Tabernaculum octangulare.
_Hoc tabernaculo aliquoties usus fui pro expositione quadraginta horarum.
Si colores scitè inducti fuerint in duos ordines telariorum, resectis
omnibus quæ ad molem ipsam non pertinent, spectatoribus imponet, & solida
videbitur. Oportebit autem exemplar externæ faciei eruere ex parte ~DF~
vestigii & elevationis; exemplar interioris faciei eruere ex parte ~EC~,
servando in omnibus regulas quas hucusque tradidimus._
The SIXTIETH FIGURE.
_An Octangular Tabernacle in Perspective._
I have sometimes made use of this Tabernacle for the Exposition of the
_Forty Hours_. If the Colours are laid by a skilful Hand, on two Ranges
of Cloth, and the Frame cut away according to the Out-line of the Work,
they will wonderfully deceive the Eye, and appear as solid; but then the
outer Range must be drawn after the Plan and Elevation of the Part DF in
the foregoing Figure; and the inner Range after that of EC; in all things
observing the Rules hitherto deliver’d.
[Illustration: FIG. LXI.]
FIGURA Sexagesimaprima.
Modus erigendi machinas, quæ constant pluribus ordinibus telariorum.
_Ex figuræ inspectione addisces modum erigendi machinas quæ constant
pluribus ordinibus telariorum. Tabernaculum hoc nostrum indiget duobus
tantum ordinibus; nam telaria propinquiora oculo exprimunt faciem
externam, remotiora exhibent faciem internam. Ne autem lateant stipites
quibus telaria sustinentur, medietatem telariorum adumbrare omisimus.
Recta ~LS~ est linea plani, recta ~DG~ est linea horizontalis; ac
punctum distantiæ quod cadit extra paginam in recta ~CG~ prolongatâ,
debet esse remotum à puncto ~C~, quantum in superiori parte figuræ
quinquagesimænonæ, punctum distantiæ est remotum à puncto oculi. Eadem
horizontalis ~DG~ secatur normaliter in ~C~ à recta ~EF~, quæ est sectio
externæ faciei tabernaculi, & ex ~C~ incipiunt divisiones in partes
æquales pro reticulatione anterioris faciei telariorum, ut dicemus figurâ
sexagesimasecunda. Recta ~IL~ quæ est sectio internæ faciei tabernaculi,
distat ad libitum à recta ~EF~ cui est parallela. Porrò, per divisiones
rectæ ~EF~ (ut vides in ~M~, ~N~, ~O~) ex puncto distantiæ ducendæ sunt
visuales ad rectam ~IL~ pro reticulatione aliorum telariorum: distantia
enim ~DC~ facit ut augere oporteat ea quæ in telariis pinguntur, alioquin
justo minora viderentur. Atque hinc dignosces, cur arcus qui in telariis
anterioribus pertingeret solum ad ~B~, in posterioribus elevetur usque ad
~H~._
_Figura sequenti proponemus modum delineandi faciem internam telariorum,
adhibita reticulatione externæ faciei: ad intelligentiam verò illius
methodi, fiat in hac figurâ recta ~HP~ parallela ad ~DC~, ac recta ~BC~
dividatur in totidem partes æquales, in quot partes divisa fuerit recta
~PC~._
The Sixty-first FIGURE.
_The Manner of erecting Machines, that consist of several Ranges of
Frames._
By casting your Eye on the Figure, you’ll readily apprehend the Manner
of erecting the several Ranges of Frames. This Tabernacle last describ’d
needs only two of them; the Frame next the Eye represents the outer Face,
and the hinder Frame the inner Face thereof. I have here describ’d but
the Half-Breadth of the said Frames, that you might have a Sight of the
Poles and Braces which support them. The Line LS is the Line of the Plan,
or Ground-line; the Line DG is that of the Horizon; and the Point of
Distance, which falls without the Page CG prolong’d, is as far from the
Point C, as the Point of Distance is from the Point of Sight in the upper
Part of the Fifty-ninth Figure. The Horizontal DG is cut perpendicularly
in C by the Line EF, which is the Section of the outer Face of the
Tabernacle; and from the Point C begin the equal Divisions for the
Net-work of the foremost Frame, as is shewn in the Sixty-second Figure.
