francis be there!l: oient trepez, as
lean Coufin, M1rolois, & quelques-VNS aufli of those who made it in latin,
like! Author of the book entitled ..NTA.gma in quo,,, air eximùque,
& C. reply d'vnequanritéae bellesfigures, fansno prcccptenyir.!l:rull:ion,
f111on in genm.l, which heapplies by way of example to the pyramid
or Tetraedre the most( 1mp1e of all these bodies; & this auec error, like ie
it shows fur the oil: Iefnlc Propofirion of the first; lure, what makes me

..gnaw, or ciuecen'e!l: notemefmcwho made the figures &the difcourse of this
hure, or what again.let these flowers appear to be made in Alfez de craccc,
e!l: if properly examined, there will be a lot of mistakes. Pgur others
who in one eferit; ilsl * ONR does in li ab methods!l: raires & fpeculatiues,
as Vbalde Guide; or Li embroüil!ees, CME Daniel Barbaro, that he c!the:
tres-dif!icile dclesreduce in praetics, fans other cognoilfancc. The yen has

PREFACE.

there is still some evidence of this diuersinll effect:rumens, which oblige
in order to make them perfect:
all mechanically, & does not give more than satisfactory: ion NY of cognoif.fance by flogging these regular bodies, qudi faifoit of irregular & at
phancaifie. '

Céfi pourquoy me voul: it fatisfairc moy mcfmeencecy, & dè,
manufacture of other products
geometric shapes and patterns of your bodies,
vrays, Principes De La Perfpeél: iue, & me fuisrefolu delesmcttre Au jour, adioull: antatn
propofitions perfonne as a corollary, the faults which I ' ay re;.
marked in a few times by these hunters: what happendedby océafion
of propofer in a few difcourses, & explain in this first Liure, which
deals with these bodies, principles, & general vnemethode dela Perfpeél: I..
!the common, as a fan of those who would like to exercise it fur these bodies, &
they shall not have any cell:cfcicnce;so that they may learn at once•
cir & mcmecnPerfpec1: strong plans,
bodies & crazy figures, fans in Go get the alloying precepts, that they
icy trouuerom reduced in abregJ. In addition to this, fila method that I propofe
the Common Agricultural Policy, such as the
will it, as iecrois, be more clearly explained, even more
briefuement, what will not VN petitfoulagcment to practitioners, who
will still wax this convenience & vti!Ty, only through the application of re -.
general rules of which we are responsible for these bodies; they will be able to put
in Perlpeél: iuetour which will be more difficult, with the failures of the
Tori, Lill:es, Feüillets,Tigettes, Scrolls, & other ornemens d' Has rchiteél:ee,
poumeu that they cognoifséc their natural& geometric mcfures.'

For the Doel: es, if there are some vns that take the trouble to read this
ouragc; i them pray that in a few places, r

_

to make me more 111cellig1ble, 1C dedmfc & repeats some principles
queiduppoferois was!in'auois to make up to them;..aislebutdc mon deffeü1
2 Geolnetric Pre-ludes.

Parallel lines make those, which elhnt produced at the infinite do not compete
or do not meet IAM but, as in the fourth figure
linese F, G H. the non-parallel, on the contrary, the HNR products meet
at some point, where they fonnentvna11gle plan, which dl: said by
lahuiéhelineddininon of the first of the Elems of Euclid, hnclination
of two lines, which is a single line,

_

he will say, " as in the fifth!"INE figure, the linessi K, L K, quilfc meet at point K, form the plane angle I .((L: La ddinitionlajou (the, & ne Fr meet direel: emenc; as you can see
en !I m, L K, fe meet direel:einét

..up.oillt M, only formenrpoint of angle"; also do only vne mefine line
right.

•

- Anglefolide dl: the meeting of,, 4 or plufiers plane angles, &
because we can't repref the paper, thread•we don't put it in
perfpeél: iue, you will have the example of the body that we will write below.

Perpendicular line Eyelash: the one, which falls to lead fur vne other,
as when we laiffons hang VN lead fur some plan put of
niueau, or parallel to the horiphon, it expresses vne perpendicular line:
yourecognoio: ground when vne line dl: perpendicularly barking
furvneaucre, if she makes both sides&sides equal angles, & by
confequent both right,, as it appears by the dixiefmedefinition
of the first of Euclid's Elemes, the whole will be better understood by the fixiefin
Wire, where the AB League falling to lead fur the EC line, makes the angle
ABC, & the angle ABE equals & rightst?usdeux: that fi of point D
fur the mefme Line E C, we do obliquely, or bias fall the line
It is possible that it does not read:
makes the angles on both sides unequal, the obrus vn, the acute aucre, lef


* what do ddinis in c..C strong; the ang1eobrus dl: celuy, which ell: larger
that VN droir, such as dl in the angle figure D B C, which dl greater than
the sharp angle, ell:.ckfiny, celuy qui eft
smaller than * VN right, as in Liguria the angle DB E, which dl: more
small that right A BE, of the amount of DBA efpa.
The Triangle Eyelash: the most fimple, ink the fupeditics comprifes delignes
right: the dl: di!l: ingested by a large number of workers. ,js,

* * Premic; rementàraifon defes paste the ELT diuifê in equilateral triangle,
jfofcele & fcalene: the equilateraf CIL cduy triangle, which A) es three coll: czlc9aux, such as ell: the triangle marked 7. trianglelifofcde ell celuy, quil
.

na that two Roo: ez equals, & troifie!ine d1fleren t in size of
two Nm, commclafigure8*, 9Ù AB,AC strike ' equals, & the
I know better than any of them. The fcalcne cO:
three coll: ez unequal, as the triangle marked 9.

