THEORY AND PRACTICEے
ے
OF THEے
ے
CUTTING OF STONES.ے
ے
AND WOOD,ے
ے
FOR THE CONSTRUCTION OF ARCHESے
And other parts of the Civil & Military Buildings.ے
ے
orے
ے
STEREOTOMY TREATY,ے
ے
FOR THE USE OF ARCHITECTURE,ے
ے
By J \ f, FR EZI ER, Knight of the Military Order of Saint Louis 1Dire‚l: eur of the Fortifications of Brittany,ے
ے
New Corrected & Enhanced Edition!ے
ے
FIRST VOLUME.ے
ے
,ے
ے
IN P_ARIS, RUE DAUPHINے
ے
ے
At CHARLE ..- ANTOTNE JOMBERT.ےRoyetl 'printer
Fon Artillery;ےat Yimage Notre-Dame.
ے
...... - ....- "" iNliN ? fJiŒQil ,, W ,,,. iŒ ? ..._._...,.ے
Mr.ے
DCC.ےLIV.


Iے
ے
1
ے
1ے
ے
ے
rے
ے
.ےI.
lے
ے
ے


,.ے
f11ے
PRELIMINARY DISCOUllS ْے
PREMIERDISCOUR S.ے
ON THE UTILITY OF THE THEORY,ے
In ْ the Arts relating to Architecture.ے
- .. I propose in this work to give fa_eTheory of the Sel: ions of the Bodies, as much as itے
is necessary to demonstrate the use thatے
can do in Archite‚l: ure for co.nftructionے
vaults, & THE PIERRESET OF WOOD CUP, what pei: fonne had not yetے
fact;ے& because I take a different route from those who have:
treated of this matter, which fe are so limited to Practice,ے
whether they ignore the theory, or ignore it: I willے
try to establish its usefulness.ے
Vitruvian, which can be cited for a good connoiffeur inے
Arts, because it is recognized for a famous Archite‚l: e, &ے
that he was, moreover, an engineer from Augufte, there were two choices.ے
fes (*) f‡avoir, Ouvrage & le Raiformement;ےone, he says, efr (") E- .: duab: u rebu.s / ingulas Artes e.Jjٹ compofltas, ex OPERE & ej11s RATTOCIN ATION
E;ےex his, iutem unum proprium eD "ٹ eorum, qui fingulis 1 ْ ebus June e ... ? rcitati id effi
-OJieris efJUlu.s;ےalurum commune cum-omnibus l) o‚lis!ےid-eft RAl10CIN.tlTIO.
atے
,.ے
f11ے
PRELIMINARY DISCOUllS ْے
PREMIERDISCOUR S.ے
ON THE UTILITY OF THE THEORY,ے
In ْ the Arts relating to Architecture.ے
- .. I propose in this work to give fa_eTheory of the Sel: ions of the Bodies, as much as itے
is necessary to demonstrate the use thatے
can do in Archite‚l: ure for co.nftructionے
vaults, & THE PIERRESET OF WOOD CUP, what pei: fonne had not yetے
fact;ے& because I take a different route from those who have:
treated of this matter, which fe are so limited to Practice,ے
whether they ignore the theory, or ignore it: I willے
try to establish its usefulness.ے
Vitruvian, which can be cited for a good connoiffeur inے
Arts, because it is recognized for a famous Archite‚l: e, &ے
that he was, moreover, an engineer from Augufte, there were two choices.ے
fes (*) f‡avoir, Ouvrage & le Raiformement;ےone, he says, efr (") E- .: duab: u rebu.s / ingulas Artes e.Jjٹ compofltas, ex OPERE & ej11s RATTOCIN ATION
E;ےex his, iutem unum proprium eD "ٹ eorum, qui fingulis 1 ْ ebus June e ... ? rcitati id effi
-OJieris efJUlu.s;ےalurum commune cum-omnibus l) o‚lis!ےid-eft RAl10CIN.tlTIO.
atے


Jے
GJlli f1L <-1ur umbiŒicumے
cr.:intے
naked.ےTitus-
1 ... ivc.ے1.ے1-1, ..
