RE.SOLUTION 
D E S 

(THE MAIN ATREASES 

PR O-B LEME S 
OF ARCHJTEC TURE... 
:f Il E MI IZ R 'PRO ./J LEME R . SO,LV. ":Describe GŽometriqu_eflient es ptujie#rs m1111iŽres .fl1 tout d "11111rait, k Co11tot1r de t'e-fl4r, -ft di-in#o- du Colo1111es. 
P R E M I E R D I S C O U J l S. 

i the various jobs that I have found for the King's fcrYice in foreign countries and in your prisons in this Kingdom, have given me the advantage of being able to con- JidŽrcr to help the greater part of the Baftimens an- A z. ciens. 

ciens & modernes qui font dans le monde; & fi cette facilitŽ jointe ˆ une inclination particuliere qu'j'ai tožjours ež‘ pour l'ArchiteŽture & qui m'a fuisufemcnt foigneufemcnt rechercher ce qui pouvoit eftre de plus remarquable en chacun d'eux, m'avoir m'acouftumŽ les yeuK ˆ quelque difcement de cc qu'on appelle Grand & Beau dans cet Art : I have some right to say my feelings on the subject and to say that the Architecture needs to be studied in order to achieve perfection. And since I have not once before boasted that I know what it lacks, (this art is too much of a deep knowledge and experience;) I have at least one extraordinary joy, when I see that there are some pros. 
This is what makes me feel that I have been able to express the thought of this one, which was proposed to all the Architeleles for EftrŽnes, at the beginning of the 20th century. 
.. I the year 1.64 ... a Par-x, as he says, i.e., a Pro.wheat to be reshaped touching the refloating perfelion or èvm,ir of the Co-lonnes, affected imperfectly by P-itruve & 110n still reshaped:, settled only imperfectly, as long as Architeelonically it is perfectly possible, which make the terms of which it will be made. 
. . 
And I thought, I said, that a man is doubly loŸable, who, not content to seek what is not yet known in the Sciences, & to confer on the Public the fruit of hard work & of long vigils, still wanted to quote the others to the full, & to awaken their sleeping virtue, by proposing to them to reform that which he could already reconnoiter by study. As much as it is to an all femblablc feeling that we owe.cc that we have made the most beautiful dahs the Mathematics, & that it is a fact that it never makes more notable progress in these f ciences, than when the great Geniuses fe do,. in qivers žŽ.cles, propofez one to the other of the queftions, & that by a species of emulation honncfte their soul s'eft inflamed of this generalcuf.t ambition, which has produced us 9'ivragcs i c:rccllens, that ib. k. 
'1 

OF THE DECREASE IN -coLONNES. s-
They are more likely to start from the intelligence of the Angels, than from the laborious meditation of the human spirit. 
And I have received what is good from my own mind. gnifique que des fciences MathŽmadques, qui par l'indubitable veriM tŽ de leurs dŽmonfirations remplffent -entiment la capacitŽ de noil:re ef prit, & ne l luyfent rien ˆ dŽtir fur le fµjet qu'ellC'S luy ont expliquŽ: Il eft aifŽ de comprendre qu'eft d'elles qu'elles doivent encore attendre cc qui manque ˆ. It was easy to understand that they still have to wait for the missing element. That this reading, by which the difference between being able to make a work, or working blindly, can only come from the liberal hands of Geo.metrics. 
How much, then, will he do to (hopefully, that those who work in the Architeaure will want to apply themselves to Mathematics, or that those who work in this field will give some of their time to the Architeaure? And for this subject one must encourage - & receive pleasantly all the teachers who can contribute to bring men to this study, in the name of the Architeaure. The author has explained this Paraaox a little more clearly than he has done, &: if he had given to hear what eyelash: this way of diminishing the Columns, which he calls Perfumes: because these strong differences of opinion, which are so important for the eye's satisfaction, & which have no certain foundation in nature, depend so much on the taste, & the truthfulness of opinions, that a Column may be too suave for some, as the Italians call it, or too loose, as others will find it too crushed. 
Strongly, that it seems that to work with some fruit in the evolution of Fon Paradoxe, it is right and proper that it has been determined that it has been born, i.e. that it is understood by this word 'Perfectly,' & that it has been put cor-. to take, fi this way of describing that he proposes to rebuild Ar-.thiteŽloniquemmt, and is already in some way, at least mechanically, among the Workers; or fi it is in a completely new way, a new way, a new way, a new way, a new way, a new way, a new way, a new way, a new way, a new way, a new way, a new way, a new way.