Second sorting..ngle ell diuifcf, iiraifôn des angles, qui compo
..in ..ro; except for efpcs, F..auo1ren orcho..onc, amblygo•

· •

•

do,&:


Geometric Preludes:

ne, & oxygone;orthogoneou reel: angle e!l: cduye, who has vnanglcdroir,

as the line appears from point A to the point C, the

straight line, the triangle ABC, FERA dic * orthogone. Amblygon or

obcusan < > le e!l: the one that has the VN of obrus fesangles, or larger than vn

right, what feroic in the mefmefigucele triangle d BC, end of the point

D on men oit VN straight line at Point C: 0 xygonc or acutangle e!the:

cduy •which * to necks Fes three acute angles or ..rights, such as
that feroic in the mdinc figure the triangle d BE, fi of the point D, on me.noitvne line droiceifques en e.

Circle dl vne figure plare comprifc d'vne feule curved line, that
we call ·circumfecence, which e!L: Crice by the vne of both
iambes of the common Compass, the other remaining fixed & arrdlec in vn
poinc, which we call the center of the circle, such as e!l: in the tenth figure,
that lc dcfcric, A. Diamecre of the circle ellvneligne,which.pa{!àntpar the center, e!l: end of Part & part iufques at IARC, onference,
like the tray line. Portion or arc of Circle cftvncfigure comprife
part of the circumference of the line, which,
like li..ure F.

The e quarters!L: Ligurian vne with four droid lines, equal
& joined enfemblc at right angles, the vnziefine ligure you the reprefence;
& the line, which Ell led from VN quince to L'aurre oppofé, is called
diagonal or diamecral of the quarter, the one in the mefine figure e!l: to
Line G H. The Quarrelong dl: vne figure as you see it marked
of the number A. which cllcompolec of quarre straight& joined lines
at right angles, it's not even Square,but it's not even square.the:
i.e., that two of the islands are larger than the other two;
neantless, that each line Ell egalc to.the one who luy Ell oppofee &
paralldc: from whence it is called sufficienttothelogram: the line, which
cil menee from the vndefes coinis to the other oppofe, is called diagonal auffi
or diamecrale, as the line I K.

The creizitfine ligure dl: again vne efpcce of parallelogram, appdlé
Rhombe, or more commonly vne lozange, which ell cqmpofee
from quarter glue equal, but from anglesinegals, two ofquds are obtuse,
& lcsdouxaucres acute.

Rhombojde ell vne ligureprefqqfimilar to the precedence, at.Ili
from four angles & quarre paste: to the other difference sewstimes, that
the Rhombe having the unequal angles, has none less the quarre coffez
cgaux, the Rhomboide has ny angles ny glue them equal, like
you can see in the corziefme ligure, it is!l: quarriefme efpece
parallelogram.

Other ligures of quarre paste, which are not comprifes
previous clinicions, i.e. ciui nefonc, nyquarrez, ny
quarrez Longes, ny Rhombes, ny Rl;iombo1de.s, fonc appdlees ccapezes,
thefquelles for irregular cflre are of forcese plufieurs, the Ligurian
marquee 15, you represent vne, ie must put vfage to the

A Ü


4 Geometric Preludes:

quarriefme & last liure de maperfpcél:Eui , aulii although the.Pentagon
irregular marked 17: Il dl: called irregular penngone, pource
that he has ny angles, ny co!l: ez equals, what the Pentagon has
regulier, as seen in the example in number 16.

Au re!l: number of figuretplates regularto co!l:ez pro


..the number of their angles
C > U deleurs co!l: ez, as it is said in Hexagon that has fix angles & fo:
pans, as Figure 18, for what,.. in Greek fignifie fix,& ,,.,,,._
lignify VN angle or VN corner. For the mefme horseradish the figure fe says
hepcagonequienafepr,..mmela figure19; OEL: ogone who enahulh,
Enneagonequienaneuf: Decagon which has ten, endccagonc, which l1
at vnze: dodecagon, who has twelve, & C. cecy fuflira for delini..
we must now give the Prael: ique of a few
P R O B L E M E S.

In the event of an explosion of the fi gum contained in the faiuans.

U.S.A.
U.S.A.
Ncore.that the problems, Queenie defire propoG: rpour feruir à la
praél: here's what!l:e perfpeél:iue, puilfent,s' expedieren diuerfes ways,
no less like incense don't put icy nothing fuperflu, &;
what else will the most curious fe be able to satisfy in those who deal with
practical geometry exprelfement, i.e. enfogneray, only
the most farnilieres , the most general, & who can fernir eri all meet,
for the convenience of those, who do not yet exercise
* cnla geometry.do

PRE MI ER PRO PO S I TI ON.