J ;.ے-16,
iy SPEECHESے
the case of the People who learned it;ےthe other efi of
s‡a vans rebellion.ےNot everyone thinks that
him ;ےmen, for the most part, know (i little the
nature of the Arts, that they believe that one cannot make it skillfulے
only through experience;ےthey look at Theory as a
vain occupation, which has for object only chimeras, of whichے
the Arts does.ےget no benefit.ے(*) We have vt1, they say, of
Great Men in Civil Architecture, & even in the Military, who fe difungu‚s by their Works fans beے
Geometres ni Algebrifies, therefore one can fe pa.OEer of these Sciencesے
to become skilled in the Arts.ے
To answer this false sniffing, which many people thinkے
to demonstrate by the interest they have in establishing it;ےI will say
that abolutely speaking, in the food reserve, theے
men can do everything, even clothes in theے
Cold countries, witnesses the ancient Gauls, our Ancestors, & more.li
their Nations of Savages;ےbut since Nature defied us'
committed to work, & that with a little application itے
gives us the indufirie to add an infu—t‚ of agremens &ے
conveniences in the Works of those who preceded us, &ے
reconcile the beauty & the solidity of the Buildings, which ga_ranti us!
do insults of the air & infulces of our enemies, it bloomsے
that it is not to act as raifonnable men, that to harness1 ?ے
dre that the experience falfe us to make our needs;ےbut that
we need to think about how to provide for those who canے
we happen in the execution of our de! feinse, & ْ to combineے
these means in so many different ways;ےthat we
always choose the fپrs, the shortest & the easiestے
, which is referred to in Theory sheet.ے
Let me allow a comparison here to make thisے
more fenfiblc truth;ےbefore we have formed the main roads
by straight, solid, & convenient width panels, weے
communicated COJllme today from one Villٹ to another,ے
(?) See the Ptnf‚es crfr?IJuesfur les Marhima.riques by CAl \ TAUD,ے
, but Ma1h, emati4ues have contributed little (.. the perfcfپon of beautiful Arcs! A Pari :. l73itے
?ے
,ے
Jے
GJlli f1L <-1ur umbiŒicumے
cr.:intے
naked.ےTitus-
1 ... ivc.ے1. 1-1, ..
J ;.ے-16,
iy SPEECHESے
the case of the People who learned it;ےthe other efi of
s‡a vans rebellion.ےNot everyone thinks that
him ;ےmen, for the most part, know (i little the
nature of the Arts, that they believe that one cannot make it skillfulے
only through experience;ےthey look at Theory as a
vain occupation, which has for object only chimeras, of whichے
the Arts does.ےget no benefit.ے(*) We have vt1, they say, of
Great Men in Civil Architecture, & even in the Military, who fe difungu‚s by their Works fans beے
Geometres ni Algebrifies, therefore one can fe pa.OEer of these Sciencesے
to become skilled in the Arts.ے
To answer this false sniffing, which many people thinkے
to demonstrate by the interest they have in establishing it;ےI will say
that abolutely speaking, in the food reserve, theے
men can do everything, even clothes in theے
Cold countries, witnesses the ancient Gauls, our Ancestors, & more.li
their Nations of Savages;ےbut since Nature defied us'
committed to work, & that with a little application itے
gives us the indufirie to add an infu—t‚ of agremens &ے
conveniences in the Works of those who preceded us, &ے
reconcile the beauty & the solidity of the Buildings, which ga_ranti us!
do insults of the air & infulces of our enemies, it bloomsے
that it is not to act as raifonnable men, that to harness1 ?ے
dre that the experience falfe us to make our needs;ےbut that
we need to think about how to provide for those who canے
we happen in the execution of our de! feinse, & ْ to combineے
these means in so many different ways;ےthat we
always choose the fپrs, the shortest & the easiestے
, which is referred to in Theory sheet.ے
Let me allow a comparison here to make thisے
more fenfiblc truth;ےbefore we have formed the main roads
by straight, solid, & convenient width panels, weے
communicated COJllme today from one Villٹ to another,ے
(?) See the Ptnf‚es crfr?IJuesfur les Marhima.riques by CAl \ TAUD,ے
, but Ma1h, emati4ues have contributed little (.. the perfcfپon of beautiful Arcs! A Pari :. l73itے
?ے
,ے


PRELIMINARY.ے
but 011 remained much longer on the way, we experienced ...