-P R E M I E R. P 1t o- B L .E M B 
t.:::: <a form different from all those of which we -a jufqu'icy di. The more these vague & indeterminate Propotions, & in the explanation of which the strong has more part than the raifonnement or the vivacity of the imagination, the more they are defeated, the more the honour which is due to the one who has rightly explained the enigma, depends only on the whim of the one who proposes, who can diffimulate as long as he likes it, 
...and still say we haven't quite got what he wants yet. 
The Ionic and Corinthian women, as Vignole had once remarked in drawing Columns in the manner that Vignole enfeigne for the Ionic and Corinthian women, that the line of their Contour is that of Nicomedes: I tell M. Bofl�, who sent me to see it in January of the same year, I 664. I tell Mr. Bofl�, who took me to see these Ejlenes to all the Archites, that although I do not eulphasize the art of guessing, & that I con.felfaff'e ingcnuously my ignorance on the subject of this Paradox, I wanted nevertheless to propose more clearly a Problem of the Ejlene to all the Archites. 
mef me nature ˆ fon Auteur, que je mis par maniŽrc de jeu fur le dos'de fon Žcrit, en ces termes. Another Problem. The meen of de.sort everything in one go, & fans lembarajfer of many points trot1vez ,!ont on fart on for the Cherches, the most elegant way which makes in ufage parmy the modern ArchiteŽles for ltrT".o-1r & decrease of the Columns? And what is the _figure.? 
.elque jours aprŽs le fieur Bofi� m 'ay:mt priŽ de. I would like to explain my thought, and I made it the subject of the Letter which makes the following diffcourj. 
�} 
SE-

OF THE DlMINATION OF THE COLUMNS. 7 
S E C O N D D I S C O U R S , 
,, ov 
L - E T T R E A M. 


SVR. LE. MESME 
Ji11Jim1tio11 tkJ Colo1111es, . de ta deftriptio11 de Ja line pi fait le C¡". - turn of the lfJ1liqws. Corinthieues, f¤ eot11pofŽe1 . 
M
†NSIEuR, I don't know how to guess for you what the lies of this man you are talking about are, as he says, that he has proposed for EjfrŽ.nes .-1 all the . But I can tell you about the fullness of this story that I wrote half on the back of a printed book, in which I will tell you first of all that I have no part, and then that it is more than two thousand years since it was found, and that I can no longer glorify myself any more, and that I can no longer glorify myself any more. that I can no longer glorify myself any more than I have once seen, by evoking the diminished Columns - the -elegant -mannered -which Vignole says he iny- for the Ionic & Coriathians, that the Seeker COl/.rbe fJUi Ja dŽ.crit, ejl k,, line of Nicomedes, which Fon calls the first Conchoid of the . By means of which ,,:the report of Eutocius, ec Geometry- pr,ect said to have solved this famous Problem of the Du- plicatio11 of the Cube filled by the Ort!cle ,.& which has so much exercised the ef.prits of Plato's fiede in the search for two proportional averages and two given right$. C'eftre celle-la-la m�me que M. Viette a de noftre temps fuppofŽe comme une pŽtition ou demande.de au fupplŽmcnt de GŽomŽtrie pour refoudre tous les ProblŽmes fulidcs, & dont les Equations vont au Cube ou au quarrŽ ;.. ne juge pas q_ue fa defcription_,.par le moyen de l.infti:ument de Ni---

FIRST PROBLEM
8 
Figurel;d, the I. PIAncbe. 
Nicomedes, fuft more me'chanic, or better to say; less geometrical, than that of the Circle by the half of the Compass, whose ufage is nevertheless received by this principle of petition or request in the first of the Elemens of the uclide. And since these mef.mes Equations are more nobly refashioned in the books of M. Defcartes, by the interferential fire of the Circle & of the Parable, which make lines of a more fimple kind & me! 
But to return to our point: Joy, that you are perfectly happy with this elegant invention of Vignole, and that you can see it in Fan.Livre, I would not like you to trace its figure with a deep course, as the translation of the words of Mr. the Mute, so that you can better judge the horsing around than you can judge the meaning of the words of Mr. the Mute. 
I'll make a run for it. 
  The first diray, then, is that, having rebuilt the column's scales, 
that is to say, fa hauteur & groffeur, & la d!minution qu'elle doit avoir au bout d!en haut, ondoitraitu11e ligne ˆ l'injinien commen�ant par.C, qui ell::UI tiers du fufi: de la Colonne, & continuant par D; puis rapporteant la mefure CD au point å, 'o� finit la diminition du haut, juf'ˆ te qu'elle coupe la perpendiculaire au point B, & que . ABjoit continuejust until E. From this point so many lines can be drawn that we will want to start from the perpendicular , & go around the circumference of the Column, and, applying the measure CD, we will find a hole both at the top and at the top of the Column ; & cct1e maniere peut eftre 
applied to rIonic, Corinthian & Compofe. 
Or you see, Monfieur : - that all' those lines that, - leaving 
of the p.int E , are comprifes . between the Perpendicular or Axis of 
the Column &. fa Circumference, are all equal to each other, &. 
ˆ 