The Line IL, which is the Section of the inner Face of the Tabernacle,
may at pleasure be set nearer or farther from the Line EF, to which it is
parallel. By the Divisions of the Line EF (as M, N, O) Lines are drawn
from the Point of Distance to the Perpendicular IL, for the Net-work of
that Frame; for the Distance DC obliges the Parts of D to be painted
larger, otherwise they will appear less than they really ought. And from
hence you may discern, why the Arch, which in the foremost Frame would
reach only to B, does in the hindmost rise up to H.
In the following Figure is shewn the Manner of delineating the inner
Frame, from the Net-work of the outer Face; for the better understanding
of which, make the Line HP in this Figure parallel to DC, and let the
Line BC be divided into as many equal Parts, as the Line PC was.
[Illustration: FIG. LXII.]
FIGURA Sexagesimasecunda.
De reticulandis telariis, quæ repræsentent ædificia solida.
_Duo exemplaria tabernaculi quæ seorsim delineanda sunt, conjunctim
habes in ~A~. Utrisque deservit eadem reticulatio, quam suis numeris
insignivimus. Postquam ergo designaveris amplitudinem totius ædificii,
cum proportione ad ipsam reticulabis pavimentum ~B~ aulæ cujuspiam quod
capiat rem totam, ascriptis eisdem numeris quos habet exemplar: ejusque
retis ope, ducentur in pavimento lineæ terminativæ totidem membrorum,
quot futura sunt telaria exprimentia faciem externam tabernaculi. Ubi
hæc parata fuerint, singula disponentur exactè suis locis in ipsomet
pavimento; ac funiculis colore nigro imbutis, repetetur in telariis eadem
reticulatio, additis ad libitum pluribus visualibus; quarum adjumento
dum seorsim pinguntur telaria, duci queant rectæ tendentes ad punctum
oculi seu perspectivæ. Alia quoque reticulatio super pavimento necessaria
est pro internâ facie tabernaculi: ac duæ reticulationes pavimenti eam
inter se proportionem habebunt, quam habent divisiones rectarum ~IL~,
~EF~, figuræ sexagesimæprimæ. Hujus retis ductu fient lineæ terminativæ
telariorum cum reliquis, ut jam indicavimus._
_Juxta hanc methodum nequeunt duci lineæ terminativæ interioris faciei,
nisi fiat in pavimento aliud rete deleto priori, quod esset valdè
laboriosum. Postquam ergo ex vestigio figuræ quinquagesimænonæ eruta
sint duo exemplaria, in exemplar faciei externæ transferatur recta ~PC~
figuræ sexagesimæprimæ, in exemplar faciei internæ transferatur recta
~BC~. Si autem recta ~PC~ divisa fuerit in quindecim partes æquales,
dividetur ~BC~ in quindecim partes æquales, atque ope harum divisionum
reticulare oportebit utrumque exemplar. Porrò licet quadrata in reti
exemplaris faciei externæ sint majora quadratis exemplaris internæ
faciei, nihilominus idem rete pavimenti deserviet pro ducendis lineis
terminativis utriusque faciei. Quæ dicta sunt de duobus exemplaribus,
valent de aliis quotcunque. Exempli gratiâ; si construere placeat quinque
ordines telariorum, fient quinque exemplaria in papyro. Si in omnibus
exemplaribus usurpetur eadem reticulatio, in pavimento facere oportet
quinque diversas reticulationes. Si autem in exemplaribus fiant
quinque diversæ reticulationes, in pavimento sufficit una reticulatio._
_Curandum est ut singula retis quadrata in telariis sint exacta, omnesque
illorum anguli sint recti. Modus expeditissimus faciendi angulos rectos
est hujusmodi. Posito uno crure circini in puncto ~F~ lineæ rectæ ~EF~,
alioque crure posito ubilibet in ~O~, fiet circulus ~GFI~, & ex puncto
~G~ diameter ~GI~. Si recta ~HF~ transeat per puncta ~I~ & ~F~, est
normalis ad ~EF~._
The Sixty-second FIGURE.