see a longer tiredness, one was subject to <remain stuck.ے
be, & fouvent to go astray.ے
Before we had co.fulc‚ the Geometry & 1a Mechanics e11ے
'Architects, we make vaults of the same materials as today;ے
but we couldn't get any better of the balance of effortے
their Pou / Jٹe, & the refپ.ance of the Pi‚droits which it tends to dismiss;ے
strong than f..willing to keep a suitable environmentے
between the too much and the too little of their shoulder, one was fujet to yconfommer W1e fuperAue depenfe in materials, or to the wayے
collapsing from too much foibleffe: experience still provides usے
to show examples, to the shame of those who mingleے
of conftruaion fans connoiffance of Geometry nor Mechanics,ے
& to the great pity of the one who builds.ےWe make
aufii of the hangers of different efpeces, circular, furbaپi‚s,ے
overheated & rampans;ےbut or did not know what the
curve that best suited them in the circumstances ofے
terms given.ےWe meet in the execution of difficulties
that we had not foreseen, and that we only refuted asے
me the Gordian knot, demolishing & cutting several timesے
the parts of arches which do not cross, until the eyeے
was less affected by their deformity, from which it greatly refutedے
loss of time & materials;ے& because the trial and error
has success only by chance, such works lasted little, usedے
in many ways, & rarely satisfied the view &ے
the spirit of connoisseurs!ے
Where then does the Practitioners despise] a Th‚orieJ 8ٹے
do they count it for nothing at the cost of the experience that they cannot boast of?ےI find two riffons: the first one is for
divert the shame they have from not being able to give other reason- 'ے
fon of their Works, that of the imitation of those whoے
paffent for good, & the convenience that they noticedے
in practice, although they do not do enlightenedے
to go back to the caufe.ےThis efi raifon: taken from vanity
of the human heart;ے! "man to rise for fese_ tgaux, affe‚tee
.. 1)ے
Jے
lے
Jے
PRELIMINARY.ے
but 011 remained much longer on the way, we experienced ...
see a longer tiredness, one was subject to <remain stuck.ے
be, & fouvent to go astray.ے
Before we had co.fulc‚ the Geometry & 1a Mechanics e11ے
'Architects, we make vaults of the same materials as today;ے
but we couldn't get any better of the balance of effortے
their Pou / Jٹe, & the refپ.ance of the Pi‚droits which it tends to dismiss;ے
strong than f..willing to keep a suitable environmentے
between the too much and the too little of their shoulder, one was fujet to yconfommer W1e fuperAue depenfe in materials, or to the wayے
collapsing from too much foibleffe: experience still provides usے
to show examples, to the shame of those who mingleے
of conftruaion fans connoiffance of Geometry nor Mechanics,ے
& to the great pity of the one who builds.ےWe make
aufii of the hangers of different efpeces, circular, furbaپi‚s,ے
overheated & rampans;ےbut or did not know what the
curve that best suited them in the circumstances ofے
terms given.ےWe meet in the execution of difficulties
that we had not foreseen, and that we only refuted asے
me the Gordian knot, demolishing & cutting several timesے
the parts of arches which do not cross, until the eyeے
was less affected by their deformity, from which it greatly refutedے
loss of time & materials;ے& because the trial and error
has success only by chance, such works lasted little, usedے
in many ways, & rarely satisfied the view &ے
the spirit of connoisseurs!ے
Where then does the Practitioners despise] a Th‚orieJ 8ٹے
do they count it for nothing at the cost of the experience that they cannot boast of?ےI find two riffons: the first one is for
divert the shame they have from not being able to give other reason- 'ے
fon of their Works, that of the imitation of those whoے
paffent for good, & the convenience that they noticedے
in practice, although they do not do enlightenedے
to go back to the caufe.ےThis efi raifon: taken from vanity
of the human heart;ے! "man to rise for fese_ tgaux, affe‚tee
.. 1)ے
Jے
lے
Jے


'v1 SPEECHے
ے
ے
'to misunderstand the chofes that he misses, & seeks to make pa ..:ے
rade of the little it poffede;ےfrom there lives, that we feign mutual despair
in the world, & that science, whose beautyے
& the utility makes little known by the multitude, not highے
to the rank it must hold above the practical sheet;ےinattention
& Cover the lack of light of the people in place, favorite [ے
ent the false false judge that one carries fur the merit of theے
routine;ےsince we can see that it is worth working.ےto acquire
useful connoiiiances to the needs of life, or to the ornamentation of ْے
the spirit is usually very useless for fortune;ےit?s fair, ..