ON THE DIMINUTIO. OF THE COLUMNS. 
to the right CD. Of strong that fi we call the point E, the P:it; the Axis of the Column, the Rule or Canon; 8c the 1st line C D, 
.rInterval: I don't see anything any more that prevents me from calling the curved line that palliates from A by all the extremes you're looking for! re Concho•de des An‰cns, since this is the route of theemefmc; -& that you will know even better- by the jriftrumcnte- that NicomŽdes invented to describe it, in the figure efi: the-second of the first Plank; in lacquer 11th, after! s avoir dŽter.minŽ comme deffus la largeur de la Colonne, dont la moitiŽ _e'fte-CD, 8c trouvŽ la longueur de la ligne CE, il faut prendre trc,i. eTŽglcs de bois ou de mŽtai1 G F, l D, HA, dont les deux 'G F,e& ID , font attachŽes enfemble ˆ l'Žquerre ou ˆ angles droitsecomme en D; & par le milieu de la rŽgie G F il faut paster une petite petite canal ˆ taeu d'arond‘ve qui .Žtend en toute la longueur de la rŽgte. 11 s'en fait une autre de mefme dans le milieu de la. re.gle HA, qui s'Žtendc indefinitc vers le bout H , mais quie vers l'autre bout fe termine en K , en forte nŽanmoins que lae‰i ft:mce A K, ne foit pas plus grande que la di ll:ance CE. Run away from the end of the HA ruler to point A, where the AAB line is equal to the CD line, and attach a wooden or metal knob to point B, which can run through the channel of the G F control unit. Another female must be attached to point E, in the middle of the control panel ID, which can flow into the control panel channel AH, so that rule G F can be applied to the column, with point D responding to the bulge, & the control panel AH moving by moving forward or backward on button E, as if for a pivot or pole, while the other &outo. B moves along the said axis, that is, along the two channels of the control unit G F; point A describes by these two movements the curved line A a aC a , for the contour of the decrease of the Column which is called t,-rru-,� . ar Vitruvius, .e-in which line .out of the straight lines:, as b a, drawn .d� Po-ek, & comprifcs between the Channel of the control room' G F, that is to say, en-eB ttc. 
Fig. II. of the/. Plancfo 
ro P Il E M I E R-P R O 8 L E M E


The column and the circumference are all equal to each other, and to the interval A to B, or CD. En quo y il y a paroi {l: ttue.la ligne courbe que ctt inilrument a dŽcrite, eO: la mcf me que.celle que Vignole a prŽtendu dŽcrire. And fi y your rules eO:anr of an.indefinite.size, you do in strong q. the buttons B & E can move so far forward or backward along the rules AH & DI, that the intervals, like AB & CE, can be so strong that the intervals, like AB & CE, can be so weak. It is obvious that this instrument can be used to describe the Column Curves, no matter how high or wide they may be, because all their difference is confined to the intervals. The other side of the Column will be described in the same way by changing the instrument's place. The other column column will be described in the same way by changing the space of the instrument, bringing it to the other side. The other Column cofl:e will be described in the same way by changing the inftrument in place, bringing it in from the other side. In short, Monfieur, it seems to me that my Problem has been well solved by means of an inftrument; and that fans-embarquˆchercher.ccs infinite points, as Vignole wants, by which this search can be gently brought to fruition, which, in the rigour of this always imperfect rigour, can now be drawn out in one stroke, uniformly and in perfection. It is a challenge: I wanted to tell you about it, while waiting for the Author of the Paradox to give us some shocking confidential information on this matter, so that there is reason for the Ejfrlnes to make an effort. You are afraid that although there is a reason to be furprised,. that for so many feccles which have produced great men,. that for so many feccles which have produced great men,. that for so many feccles which have produced great men,. that for so many feccles which have produced great men,. 
For the Architecture, those who have well traced the diminutions and the swelling of the Colonnnes, perfoone, at least as far as I'm concerned, has not given any thought to this way of describing that the late Vign.e, . that since then so many brave Archite.es have believed fortunately ... mentally fervent in their invention, ... fans have said nothing of the nature of.
the Curve it produces, by means of the challenge of eigning it all from a- 
this-

OF THE DECREASE IN COLUMNS. 11 
. 