_Of making the Net-work on Frames, for representing the Architecture as
solid._
You have jointly in A, the two Designs of a Tabernacle, which are to
be drawn separately; the same Net-work serving for both, which is also
mark’d with Numbers. When you have therefore resolv’d on the Size of
your Work, on the Pavement of some Room capacious enough make a Net-work
answerable, and affix thereto the Numbers, as in your Copy: By the Help
of which, you may on the Pavement describe the Out-line of all those
Members that are requisite to the outer Frame of the Tabernacle. This
being done, let the Frame be laid exactly in its place on the said
Pavement, and with a black Line strike thereon the same Net-work; adding
as many visual Lines as you please, which will be of Use for drawing
Lines to the Point of Sight, when you come to paint the Frames asunder.
Another Net-work on the Pavement is also necessary for the inner Face
of the Tabernacle, which should bear such Proportion to this, as the
Divisions of the Line IL do to those of EF in the Sixty-first Figure; and
by this means the Out-lines of the inner Frame, _&c._ may be drawn, as
has been shewn already.
Thus the Out-line of the inner Face can’t be describ’d, without rubbing
out the first Net-work, and making a second on the Pavement; which would
be very troublesom. Wherefore, from the Plan of the Fifty-ninth Figure,
take the two Designs, and transfer the Line PC of the Sixty-first Figure
on the outer Face, and the Line BC on the inner Face. Then if PC were
divided into fifteen equal Parts, BC shall be divided in the same manner,
and by these Divisions make the Net-work on each Design. And although
the Squares of the outer Face be larger than those of the inner one, the
same Net-work may nevertheless serve for giving the Out-line of both.
What has been said of these two Designs, may be understood of many. For
Instance; if five Ranges of Frames were requir’d, five Designs must be
made in Paper. If in all the Designs the same Net-work be us’d, then five
several Net-works must be made on the Pavement; but if the Designs have
five different, then one Net-work on the Pavement will suffice.
You must be very careful that all the Squares of the Net-work be exactly
divided, and at right Angles. The ready way of making a right Angle is
thus: Placing one Foot of the Compasses in the Point F of the Line EF,
and the other at pleasure in O, describe the Circle GFI; and from the
Point G draw the Diameter GI. The Line FH drawn by the Points FI, shall
be perpendicular to FE.
[Illustration: FIG. LXIII.]
FIGURA Sexagesimatertia.
Vestigia ædificii quadrati.
_Vestigium geometricum ~A~ hujus ædificii habet in ~B~ suam
deformationem. Discrimen inter pilas ~C~ & ~D~ oritur ex eo, quòd in ~C~
posita sint vestigia stylobatarum, in ~D~ autem posita sint vestigia
coronicum._
The Sixty-third FIGURE.
_The Plan of a square Design._
The Geometrical Plan of this Design A, is brought into Perspective in B.
The Difference between the Parts C and D arises from hence, that the Plan
of the Pedestals is plac’d in C, and that of the Cornice in D.
[Illustration: FIG. LXIV.]
FIGURA Sexagesimaquarta.
Ædificium quadratum.
_Ex deformatione vestigii & elevationis, methodo consuetâ eruitur imago
totius ædificii, quæ potest esse exemplar aræ maximæ alicujus Ecclesiæ.
Hanc machinam, non sine communi approbatione, aliquoties adhibui, in
apparatu quadraginta horarum; locum in medio vacuum occupantibus Angelis
cum nubibus, additâ figurarum aliquot copiâ in parte inferiori. Modus
faciendi in telariis remotioribus ab oculo partem tholi rotundi quam hic
vides, deducitur ex iis quæ tradidimus in projectione circulorum._
The Sixty-fourth FIGURE.