To 'IJ1le straight line donnu, memr'IJne other line; right parai/el,

d ' * 1; ne dijlance donnu.

~

S
S
Qir cnla ..guremarquee 4, auhour why!l: eplanche,lalignedonnee
G H, alaqudle it is necessary to conduct vne parallel of the D1FTANCC HF.
E compass!L: antouuert dela clill: ance donnee, point G as center
liver defcritvn arc marked e, & dupointH as cen..
be, vne other portion of Circle marquee F, * after liver tiree B Line.
EF, rouchanrelcs two arcs of circle at points E, F, fanslescut, &
die will make the parallelerequife, by the thirty-fifth1st definition of the first
des Elem. from Eucl. What a problem!l: Big vfage, & we must
feruir in touteslesoperaqons·beyond perfpeél:iuecommune, donrnous
will deal in this first liur
ue, the horizontal line cil: touli_ours fuppofee parallel, to the line..
terrç.


Geometric Preludes:

PROPOSAL II.

On vne line droi8e donnu, @ vnpoint given in icelle, ejleuer-rjm lignt
• * * * * * * * * * *

•

point given out of icelle, a6baijfar vne line

droi8e perpendicular.

•

P
P
Or ' the first part of this P..opofitionr, foit en la vingtief.:
I see the right Line: E given A B, where from point C,
must elleuer vneperpendicular: having taken from point C vn equal efpacc
on the other hand, fur this mefme line, as feroit C A, C B. d11
point B as centre, intcrual to division; because it was more
great, that BC, was of the written arc of loss of, & of point A, as
centre, melineinccrual that deuant liver defctic vn other arc femblablc
F G, & from Point C liver elleueevneligncdroice, iufquesat point H where
they intersect it necks two, & elleferala perpendicular requested,
by the vnziefine propolition of the first of the elemens d: Euclid.
For the fecondc part of this propoficon, liver the Melin straight line
donnee A B, & the point given outside icelle H, from which faucabbailfer vne
for mediculairc fur ladiceline: from the H-point to the centre; liver of the arc
from circle cutting line AB to P?ints I K, which includes
IK foie diuif.! in two at Point C, & the abbailfee line from point H
fur point C, will requife by the twelfth propofition of the first.
0 r as it arrives * poke that one would like elleuer vnc line
perpendicular fur someone else's extremity, the preceding method
dbnt vfage in this case;..n will be able to feruir this-cy.
In the twenty-vnielinefigure liver the line propofee AB, at the head of the:
what A, must elleuer vne perpendicu1aire: the vne of the legs of the Compass
dcmrnrit motionless at Point A, of whatever ouuercure this liver, fopp,.,
fez of AC, is the other leg in C, which remains immo
* the other two arcs of the circle of, and from the point where the two arcs of the circle of, and from the point where the two arcs of,
which will cut the arc D, & from the pointdcfon interfeebon liver abbailfeevnelignedroiel: efur A, which will make the perpendicular rcqu..e. It is necessary to mark for the Prael: ique of these perpendicular lines , that enropcranc especially as the. * Compasses will make large,
all the more so!l:ementreüllirnntlcs opcrations.r

Proposal Ill...

Donner lem'?Yende cognoiflre, jivneligne ejl perpendicic11 / aire Il'vneautre;

* to use the right line: e e!l: perpendicular to vne other; r

as I read in the example propof.: delafigure 1.1.DA c!l: pcrpendii-

A iij

•



'6 Geometric Preludes:

. a B, of the ccncreC middle of the line, of the imerual CD, or
(1or CE,liver defcritlaportiodecercleD AE, which palfantparlepoint

A,the angle must eftre .cenfe right; if he palfe by de!if it must be done, it must be done.

obtuse, if it cuts the lines AD or A. B, it must be sharp edge, by the

thirty-vniefme propofoion du troificfme.

Otherwise it can happen in this way that fume phu

.

general who ell:,that putting fur the line AD five diuifioni efgales ·
at difcretion, fur la11gne AB tr01s fcmblables, the Compass ell: ant ouert
the grandeurdecescinqpremieresdiuifions prifes enfemblc, & the vnc
de fes iambcscfl: ant mife.au point l fur the line AB, The Other must fall
iull: ement fur point 4, cn !aligne AD, fi !Angle ell: straight, otherwise
if it efl: ohms, it will approach towards J, or if it Ell: acute it will recede
around 5. This preuuedl: fondeefurh ma: < trigonomecry Island,
quidit, Qu * é triangles reél: angles the quarree root of the fomme des
quarrez of the " two side, which make the angle dtoit, dl: I hypothenufe

PROPOSAL IIII.

Diuiftr vne line jroiele donnee as parts eg4fts '1"! we want4.