...this thought has come to me, from which I glory less than the honour you do me to love me. I flee. &c. 
Ce z. 4. 1a1wier l cS 6 4- 

THIRD SPEECH 
$'VR LA NAT'VRE AND 'DESCRIPTION
. 
. 

I 111 lieg11e qt1i f11it le Contour des Coton.nes 'DoriqMes . T()ftllnu. 
A
YOU HAVE been to the owners of the Curved Line, - which is the outline of the Ionic, Corinthian Columns. CompofŽcs, I have wanted to confide in the other way that Vigno- describes it, & of which it fc fcrt po.ur the decrease of the To.fcanes & Doric Columns. And after having meditated deeply on the nature of the Line which it produces, I have recognized that it is a Line of the same nature as that described by a Reche, or any other chof c drawn and thrown horizontally, in the opinion of those who believe that a weight falling from the surface of the earth {will be found only after about 20 hours in the Centre (when the earth is moving daily,) & pi1. ffant outre par la force qu'il auroit aquife en fa chete, il arrivroit au bout n'autrcs fur hours ˆ la furface des Antipodes, fi le chemin luy eftoit ouvert : - Hence, during the course of one to three times by the Centre, it will reach the same place from where it was first started, through the air, where the other obstacles from the outside will not stop it. - I say, therefore, that a puffed line v:igour.fement, &. parallels the horizon dec'riroi.t e il fonffage une Ligne de la mme natureeBe2. de
Fi1,. /. iela II. Plan.che. 
de eellŽ dont on fc {ert pour la diminution des-Colonnes-Tofcanef & Doriques , fi_ ct;ttc -opinion eftoit veritablc: parce qu'efiant' portŽ d'un mouvement de Lation Žgale & uniforme, qui luy cft. The first is a movement of equal & uniformtion, which is printed by the impulse, & which makes that the diftanccs that it par-.court make between them in the same proportion as the times that it: employs to go through them, (i.e., like the Arcs of the Equa. tur qui paffent cependant fous le Meridien,) &. d'un autre-mou-.vement inŽgal,_ & qui s'accro”t continuelment, que fon pro-.pre poids luy infpirc > & qui dans l'opinion fufdite_ fe fait fur la proportion des Sinus! The first is the one of the two, and the second is the one of the three, and the third is the one of the three, and the fourth is the one of the two, and the fourth is the one of the two, and the fifth is the one of the two, and the fifth is the one of the two, and the fifth is the one of the two, and the fifth is the one of the two. The other is uneven, continual-.lement precipitated, & responding to the sine vcrfes of the mcfm-c. 
Bows ... But the Tofcan & Doric Column Contour Line. (e fled by the. corpofitio_n 4th two similar movements,. so that- ie would demonstrate it cy-deffous_;. & partant lˆ Ligne que dŽcriventent- les corps jettez. hori:tontalement,. comme un trait ou une arche- dans l'opinion fufdite, eft ˆ peu peu-la mcfme que celle dont-on- fe fert pour la diminution-des Colonnes Tofcancs & Doriques . For the demonstration of what I have just said,. it is only necessary... . ...to have the usual practice of the Workers for that purpose, as described in this Line, which is done in this way. The AC Line, forms the Axis of a Column to be reduced, & two-thirds of the tone.
. yell ,_ fi one wants the reduction to begin- at the third; or half, fi on: defirc that it begins- in the middle of the. Column. Line AB, forms the module or half of the - f groove, in which case as a radius the circle B ST V 7 is formed; Then the part AG, for the half diameter of the column, should be taken from above, so that B G forms the greater reduction,. ti.r4:r Line G E parallel to AC, which cuts the circle at F, _the por- . 
_ntion 