_A square Design in Perspective._
From the Plan and Upright in Perspective, this finish’d Piece of the
whole Work is delineated after the usual Manner, and may serve for
the Design of a great Altar in a Church. I have sometimes, for the
Solemnity of the _Forty Hours_, expos’d this painted on a Machine, with
an universal Satisfaction; Angels with Clouds possessing the higher part
of the Hemisphere within, and Groups of Figures the lower part. The
Manner of designing on the inner Frame, that part of the said _Cupola_
which you here see, is deduc’d from what has been before said of putting
Circles into Perspective.
[Illustration: FIG. LXV.]
FIGURA Sexagesimaquinta.
Vestigium ædificii rotundi opticè imminutum.
_Qui sedulam operam in circulis deformandis non posuerint, eosque minimo
negotio ex usu describere nequiverint, frustra conabuntur projicere
vestigia ædificiorum rotundorum. Ad vitandam confusionem, proderit in
vestigio notare primùm lineas occultas membrorum præcipuorum; iisque
translatis in elevationem, addere sensim reliquas. Hac industriâ ego
ipse in hoc schemate usus sum. Quum autem experimento didicerim summam
arduitatem harum descriptionum, aliam regulam adhibere jamdiu cœpi, quam,
ut suprà diximus, in aliud Opus reservamus._
The Sixty-fifth FIGURE.
_The Plan of a Circular Work in Perspective._
They that have not diligently apply’d themselves to the putting Circles
into Perspective, and, by a constant Practice, render’d the Work familiar
to them, will in vain attempt that of the Plans of round Buildings. To
prevent Confusion, you’ll do well, first to mark the occult Lines of the
principal Members; and after those are transferr’d into the Upright, then
proceed to the rest, as I myself did in this Figure. But having found
by Experience, the great Difficulty of describing these round things, I
have long since made use of another Method, which, as I said before, is
reserv’d for another Volume.
[Illustration: FIG. LXVI.]
FIGURA Sexagesimasexta.
Projectio ædificii rotundi.
_Mirifice oculis imponunt imagines rerum rotundarum, si omnibus resectis
quæ ad eas non pertinent, exactè delineatæ ac depictæ fuerint. Hanc
figuram ex vestigio eruere oportebit methodo consuetâ, eamque in
Templo S. Ignatii Collegii Romani construxi pro feriâ V & VI Hebdomadæ
sanctioris. Intra arcum, super altari, locus erat urnæ sepulcrali, cum
Venerabili Sacramento. Sub altari visebatur simulacrum Christi Domini è
Cruce depositi: in medio columnarum, imago Beatæ Virginis dolentis; super
balaustiis Angeli lugentes, cum instrumentis cruciatuum Salvatoris._
The Sixty-sixth FIGURE.
_A Circular Design in Perspective._
The Appearance of round things, if well design’d, masterly painted, and
the Frame cut away to the Out-line of the Work, do wonderfully deceive
the Eye. This Figure is drawn from the Plan, as usual; and was put in
execution by me, in the Church of S. _Ignatius_ of the _Roman_ College,
for the _Thursday_ and _Friday_ of the Holy Week. Within the Arch, on the
Altar, was plac’d a sepulchral Urn containing the Holy Sacrament. Beneath
the Altar was laid a Figure of our Saviour Christ taken down from the
Cross. In the midst of the Tambour, was a Picture of the Blessed Virgin
in extreme Sorrow; and on the Ballustrade, Angels mourning, bearing the
Instruments of the Passion.
[Illustration: FIG. LXVII.]
FIGURA Sexagesimaseptima.
Vestigium geometricum, ac prima præparatio ad figuram septuagesimamprimam.