S
S
ILO in the twenty-second row is the line: e AB propofee
to diuifer in ftx equal parts: Li must at the ends of this line
draw two parallels to the vnedthe other as you see from the
the prefcnt example lines A F, BD, which * fe will do by forming
centers A & B, arcs of circles E F, CD, subtracting as much
from vn like other: what ell: ant ainfi prepared foiem prifes fur clucunc
parallels, as many parts as one will want, & from which ouuercurc
we will want : in· strong allesometimes there are cougurs vne
less * than the number of parts per lcdwho want to diui(E. R La ligria
propofee; as in 1 ' example, voulan.t diuifcr the line AB in fix
equal parts, just take five for the parallels as
they are marked, & conioin these diuifions by straight lines 1,5:
2, 4: 3, r-4," .,,1: who will leave !aligne AB enfo: partiesefgalescom..
me the ell: den...ndé.

Those who (stink the vfage of the measure of proportion, will drink
many this o peracion, comine auffi other plufiers; for by carrying
the line AB at the ouerture of the number uo, fur the line of the parts
efgales, f ouuemire of the number 20, their enr * will give the focieline part;
20 eftcomcnu fix times in 120, ain / i in all
Les diui!right line ions: es, where you have to carry the line to diuifer
furia line of the efgalesparticipation of any number, which fe
puilfe conveniently diuifer in as many equal parts as you want
diuiler voftro line, then take auec the compass as the ouucrturc
of the quotiem fur the m<: frnclignc: & we will have the required, as in

•



Preludes Geometri
SIU;

q


the example propofe W dl: the quotient _of uo diuifeparfix ,& par con..
icquent costs the line dl: Ant porcee to the ouuercure of 12.0, that of 2.0

in must give the fo: iline part. · i,

P R O P O S I T I O N V.

Diuiflr VN circle in 4·

, 8, 16, (!the e. equal parts.

Silk in the twenty-troi!iefme figure K circle at diuifer AC BD, lc: se

two diamctrcs intersect in the Centre at right angles to each other.[
cntlacirconference in four equal parts points AC BD, & para.
this means drawing straight lines from A to C, from C to B, from B to D,
deD * in A, we can infwrite said Circle VN perfect square: if we
wants to en4a mefine manicre infrire en OEL: ogone, oufigureàhuiel:;?IIS,
one diuiferachafque quarter of a circle into two equal parts, as pat
example the quarter of a Circle C B, defcruant of C & B as centers,
the interualto difcretion because it was bigger, than half of the
quarter cut, the arcs F & G to cut in & out circumference,
& the mcnee line by the points of their interface: ions will cut
this portion ae circumference in two egalemcnt, & will give the
I,.uiel: iefmc part of the whole circle , & by confccent the co!l: OEL: ogone
infringe the circle mefme; which huiell: icline part of circumference
in other equal parts by Iamefmemetho


from, Will Give B feizieline part of the entire circumference, & by coll.:
foquentle cofl:éd'vnefigureàfeize pans equilaterale & equiangle, &c.

COROLLARY.

It cfl: to notice that by cerce propoficon one can diuifer everything
arcde circumference whatever it liver in z, 4, s., 16 equal parts, & c.

-

still that the Liver Center ignored.

PROPOSAL VI.

On vne straight line & avn point given in icelle do; n angle reelilignf

efj,al. VN angle relliligne donni.

•U.S.A.

S
S
Goose in the twenty-fifth line appears the line right: e E F, fur la.: equdle to the pom r e must fa1revn angle reehline, efgal to the angle re


..

line B of figure •..: from pomt A as interual centre to
difcretion was to write the..RC Circle D C cutting dcnx lines AB
AC, "' Jjointts of. & , c, & from m, e

eline o..uermrc of compas fur la li..egne or fe must be false, because it is not true, because it is false.:
the arc of Circle G H, thenin subtracting vne portion equal to that

.

qu1e!l: compnfe between pomrsD C, which you will mark GH, foit
mcnee vne lignedroitedu tip palfant by H, & she formeia
year•
gle H E G equal to the..ngle c AB, what it neilloic to do. -·---


I


Preludes c..ometric.

PRO POSITION VII.

Dansv.fcercle given infrire VN Pentagon 011 VN Decagon regulitr.

The
The
A method of conlhuire vntriangle equilarer: tl fur vne line
donneefe pouuant draw from the Ligurian foptidine of this board, ren laqudle of the Centers a & b extmnitez of the straight line donnce,
del'inrerual AB, The Arcs of Circle AC, b c ell: ant form & s " intersperses
in point C, the straight lines led from the point of. their in
..erfcél: ion C, in A & B, will form the equilareral triangle requested,
Having more and more the fourth propo / irion of these preludes, by the
fiugure * J, adorns the way to'infrite in VN given circle: vn
quarré, vne ligure à huiél: & _feize pans, & c. The Hexagon CF elsewhere
this is a very faci1e to defcrirc, as can be recognized in the dixhuiél: iefine
ligure, in which the half diameter of the pig punctuated a B, or the mefme or compass war, auec which said Circle
a efie defcrit efi the glued of the Hexagon, which must be there!l: re infcrit, as
the tefmoign the lines AB, B C, C D, &c. which all make equal :
it fakes that what re!l: E more necdtary, F liver..auoir infcrire vn
Pentagon or VN Decagon regulier had VN circle given, 1 * vn & the other
we deuant feruir to form the geometric PBN of liciofedre >
corn which we put in perfpeel: i u f the vh of FES angles folides:·
Ccfi why i ' en ayvoulu propofcr vnemethodc the most expeditious
* & the best he has me ellepo!hble: because even this problem fe
pui!faith strong well execute p..r to vnzielme propofitionrdu q..atriefmcr