OF THE DECREASE IN COLUMNS. 1.31 
The amount of money that B F ... must be shared in as many equal parts as one, 
will want, as in points S, T, V, as well as the A C axis, in points 
H, K, M, provided that line A C contains .tnnt of parts Ž-. 
The arc BF is the same as the arc BF. Finally points of the d.vižons of the Axis are necessary. 
To elevate Perpendiculars,. like HI, KL, MN, which fail. 
...met at the points 0, X & Y, by other parallel lines -... 
to.the Axis, & drawn from the points of the Arc B.F, in such a way that the fe reciprocally respond to each other, that is to say, that the one which starts from the first point of the Axis H, like HO I, is met in O,. by the one which comes from the first point of the Arc S, like P S O, & the one which starts from the second point of the Arc T,. like QT X, fe ends in Xs.., ...then the one from the second point of the K-axis, like KXL, and then the others. And paf-. fant by all the points BO X Y E a softened line, it will do. the one that ron is looking for in the decrease of the Tofcanic Columns: & Doric ... And fi we call point B, the top of this line curves over- 
-A line AB, r.Axis or.I Diameter, the lines PO, QX... -A line AB, r.Axis or.I Diameter, the lines PO, QX.., RY ,GE,.s&c. the ordinates;. we will see that. the ordinate QX,. containing _au..so many parts of the line AC, . or -from fon-eg.tle G-Es,. . that the arc.sBT contains some of the cells of the arc BF, the ordinate QX, eft to,sl'ordinate GE, like the Arc B. T, efl to r Arc B F;. The mef meschofe fe can say. of all the others ,.it will mean that the ordinates between them will be like the arcs between the vertex and the said ordinates: & so that this lig_ne Cour--sbe cft uno cf-spiral, or-bflJale species.... -sIn addition,. fi.we take the radius AB. for Total Sine, lCllsportions of the -Axis B P ,BQ,- BR,.B G, (I. will make the Sinusverfessdes Arcs, B S, B T, B V, B F, &c. & by confeccnt us
.ourrons ourrons appellcr cette Courbe 11111 lignt Spiral or -Eliptif11e, da111slalJuelle les portions de l' å:te fo111 les Si11us verfes des ,dr�s, fUì fonts11J1r1.t11Jt ,o,,,,,,,, les ,rdom1Žes -. 

Now fi we make another hypothesis, & {if we take point A , for the center of the earth, line B A , for 
k demidiameter, & the BV F bow, for a portion of the Equator. It dl: confta.nt that in the thought of those, who, as we have said cy-ddf'us, believe that a weight falling freely from the furface of the earth runs through the efp:1ces of deep Diameter, in the same way that the Sinm verfes of the Bows of Ecuador do, who are however crazy. This mefine weight ( fup.pofŽ que la terre fe meut du mouvement journ:ilier) arrives necefliently in the centre, when a quarter of the Equator is flattened from the moment of the crest, I mean, after i•x hours. That is to say, that the weight falling from point B, ar.rivcroit to point P, when the first arc of the E1uator B S, at the sunken strait, crosses the line BQ... The line B G in as much time as it takes for the Arc B F; & finally the line BA, that is to say, the whole half of the morning, in as much time as the Arc B Z, that is to say, the quarter circle of the Equator. And as the quarter of the Equatorial Circle is preferably in fixed hours, it seems that in this opinion the weight is lower. The same weight (fuppofed the daily movement of the earth) will arrive at the end of the fixed hours in the center: and then it will go up in propor-: -The first is the one which is the most important of all, and the second is the one which is the most important of all, and the third is the one which is the most important of all, and the fourth is the one which is the most important of all, and the fifth is the one which is the most important of all, and the fifth is the one which is the most important of all, and the fifth is the one which is the most important of all, and the fifth is the one which is the most important of all.
miŽremont parti.o
It is therefore assumed that this is the genius and the nature -of the dead men's chofes-. 
f.1..u-

D-E THE DIMINUTION OF THE COLUMNS. -If 
t:,ntcs; fi nou. let us take the comic line for the cf pace, that an arrow drawn horizontally from the point:Must travel in the time that -the Arc B F of the Equator or Parallel fon will have passed the Meri-e< link, it is contfant that the arrow will however be defended by its own weight of the whole length of the line B-G, which is: the.Sinus verfe- of the mcfme Arc BF. Et ž. nous divifons le fufdit Arce:B F en parts Žgales comme aux points S, T, V, & la ligne BDeou fonŽgalc AC,en autant d'autres, aux points I,L,N ou H,K, M.., .e,. as long as it is said; he will see that the movement of Lation,andJUNE a. eHŽ communicated to the arrow by the impulse, !don the.B D line, being uniform, the arrow will have run l7ef pace B I in the. mcf me temps que !'Arc B S aura patfŽ: & co.mme cependant elle-efera dcfcendu‘ par fon poids de la longueur de la ligne B P otre10, la fleche fe trouvera alors au point O, o� les deux lignese
... of the Uniform B I, or P Oe,. & de-cook B P or I O, fe.meet. Everything of mcf me-it will make e-n X when the Arc B T at the-:.raffŽ, because it cft cri cc point where fe find the line of La.etion equals BL or- QXe,. & that of the BQ or LX crust,.equi fe do both in the same time of ..erArc BT piling. And the same chofefe can say of all the points of the BOXYE curve; it is obvious that it is the one described by an arrow in the fufdite hypotefe; & that, by conferring dimension. line eft the mcfmc than the one cft described for the decrease of the Tofcan & Doric Columns: that-that it is necessary to dementr. lnfl, ...eQ!ie fi l,.on deftre en dŽcrire la fiere tout d'un trait, & fans ment pottr-e
gu describe Ir-
A.

cu.-e obligc, .de 1er. fcervir de p1ufi1eurs 
points find , we can 
dimi11111i.