roit aiTez to annoy any emulation, stop the progress of ?ے
'Arts, & recall the barbarism of the fiecles of ignorance, fi la Nat: Ureے
had not provided for the blind injufپce of men.ےShe touched
to this penalty the reward of a fatisfa‚tio11.ےinterior,
(*) Vir- (. *) Who is late able to foutout against them.ےdisdain of a
ے
; ..:; .. nfnr; .. ftupid indifference, or a prefomptueufe ignorance.ےIndeed_
ے
Ji.s efl, & -fet, fans the attractions of science, & a certain love forے
ے
reElٹ f (l, sti V - ?
ے
, rr, r.ے,
ے
merces efl ertu, quh-1 ce qm pourro1t hire a man 1en1v a con
ے
ے
.fecijfٹ.ے
ے
facrer, fes veilles fans interest, au feul bi. en du Public, qui four
ے
ے
The city of people more difficult to criticize than to recognize childhood,ے
to point out the smallest faults, than to pardon them in favor ofے
what should more deserve their attention: ention & their applause?ے
ے
The raifon feconde of those who prefer the leaf Practical to theے
Theory, can be deducted from the bottom of.ےtheir ignorance
, because they attribute to it the effects of Theory whichے
their unknown.ےo'AvILER, famous Author in Architecture, '
provides us with a proof, & a comic example on the pageے
ے
274. e The severity of the Rules of Geometry, he says, is less than theے
Practical, like THE EXTENDED CfJERCHES METHODے
// AUT MlEUXQUE LES.FIGURES GEO / v! ETRJQUES.,ے
lover that in this Art Practice is preferable to ْے
Theory.ےWe can't help laughing at such a decifion,
which obviously shows that the judge does not hear the state of.ےthe
quefl: ion, & that he wants to scold what he does not know;ےindeed,
iii have f..Ci que .. f.herrhe ra / ong‚e ti1‚e du plein cei ..] tte 2. du ْ.ے
ے
ے


PRELI Œ \ 1 INAIR E. vijے
furhau! r‚ or furbaiff‚, ‰toil a very Geometric ellipfc,ے
he would not have used this ridiculous language.ےMost people fans
Theory speak & think like him, because for lack of prin ..ے
cipes they arrive only with great efforts & ْ a long flightے
practice with a few conno connoisseurs: iffances of chofesے
are most helpful to those who have theory;ےwhere does it come from
that they make a big deal of the least, and fe believe bigے
men for having made their way through a few rough roadsے
Practice, even though these so-called Inventors can not sharpenے
of the jufteffe or the reuffite of their groped operations,ے
of which they see neither the difference of the cases, nor the proof;ے
strong they think they have done well, evenے
that they have only approached truth, and that they have notے
took the safest & shortest view;ےhowever because they
know no other way to do it than experienceے
, they do not believe that there is a better master, ap.
puyez fur the proverb they cite about, Experiemia rcے
rum magiflra.ے
I do not claim here to diminish the merit of the experience, Iے
-connois 1a born in several chofcs;ےfor example, in Phyftque
she sees objects & effects as weے
was not warned by the sniffing;ےdon't doubt
that it was indefensibly necessary in the Arts whichے
.depend on habit, & in those who cause problems.ے
ques, like war;ےbut it the eye: much less in
those that emanate from science;ےc'efl: an ambiguous guide, as
the stick of a blind man, who only leads him to lead him very.ے
imperfectly, in that he does not <fiے
that he could not take one for the other, & fe to precipitate, fi the caseے
: gets there.ے
This diftinaio1,1 indicates what to think about the Scien ?ے
this & experience necessary for an Engineer;ےsince my state
laugh at War & the Arts dependent on Mathematics;ےthis
it would be wrong to decide against quoting Theory only to quote elite people.ے
-! f‚.s to the dignities by! es military a‚lions, though ..- .. o.cnes at aea llJے
?