_

of Euclid, in fa1fant VN tnangle which att the angles QM make to the bafe,
doubles from each other, & even more easily this fc: mble by merhode,
let Alber d bring some..RER au ,.liu, practical faGeometric; no less
why Euclid's cell is too fpeculatme & d1/Jicilepour
those who engage in practice ,to whom the pretends principled feruir

the ouerture of two points, also di!hns of the center, will give
the amount del ' angle requife, as in the example propofe in the
twenty-fourth Ligurian line,the AC line, bearing 60,
fur FA line of circles the dill: ance CD feraiuilemencl'ouuercurede45,
& par confecentlaquanricde del'anglepropof.f, 45 degrees.

Now it is!l: easy, fur this foundation, to infringe all iortes do


10 Ceomecric Preludes:

polygons in vn given circle, leaving the amount of the angles of their
centers: Gold the corners of the center make those, which were two right dots,
who from the center of the circle, where they make infcrrs, make meneesà.d, ux anglesprochains,
as in the eighteenth figure, the angle of the center
Hexagon, e!l: the angle tray, that.form in center A , the linesba, CA: '.however, the quantity ofcesnanglesfe cognoifira, diuifànq6o, per
the number of coll: ez in the figure., or propofe Polygon: as if
a vn rriangle to be inferred in VN circle, for what the triangle has three paste,
J; mt diuifer 360 per l, & shall come ao, for each coftate of said
rriangle: fivnpentagon, forceq.'ilacinqcofl: ezdiuifant 360 by 5,
come 72 -, which give the quaritity of the angleducenter of said figure:
C'effl: why taking the strength of the efpace of 72, degre,
fivefollowing, onmarkingfive points, then efl:
straight by order, from rvn to the other, we will have VN Pentagon regulîer,
as it dl: reqws.

We peutaullifuiuantccfondementfairelemefmeparlccompasde
of proportion: because bearing fur the line of the circles, to the ouuerture of the number
60, the Demy-diameter of the circle, where one wants I. nfwrite the Polygon,
the ouuerturc of the number of degrcz, which contains the angle of the
Polygon or figureregular, will give the coftedof the mcfine figure, as
for the Pentagon defwritten in the z6'. figure, having led to the egg a number
60, the demy-diameter KC, the egg of 72-will give
B G, for the co!h! from the Pentagon to the mefine Circle: golden angles
interieurk of the main regular figures, for those who will not want
do not bother del es seek by the fufdite rule, Do: du
triangle, no: from the quarter, 90: from the Pentagon or figure five steps,
72 -: del ' exagone, or figure to f, X pans:, 60: of the heptagon or figure to feptpans, jl.: del'oeeogoneou figure in huiél: pans, 45: del'enneagone
or nine-sided figure, 40: of the Decagon, or ten-sided figure, L 6:
&r.

End of g, re / 11der Geomuriqu, s.


THE

PERSPECTIVE •

CVRIEVSE.

Containing 11 ' 4 principles of perjpefliue, EiJ,, me Methode grner..le, po11t

or _science_ mirrors & reflections for what they deal withobjects,

shortening, or putting eQ perjpe {/iuè all strong fgure-plattes
and:, fa / ides ; even if they affect the plan * only ' tn ' 1 /
line, where in 1m point, ' llerijiupareexamples is five
other.
D E F I N I T 1 0 N S.
;
-.
'Generally prifè: dl: vne fciencc, which
nlcgnie to difwner & properly iuger objects of
the wish: _ die includes fouz foy three diifercn..
tes cfpece;; the first, which retains the common name
of optics, deals with objects qu!fevoientfi..
plcment & direel: emcnt, it is called auffi pcr_
fpeél: Eui: feco,nde efpece Fe names catoptric

who fc see by ref!exion .!s body eolis, as when we see
some chofe in vn mirror: the troiiieefmc efpecce is called dioptric
or mdtptic, which treatsofwants to trawlers of two or more
as seen in the trauers of
the air, the water, the water, the water, the air, and all these
three efpcces may be: re, or fpculaties, or poGciues; fpculaties, fi
they concur with the reasons for such appearances,
they pre-write tiles & give _ precepts, for practice,
in order to achieve or achieve the objectives, it means that they appear to the vehicle.
as they can be delusional. And C'c: ll:en èell: edernierc fa..it is felt that
we are..of these focnccs, for horseradish in nofuePre::


12 First Lure

face: have pre..ier & fccond lure we will deal with appearances, which

last, of those that make the mean of the refractive ions:

polygons, or faceted. The first pan:·

Nofire delfein, which

The perfect pofiriuc!l:vnart, quienfeigncàreprefcnterfurqud9ue
plan that this liver, the choves eat they appear to want, Horn
{1en1a rroifiefmefiguredelafecondeplanche, "letnangle ABC e!l: oir
propofee to reprove him for appearing to the eye, e!L: before Point F, per