&ire un inftmment afi�z convenient pour cet eff�t, qui doit dl-re 
ecompofŽ d'un SeŽteur de Cercle, d'une rož‘ avec fon pignon, j;
... "re "one toothed control room... of another control room, (as in the fecon-Toftanue...
the A B-F cft the 
Co-e

of Figure of- the- the- son.ie Board) where 
& Dori.

mefme que celuy de la premiere Figure de la feconde Planche j;rs. 
JI...eque nous avons c:xplanŽei c:�ft ˆ- dire, que les lignes AB & 
d:.. ...L... 

.A.F de . fecondc Figure are ig.alca au; modulo-,. &; the.Arc B. Plamhe -.e
FIRST ISSUE

8 

Figurel;
d, the I. 
PIAncbe. 

Nicomedes, fuft plus mŽ'chanique, or to put it better; minus 
Geometrical, that that of the Circle by the Compass self, whose 
l'ufage eft nŽanmoins recept par ce principe de pŽtition ou demande 
in the first of the Uclide Elemens. And since these women 
Equations fe refold more nobly in M's books. 
Defcartes , by the interferential fire of the Circle & the Parable, 
that make the lines more fimple & me! compof that the 
Conchoid; it does not need to be used for the solutions. 
higher equations; higher equations; & the fuppofiations of 1\1- Viette 
are very fast & very real. 

But to get back to our point, Joy, that you're doing this 
perfectly this elegant invention of Vignole, & that you will have it 
You can see in fan.Livre, I wouldn't worry about it. 
icy the figure with fon difcours, felon the translation of the illuftre M. 
the Mute, so that you may better judge the horsing around you than 

I'll make a run for it. 

...ant this other way," he said, "I ray found moy-111ef me; 
...and though she's less well-known, she's still easy to deal with, -ofr 
through the lines. 1st diray therefore that having refurbished the column's walls, 
that is to say, fa height & growler, & the d!minution she must 
have at the end of the top, we must draw the 11th line to the injinien starting at 
par.C, qui ell::UI third of the fufi: of the Column, & continuing by D; 
and then relating the middle cd to the point where 
high, until it cuts the perpendicular to point B, & that 
.ABjoined continued until in E.E. From there one will be able to draw so many lines that one can 
'Voudra which will start from the perpendicular, & go to the circumference. 
tle the Column, f�r lefqr, elles appl..qttant la mefure CD, on trou'Vera tant 
en haut qu'en l,as renjlž1-e de la Colonne; & cct1e maniŽre peut eftre 


applied to rIonic, Corinthian & Compofe. 

Or you see, Monfieur : - that all' those lines that, - leaving 

of the p..int E , are comprifes . between the Perpendicular or Axis of 

the Column &. fa Circumference, are all equal to each other, &. 

ˆ 

Digitized byGoogle 


ON THE DIMINUTIO... OF THE COLUMNS. 

to the right CD. From strong we call the E point, the 
P:it; the Column Axis, the Rule or Canon; 8c the 1st line C D, 

.rInterval: I don't see anything anymore that prevents me from calling the line. 
curve that palliates from A by all the extremes searched for.
-The first Conchoid of the Anacons, since it is on the road to the Mefmc; -& which you will know even better- by the jriftrumcnte- which Nicomedes invented to describe it, in the figure efi: the second of the first board; in lacquer, after having determined 
as deffus the width of the Column, of which half _e'fte-CD, 8c found the length of the CE line, one must take trc,i.. eTŽglcs de bois ou de mŽtai1 G F, l D, HA, dont les deux 'G F,e& ID , font attachŽes enfemble ˆ l'Žquerre ou ˆ angles droitsecomme en D; & par le milieu de la rŽgie G F il faut paster une petite petite canal ˆ taeu d'arondue qui ... Žtend en toute la longueur de la rŽgte. 11 s'en fait une autre de mefme dans le milieu de la. rŽgle 
HA, which extends indefinitely towards the end H , but which towards the other end fe ends in K , but is not larger than the end CE. Flight 
it had to leak at the end of the HA rule to point A, the AAB line is equal to the CD line, & attach a wooden or metal knob to point B, which could run through the channel of control room G F. You have to attach another femolable knob. 
at point E, in the JDilieu of control room ID, which -flows into the channel of control room AH, so that rule G F eftanteapplied to the EU of the Column, with point D responding to 
to the bulge, & the AH fe regulation moving forwards or backwards 
for the E knob, like for a pivot or Pole, while this &outo... B moves along the said axis, i.e. along the channel of 1... control unit G F; point A describes by these two movements 
the curved line A a aC a , for the contour of the decrease &erenftcment of the Column which is called t,-rru-,� ..ar Vitruvian, ..e-in which line ..all the straight lines:, as b a, drawn .d� Po-ek, & comprifcs between the Channel of the control room' G F, that is to say, en-eB ttc 