PRELI Œ \ 1 INAIR E. vijے
furhau! r‚ or furbaiff‚, ‰toil a very Geometric ellipfc,ے
he would not have used this ridiculous language.ےMost people fans
Theory speak & think like him, because for lack of prin ..ے
cipes they arrive only with great efforts & ْ a long flightے
practice with a few conno connoisseurs: iffances of chofesے
are most helpful to those who have theory;ےwhere does it come from
that they make a big deal of the least, and fe believe bigے
men for having made their way through a few rough roadsے
Practice, even though these so-called Inventors can not sharpenے
of the jufteffe or the reuffite of their groped operations,ے
of which they see neither the difference of the cases, nor the proof;ے
strong they think they have done well, evenے
that they have only approached truth, and that they have notے
took the safest & shortest view;ےhowever because they
know no other way to do it than experienceے
, they do not believe that there is a better master, ap.
puyez fur the proverb they cite about, Experiemia rcے
rum magiflra.ے
I do not claim here to diminish the merit of the experience, Iے
-connois 1a born in several chofcs;ےfor example, in Phyftque
she sees objects & effects as weے
was not warned by the sniffing;ےdon't doubt
that it was indefensibly necessary in the Arts whichے
.depend on habit, & in those who cause problems.ے
ques, like war;ےbut it the eye: much less in
those that emanate from science;ےc'efl: an ambiguous guide, as
the stick of a blind man, who only leads him to lead him very.ے
imperfectly, in that he does not <fiے
that he could not take one for the other, & fe to precipitate, fi the caseے
: gets there.ے
This diftinaio1,1 indicates what to think about the Scien ?ے
this & experience necessary for an Engineer;ےsince my state
laugh at War & the Arts dependent on Mathematics;ےthis
it would be wrong to decide against quoting Theory only to quote elite people.ے
-! f‚.s to the dignities by! es military a‚lions, though ..- .. o.cnes at aea llJے
?


Neiueے
tnim ingeniumے
jifleDtcipli,: z,ے
aut Difciplinaے
fineے
ingenio; er
ے
ے
fe‚lum a.rti
ے
ے
ftc..m poteflefficere.ے
ے
Y.itr.ے
ے
?ے
ے
viij SPEECHESے
ے
the routine confruel: ion;ےthe rewards due to the value i
advertise only part of the merit of a man of war,ے
which is not enough for an Engineer.ےThose of Antiquity
were fa‡ans;ےtheir wonderful inventions in the Sieges
prove it to us a! fez;ے& although since the decline of
Romans, the Sdences have in some way made divorce with..cے
War (for there are no longer such men fit to be fur Iے
Throne of the J ufپce, & at the head of the Armies) this preparationے
will never take place with regard to the Engineers, it is them that must fubfifter this old agreement of Science & War;ے
if they need bravery, good fens & experienceے
of a Warrior, they still need the skill of a mathematician.ے
Without Geometry, Mechanics & Hydraulicsے
what do they do in the conftru‚l: ion des Fortereffes &ے
Places of war, that to imitate what they have v6, & copy fouventے
mistakes?ےThe traces of the blind experience do not
rare, there are city wars where we do not recognize what ..ے
_some.ے
ے
I will advance moreover, than the necessary Sciences to the confruel: ionے
do not make useless in War;ےthey open the spirit,
provide industrial resources for maneuvers andے
works necessary for the attack & defense of the Squares, which the small value should not execute fans cc fecours.ےARCH1MEDE
was a mathematician of pure speculation, who would not have deigned to fall into practice if he had not been engaged by theے
congratulations from King HtERON parent, to make use of fesے
knowledge for the invention of War Machines;ےhowever
his attempts at trial were ignored by many of the master?sے
Siege of Syracufe he diverted, by the force of Theory, allے
the experience of these Roman Engineers, who had arguedے
with great successes their skill in conquering Placesے
the strongest;ےthe new machines had so much effect,
that he intimidated & rebuffed the Army of Marcellus, to the point thatے
this General renounced the approaches and the attacks, forced to feے
1duire to c_he.tcher by the length: from the Siege, what He in ..