1 pendicularly efieue, fur the plane mefme where dl: figured said triangle,

of the height HF; this art of perfpeel: iue in it gives the method, cit for

this flat figure, that for all strong other flat & folides, com-

But how has!L: ronomes & geographers rely on some

points & * of lines, to explain the PHA, NV nomenes & the other glo


be, de mefme the inuenteurs de la perfpeél: EU, have efrabl (a few

points & certain lines, for-the conduct of this art, from where comes that

fleeing the diuerfir of their methods, they made feruis of differencntes

lines, so no less tending all to the end, & prodwfent

the end is in the Meadow, who is it!l: to give the appearance of"vn ob


in the Seel: ion: Ord'aurant that the mot.de Seel: iondonquelque

Times of trouble, tothose, who are beginning to learn the principles of

perfpeél: iue, we will say a few to satisfy the AMAs


this art.

What the perfpefüfs commonly call feel: ion, no.us the
we can name, & will name cy-after the tableaw, or champdel ' ouurage, C'onime fi L'onus vne canvas, VN paroy, or
.someone else planr, to y rra / iron or reduce dclfus any object in
perfpeel: IU, this will be called in terms of perfpeel: IU, give the appa0
of the object of interest, in the SEL: ion, & strictly speaking, Secrion
does e!l: other chofe, that vn plan efieué to plomb fur B Line Earth put between ' object
& at the same time, the effect of the objct will be on the eye of the beholder
efl: imaginee, lailfer some brand & some Vd1:Con ige
appearance. Cecy fe will make it more intelligible by 1 ' example; as fi
we'll pick it up at the entrance of quel..EU Chamber vne door of vcq; e tranfparente
, parlaqudle celuyqui lèrit dchors, vis à la chambre, verrpit
all the furniture inside naturally perfected: EU, fur
the diaphanous & rranfparanr plan of said gate; because if it takes, as
enfeigneAlbertDurer at 4. Liu. geometry, VN brush, &
that he marked fur the glass all the places ml palfentlcsdpeces decaquechofe,
..vne rable, vne efcabelle, & C. Ilauroic all that
FEP may be 01R of the inside of the chamber, 1ms exaetemcnt in perfpeccriue,
I wish he'd stop!the{1: Con oeilen VN dererminé point, where it cf!: to be noted,
that ..that's feferoir.natural mountain, because I see us the faifons

artifi



The perfect curious.

arrificidlcment & geometriqt!emenc, by means of inuenced lines
to this fujet, from which comes only a few authors, forimiter plusprecif..lie
the narration, have clbbly in their method vndignedeseel: ion,
wmme feroitoin the propof example.f, vnelignedright to lead prifcau
diaphanous plan of this door, that will make couppee & cut I all
the lines of the efpeces, which would depart from the inside of the chamber, for CF
I will return to the eye of the beholder, who will do thehors; thehemethode; yet
what good, & more approchaqte of nature, than that, that we
want to propofer, me femblc neantless embàra/ fante, & borneeufe,
let's go .continuous transfers that need to be done from line to line,&
for this reason it will say nothing of the sum, & renew on [Eel:eur q11i the
I want you to know!h_eou praél: iqucr chez Salomon de Caus, & chez Vignole
the first part of faperfpeél:iu..:o

,

Cell on the contrary, that name auonsadcfdwre * dl: tres-exaél: E, plus faC1le
& more prompttotbperacion, mefinefelonlefentiment of those, who
they are: iquél'vne & L'autre, comniesebafiien Scrlio, qui au, Jiu. of
fonArchitcél: urela prefereathis other, & the R. P. Egnacio Danci; who
on the other hand, the Commission has made a number of recommendations to the Council.
feconde reg the who dl: cdlc, queno]ls confeillonsde praél:provide,said that
I'mbut Vignolene fc fcruicd'aucre, since I ' ve been inuencee, & * left
the first comeplus h: ingue - & n1i: Jins convenient: C'l: pourquoy
we will discuss briefly what we need to do,
so that after we could smell of
mefine, fuiuanc nolhe ddfein, give vne mechode general to do
the cleaation of the bodies of the plane forces; though they touch them, only in
vncline, or in vn point.

Of the lines (fi) of the points,, which fmt in vfaze, in this

·the , .
methotk of perjfeeriue. · ,

The
The
Main lines fonc,the line-Ground, the horizontal line;

radial lines; diamctralcs or diagonals.