Fig. II. 
of the/. 
Plancfo


ro P Il E M I E R-P R O 8 L E M E 

be the nineteenth of the Column & fa Circumference, are all equal. 
cntr'elles, & at the interval A B, or CD. En quo y il y paroi {l: ttue.la ligne courbe que ctt inilrument a dŽcrite, eO: la mcf me que.celle que.celle que Vignole a prŽtendu dŽcrire. And fi y your rules eO:anr of an.indefinite.size, you make in strong q.. the buttons B & E 
can go so far back and forth along the AH & AH & AH & AH & AH 
DI, que les intervalles, comme AB & CE, puifient auffi efrre.pris fur lefditcs rŽgles de telle grandeur que l'on Toudra; il eft 
Obviously, this inlhument can be used to describe the Curves of the Columns, no matter how high or wide they may be. 
efire, may all their difference be confused only in that of dcfdits. 
intervals. The other column column column will be described in the same way by changing its place... & bringing the other 
leaves. 
So, Monfieur, this is my Problem cft afi'ez-_ 
well refoluted parked and inftrumental; & that fanss-embaraffcrˆrccher.ccs infinite points, as Vignole wants, by lcf which we can- 
I'm going to be the one who's going to be the one who's going to be the one who's going to be the one who's going to be the one who's going to be the one who's going to be the one who's going to be the one who's going to be the one who's going to be the one who's going to be the one who's going to be the one who's going to be the one who's going to be the one who's going to be the one 
still imperfect, we can now pull this ... all the ... 
in one stroke, uniformly & in perfect harmony. 
. This is why I wanted to tell you about it, while waiting for us to 
let us have from the Author of The Paradox some shocking little furcette of confidences 
ef percr par fes Ejfrlnes. 
You are afraid that although there is a reason to be furprised,. 
that for so many fiefs that have produced great men... 

For the Architecture, which has drawn the decreases &... 
the swelling of the Colonnnes, perfoone, at least that I'm doing. 
reflects on this way of description that the Vign..e,. 
... that since the time of so many brave Archite... the feathers have believed in the faith of the blessed ... 
... and the fact that it is not possible to find a single


the Curve it produces, by means of the d.efi'eigner tout d'un- 

this-

Digitized by Google 


OF THE DECREASE IN COLUMNS. 11 

. 


...this thought has come to me, of which I boast less than 
4C the honour you do me to love me. I'm running away. &c. 

Ce z. 4. 1a1wier l cS 6 4- 

THIRD SPEECH 

$'VR LA NAT'VRE AND 'DESCRIPTION

. 

. 

Je 111 lieg11e qt1i f11it le Contour des Cotonnes 
'DoriqMes ... T()ftllnu. 

A
A
YANT AINU difourourced through the owners of the Curved Line, - which is the outline of the Ionic Columns, Corinthian 
...compofecs, I wanted to confide in you the other way that Vigno- 
describes it, & of which it fc fcrt for the reduction of Tofcan Columns 
& Doric. And after much meditation over the 
the nature of the Line it produces; I have acknowledged that it is a 
Line of the mcf me nature than that described in a Reche, or 
any other chof c pulled & thrown horizontally, in the opinion 
of those who believe that a weight falling from the furface of the earth 
{e trouverit juftement au bout de ftx heures au Centre ( ti la 
earth fe moves daily,) & pi1.ffant besides by 
the strength he has at his fingertips, he comes to the end 
n'autrcs furrcs fur hours at the furface of the Antipodes, fi le chemin luy 
eftoit open:- Hence, defending and repairing at set times an au- 
The date on which the date on which the date on which the date on which the date on which the date on which the date on which on which the 
the same place from which he first went, out of the air, where the 
other outside influences do not stop it. 
-á 
I therefore say that a puffy line v:igour..fement, &. parallelc l'horizon dec'riroi.t eil fonffage une Ligne de la mefme natureeBe2. De Fi1,. /. 
iela II. 
Board. 