_Egregiam adeò speciem præsetulit, atque oculis adeò imposuit machina
quam construxi anno 1685, pro supplicatione quadraginta horarum, in
Templo Urbis Farnesiano, ut decreverim satisfacere Studiosis, publici
juris faciendo non modò imaginem totius ædificii, sed etiam illius
vestigia & elevationes: quæ omnia eâ diligentiâ delineavimus, veluti
Opus ipsum non pennicillo colorandum, sed lapidibus extruendum fuisset.
Spatia nigrantia soliditatem designant parietum & columnarum. Cæteræ
lineæ sunt crepidines stylobatarum & coronicum. Initium delineationis
fiet ab iis membris, ex quibus oriuntur lineæ occultæ positæ in ~A~, (quæ
autem dicuntur de hac medietate, intelligi debent de aliâ) ne multitudo
linearum confusionem pariat. In ~B~ lineæ curvæ occultæ sunt vestigium
tholi qui complet summitatem ædificii. Vestigium ~C~ exhibet ambulacrum
interius. Omisimus autem vestigium theatri, quia paginæ angustia illud
non capit._
The Sixty-seventh FIGURE.
_The Geometrical Plan, and first Preparation to the Seventy-first Figure._
The Machine which I erected in the Year 1685, in the Church _Farneze_,
or _Jesuits_ Church at _Rome_, for the Devotions of the _Forty Hours_;
had so admirable an Effect, and so pleasantly deceiv’d the Eye, that
I resolv’d to gratify the Studious, not only with a general View, but
with the Plan and Elevation thereof; all which was perform’d with such
Exactness, that the Work itself seem’d rather to consist of solid Stones,
than to be wrought by the Painter’s Hand. The hatch’d Part denotes
the Solidity of the Walls and Columns. The other shews the Breaks and
Projectures of the Pedestals and Cornices. Lest many Lines should cause
Confusion, begin with those Members, which produce the occult Lines on
the Side A; understanding the same also of the other half. In B the
occult curv’d Lines are the Plan of the _Cupola_ which crowns this
Structure. The Plan C is that of the inner Vestibule, but that of the
Theater is here omitted, through Want of Room in the Page.
[Illustration: FIG. LXVIII.]
FIGURA Sexagesimaoctava.
Elevatio geometrica vestigii præcedentis, & secunda præparatio ad figuram
septuagesimamprimam.
_In hoc schemate habes elevationem ædificii sectam in longum, quam figurâ
septuagesimâ opticè projiciemus: eisdemque membris constare videbis
elevationem deformatam, quibus constat elevatio geometrica. Hinc disces
ad excogitandas hujusmodi machinas, eandem Architecturæ scientiam in
Pictore necessariam esse, quæ ad construenda solida ædificia exigitur
in Architecto._
The Sixty-eighth FIGURE.
_The Geometrical Elevation of the foregoing Plan, and second Preparation
to the Seventy-first Figure._
In this Figure you have the Elevation of the aforesaid Structure
dissected lengthwise; the Perspective thereof is describ’d in the
Seventieth Figure; and you may observe that both of them consist of the
same Members: whence you may perceive, that for designing things of this
kind, the Painter ought to have no less Skill in Architecture, than is
requir’d for the Execution of solid Works.
[Illustration: FIG. LXIX.]
FIGURA Sexagesimanona.
Deformatio vestigii figuræ sexagesimæseptimæ, & præparatio tertia ad
figuram septuagesimamprimam.
_Artificium projectionis vestigii hujus, explicatum à nobis est figurâ
quadragesimasecundâ. Nimirum, ut parallelæ sint invicem distantiores,
lineam plani deorsum protraximus, ut ex intuitu figuræ statim cognosces._
The Sixty-ninth FIGURE.
_The Plan of the Sixty-seventh Figure in Perspective, and third
Preparation to the Seventy-first Figure._
The Artifice us’d in projecting the Perspective of this Plan, has been
already shewn in the Forty-second Figure; namely, that for giving the
greater Distance between the Parallels, the Ground-line is drawn much
lower than its true Place; as is manifest on Inspection of the Figure.
[Illustration: FIG. LXX.]