What we called Line-land, & the Italians Linea Piana, or
bien line of the fpaz.z.*, n ' efl: other chofc, than the front side of the bottom
of the plan, or we want to put some object in perfpeel: IU,<: omme
in vn tableau, lahgne-terre, cil: the bottom of the mefme tableau, or the
plan of the feetion, which efi etleui right & lead, fur, said lign..:
this hgne cil: common to the geometric plane, & to the perfpeél: if: US
let's call this a geometric plan, that in no way we figure it out.
delfous of the Earth line, in which the figure efi defrite to the
natural, & fans no racours: such as efi in the first figure of the
the plan G IKH, to which the equilateral triangle
AB C, efl: defcrit enfa natural proportion: we call plan perfpeél: Jf,
this one we appear at delfusdc la ligne-terre & s ' clcend

B


* Prime Lure

1
4

iufques à la lioneohorizo..the figure is described as follows:


g
_
The ' horizontal line dl: properly the term, of the largest
dlenduë deJ:,'11:uë:dle el!: to1jl10urs parallel to the line-ground, & she: EU Water!fos de icelle, delamcfu1ehigh ,del quelle fupofel ' eye
d'guardarit, ell:: e elleuefurleplan, auqudell: L'object; commdi L'onoo

_,

fuppofoit, that 1oe1l of the Looking was elleue cmq feet high fur the
plane to which the object is repofe: it is necessary to make the parallel H'orizontal line.
get on the line..cerre de J'efface & height of five feet, as since
H, iufqueà F.

It is usually put in the horizontal line three points:
pe1Juent reduce to two; VN poinél: principalo, & two other tierso

.

Point: s, otherwise called points of d1!l: ance; what do they do
put on the side & side of the poind: Main, also move away from
Juy; & all three poinel: s fe can be reduced to VN poinel: main
& vn fire! point di!L: ance, why!as we will,
these two feuls can be
poinél: s ...

The poinél: pri.ndpal encettemethode, not ell: not like someyns
believe the poinél:, where dl fuppo!E the eye of the beholder: but well vn
poinfof
in the horizontal line direc.eement opposed to the eye of the beholder
, & which ell: the term of our main radius, such as
in the first figure the point E, which el!: named by Sal0mon De Caus,
poinél: declinator.

The third poinel:s, or poinel:s of dill:ance, make those, like us
auons of--jà said, who are set to hand& other egalemenc dill:years of
point l: main, as in the mefo1e figure point F, which we
auqns misofeul,pourcequenous def,hope,that in this praél:ique onfe
ferue d·vn fire! * poiafrde di!l: ance : & this dot: fedoit put redheads
fur the horizontal line, aufftloing of the poinel: main, as one
fuppofe..uc L * Eye of the beholder dl:_ elloi..table, or feel: ion:
or 11 dl has noticed, that usod1fonsol oildu looking, & not the
eyes, for ccqu'vn table I perfpeél: iue, for efl:re veu well exaél: emenr,
do not e!l: re look at that.

There are still contingens, or accidental points, of which we do not
let's not say anything, why can't we help ourselves, in this method,&
that's what it is.I shall say nothing of the principles of perfection.
common, quece qui ef1: precif6ment nece / do, for the intelligencedece
chalk: 6, lest he bore the lion:eur en Luy prefenta.NT
what he can do is to see my allies.

For radial & diametrical requirements, we
let's talk about it.

AD VIS


Perfpeetiue curieufe.

NECESSARY NOTICE,

For the conjecture of fugitive propoftions.

P
P
Our proceed to better order, & me to hear morefa..rcilement of the least verfez in this art, fans elhe forced to repeat
plumbers sometimes vne mcfme chofc, fay iugéaboutto point out in
C place, in the year of the next egg, that when we write
some Ligurian auphn geomecral, & that to put it in pcrfpell: Eui,
of all fosextremicez or sewsangles, we lead men
perpendicular to the line-cerre, we will call these lines r, erpendi


,

breeches abfolument, & s will hear allfours perpendicula1resala hgneterre,
if it does not dl fpec11ié otherwise, those that do in the first Liguria
the lines AC, B M, & the lines, which will naill: RAR from the extremity of these
perpendicU!areas, which lay your line-Ground, & will make mcnees to the point
main, will be called radial, as in the mdine figure the lines
c E, mE, & the lines, which punches, where will fall_erles arcs of circles
on the line.- Earth, feronr.led to the point of difl: ance, fe will name
diamerrales, as in the Ligurian mefine the lines d f, n F, because
that they nailfenc of the diagonal or diamerraled'vn Square, as we
let's say cy-apres. O!!;!nd we will talk about pulling parallel vne abfolumcnt,
it fe d01t hear parallel to the line-ground, if it does not eft ipecifi.i
otherwise.

li cil: still to note that-when we say that it is necessary to conduct
vne occult line, this means vne line, quined01r pointdemeu..
the operation has been completed, but we can only
some point, which we cherish, as lont in part. es
radiales & Jesdiametrales, & c. where does it come from that when trauaillant, we do not
mark of plain as the paper that auec tip <read comp:is; us,for the difl:inguer of the other ,which doiuenc efl:re veuës the table,the ouurage
efl: ant liny, will do them for the most part only points. For
what EFT of renuoy brands &caraéters, one must take care,
that we have marked the geometric pian of chafque figure of
capital letters A B CD E & c. & The pattern or pattern of these
small Italian.. ab cd e, chafque letter in this plan relating to fa
..emblematic, qm efl: geometric plane; as in the first figure1 appearance of the pomt A, QM efl: geometric pbn, efl: the "hard" point
_

plan perfpeél: if, & ainfi of others, what ell:ant noticed, we can
now put your hand to the egg.