de eellŽ dont on fc {ert pour la diminution des-Colonnes-Tofcanef 
& Doriques , fi_ ct;ttc -opinion eftoit veritablc: parce qu'efiant'. 
worn with an equal & uniform Lation movement, which luy cft. 
printed by l•mpulfi'on, & which makes that the diftanccs that he shorts 
do with each other in the same proportion as the time he does: 
to go through them, (i.e., like the arcs of the equator. 
who are however crazy about the Meridian,) &. about another movement. 
unequal,_ & which is continuously increasing, that fon pro-pre 
weight luy infpirc > & who in the opinion fufdite_ fe does fur la 
proportion of the Sinuses !crfcs d..s mefmes Arcs of the Equator,; he 
paroift that the Lignen,. that this trait is deteriorating in depth, will make 
compofŽe de ce, deux mouvemens, dont l'un eft Žgal, uniforme,-. 
the other unequal, continuous, and responding to the arcs of the equator. 
precipitated, & responding to mcfm-c vcrfes sinus vcrfes

Bows ... 
But the Tofcan & Doric Column Contour Line ... 
(fled by the. corpofitio_n 4th two similar movements,. so that- 
ie demonstrate it cy-deffous_;. & so there Line that describes- 
Bodies throw. hori:tontally,. like a line or an arrow- 
in the opinion of the fufdite, and that's pretty much the same as the one that- 
fe fert for the reduction of Tofcancs & Doric Columns . 
For the demonstration of what I've just said,. it's only necessary... 
.. ...to have the usual practice of the Workers for there is defi nitely... 
tian of this Line, which is made in this way. The AC Line, 
the Axis- by one Column to be reduced, & two thirds of the total


. 
. to be the first third of the way down; or the . 
half, fi on: defirc that she started- in the middle of it. 
Column. Line AB, is the module or half of the- f groove, 
which as a ray foit makes the Circle B ST V 7. 
fa.ut take the part AG, for the half-meter of the Column_. 
from the top, in strong that B G foit fa greater decrease,. tir4:r 
the Line G E pa ...OF THE DECREASE IN THE NUMBER OF COLUMNS... 1.31 

The amount of money which B F ... must be shared in as many equal parts as one, 

will want, as in points S, T, V, as well as the A C axis, in points 

H, K, M, provided that line A C contains ...tnnt of parts Ž-. 

equal to that of Arc BF. Finally points of the d...vižons of the Axis it is necessary. 

...to raise Perpendiculars,. like HI, KL, MN, which fail. 

met at the points. 0, X & Y, by other parallel lines - 

to.the.Axis, & drawn from the points of the B.F. Bow, in such a way that it 
The two parties respond reciprocally to each other, i.e. that 
the one that starts from the first point of the H Axis, like HO I, is the one that 
met in the O,. by the one coming from the first point of the Arc. 
S, like P S O, & the one starting from the fecond point of the Arc T,. 
like QT X, fe ends in Xs, and the one coming from the fecond point. 
point of the K-axis,. like KXL, & ainfi-from the others. And paf-. 
fant by all the points BO X Y E a softened line, it will do. 
the one ron's looking for in the diminishing Tofcan Columns: 
Doric... 
And fi we call point B, the apex of this line curves there-- -line AB, r.Axis or.I Diameter, the lines PO, QX., RY ,GE,.s&c. the ordinates;. we will see that the ordinate QX,. containing _to.so much 
of parts of the AC line, . or -of fon-eg.tle G-Es, . 
. that the arc.sBT contains cells of the arc BF, the ordinate QX, eft to,sl'ordinate GE, as the arc B. T, efl to r Arc B F;. & la mef meschofe fe being able to say. of all the others ,.il paroiftratratra que les ordon- -snŽes feront entre elloe comme les Arcs qui font compris entre lesfommet & lefdites ordonnŽes: & partant q..e cette lig_ne Cour--sbe cft uno cfpŽce -de Spiral, ou-bflJale... -sIn addition,. fi.we take the radius AB... for Total Sine, lCllsportions of the -Axis B P ,BQ,- BR,.B G, (I. will do the Sinusverfessdes Arcs, B S, B T, B V, B F, &c. & by confeccnt us
...let us call this Curve 11111 lignt Spiral or -Eliptif11e, da111slalJuelle the portions of the å:te fo111 les Si11us verfes des ,dr�s, fUì fonts11J1r1.t11Jt ,o,,,, the ,rdom1Žes -. 
Now fi we make another hypothesis, & {i}if we 
-let's take point A for the centre of the earth, line B A for