B ij


First lure

16

P RE MIE RE PRO P O SI " T I ON.

Vn point, trusting given to the geometric plane, the height of I ' Eye, F.!J I..
dijlanc, ejlant pAteillement given , hole the appearance

dN mefne point, < u plane perjfeflif, or in

·

letableau.

S
S
ILO in the first figure, geometrically G i k h, lepoinr A;
at the end of the line AB, duquol we want to see the appearance in larfeel: ion, or in the painting, as we will call it ry-after, which we confOit
it's lead fur !aligne-terre G H. For firstedifpofirion,
it is necessary, by the first propofition of our geometric Preludes, to conduct
the lio-nehorizoncale L F, parallel to the line-Ground G H, of the height,
q,; ' E onfuppofe the eye of the beholder efl: re dleuefur the plane (Wethe fuppophones icy of the natural height & more ordinary, heuefive
feet) & furcettelignplace the main point in L, if we want, that
the eye is Wheel opposite The point, whose wave!ireauire the appearance on the board,
or in E, fion wants, when he has little coftte, as of
efpacel..E: we are proud of E. For the point of diftance, we
will put fur the mefme line, as far removed from the main point, as the
looking away from the table; we're going to be away from enuiron.
twelve feet: Inapres ' of point A, of which we want to see the appearance
in the table, liver tireelaperprectular AC, and then putting the vne
from the tips of the compJsfur the extrernity of the perpendicular, which touches
!aligne-terreau point C, of the other tip liver concealment of written the arc of Circle A D, which will make iufterncnt the fourth part of vne circumference
circular, what efl: formerly / idifpofé, it will make it easy to do the required,
in cecre forre, point C, in the line-earth, where Combs the perpendicular
AC, liver conducted cnvs radial to the main point E, 'which will be c, E, & from point, oùfe ends the arcdecerde AD, inthe me/ineligne,foitmeneervne diarnetrale at the point of diflànce F, which will be d, F, & the point was, oùelle is entrecouperont, will be the appearance requife of the point A, which in efl: the
plan Geometral.

C O R O L L A I R E. I.

By this rndine propofition, one can aifernenc trouuer to the table
the appearance of vnc straight line donncer, as for example of the line
A B, in the mefrne figure: because li to the extrerniré B, One operates in the
mefme way, that in A, by means of perpendicular B .M , &
of the arc of Circle B N: of the radial M E, & of the diametrak N F, their
interfcél: ion in b, will give the appearance of said cxm; micé, of that
eltanc menec vne Linea droiél: E in a, we will have the appearance cnriere
from the line AB, to ab, because the right lines do not change

point


From pcrfpe&EU curieufe.

this is not the case,but it is not the case.or vne SE; L: ion..oi7
ét;, (le. staying tou!right lines, when.on a trouu, if R app; it.
çl'l, c,:, to the cab!EA. of..two poi?of their * extremitei, Vnfligne dtoJru

_

he: e nienee de I vn in L other, Ell I appearance requife defdites dro1 lines,
this•;.pounles, co.cities or circulars we patkrons, _ en:dealing with duu

'

RAC.QJIJciifçmelJ, t circles.

.UD

. .-1

C. O roll AI-R..E. * Il.
I can't.., padamefmevoye, give the apparence.de all
strong depolygonçs, - or flat figures comprifes straight lines, hole..
the appearance of all points of their angles,
by lii1 ' 1es, droiél: cs., fel..n their difpofition • ,the plan geometral; may..,
pourn greater e [cla1ralfem<im US ..n doi:uieronsque!quesexe;.
ples, fur the figures p; I. efmes,qui nou.. dç, i11e11t cy-apresferuir de.plan
.for ' regular bodies; after au01r makes q11clq11es remarks; fur Gettc
rule deperfpçél:iue;that we prç,pofons, po4renfacilitcr the imelligencc
& laerall: i Que, àcos, Qu'n'nwantromferuir.

in the first place, it is necessary that this practice be shortened, or
perfpeel: Eui.all strong flat figures, n ' ell: other than the
a way of perfecting quarrels, who have two deleurs
glue the perpendicular * to the Terr line.. , this 4cu ' ell: Ant fuppofô, it takes this,.
nirpour rules only in the EP.rfpeél: iuc, les coll: ezperpendiculai..
the main point, comm.E their diagonals,
I must see to the point of dinance: we shall die in our
Preludes Geometriqnesu, that C dl: that the diagonal d * VN squared: we
let's make cecy more famous by the example of the first two figures.
. . . . • ·

Or in the fecund fiure the quarre p q r s propoGf to mertrt: in

gu


perlpeci: Eui, having two de fes co / 1: ez p q. z__, s R, perpendicular to the
line-land, & the other two co!l:ez P S, QR, para!lcles: L the Melita line-
rtrre: it is!l: certain, that the appearance of the two ctillez perpendicular
P..R, fedoitrertcontrerfur Les radialesp E,, E'., running away from that
maximum, that all the lines, which make to the perpendicular geometric plane•
breeches at the mre-line, two in the perfpeel:"