ے
ے
yo ..ے
ے


PRELIMINAIR E. lxے
sees him get by force against the engineer!ے
f.,; or Archimec. le.ےWe can give him all the honor, because
Plutarch says, that he was the sole author of the defense, that theے
SrracuCains were only like the body & the limbs, of whichے
he felt the soul which put everything in a moment, fans whom weے
fic ufage of weapons other than mine.ےHowever this great
man, he adds, do not boast of these happy novelties,ے
he only looked at them as games,: of Geometry,
that he was little in comparison with Theory, that he thought he wasے
do more honor to e11 laiffer des Ecrits, than defcriptionے
of these wonderful machines, whose invention & useے
had acquired so much glory & a great name, that he loved forے
a man endowed not with human consciousness, but with all divine Divinity.ے
Difm, s-le fans deguifer, la feule experience onlyے
fervent imitators, who are over the topے
chofese, & having only reffource in the collection of their por ?ے
te-feuille, give like blind in the false for themے
projects, execution, & the toif‚.ے
Plutarquein vit11ے
Maml / i,ے
I would say, however, that fans want to promote ignorance, that a Satis ?.. v bu12.ےٹ is ,,;, ..
Engineer must limit himself to the study of what can be useful for the detur fecif-
practice, fans fe indulge in vain curiosities, lest in-Jife '' 1
1
..Œ ex.ے,.ےb
mgu 1sے
framed by 1 primer of the discoveries pla1Gr, plus capa les Do‚lri, —sے
to flatter fa vanity than to lead it to a greater pe :: r-rr..f0_: "ے
fe‚t: ion des Arts, it was not crazy wind diftrait & tempted to neglect NE..ea: umr cl ْ ْ 1 d ْ rے
ْے
r ْ, 1 r lid "‚ &, l med1ocrictr.ion evo1.r; 1 oit 1es premier ioms aa 10 1t ْ aa propre-habeinoras,
t of the Works with which he is responsible, & avoid the pitfall of contempt eafiJue? u ..
I hr ?.ےr.ے, d.ےrrec..JJrue that es autes 1c1ences 1111p1rent for es occupations which smokes adAr-
make within reach of the most limited efiprits;ےhe just had to be cl, ire‚lu-
firam, ut zے
able to hear & use the works of the Sea-quid of hfr & d A die.ےd S.ے.ے1, rebu.r & vans es ca mies es c1ences, qm que que rapport Artib.ےjudi ?
at the Arts n‚ceffaires at the conftruaion of Places, presenting the ca.re & pro ?
d Hے
.ےbare opus‚tu es to yvers & other cems of 101 ..! ir that laiffe the fuerit, nave of the King.ےd .. {li! umur
.ےvel defic1at,
Among the connoiffances which make us born! Fa1res, that of Vitr.ے1: ?!
Cut of the Stones, although one of the most neilig‚es, is not c.ے11
bے
PRELIMINAIR E. lxے
sees him get by force against the engineer!ے
f.,; or Archimec. le.ےWe can give him all the honor, because
Plutarch says, that he was the sole author of the defense, that theے
SrracuCains were only like the body & the limbs, of whichے
he felt the soul which put everything in a moment, fans whom weے
fic ufage of weapons other than mine.ےHowever this great
man, he adds, do not boast of these happy novelties,ے
he only looked at them as games,: of Geometry,
that he was little in comparison with Theory, that he thought he wasے
do more honor to e11 laiffer des Ecrits, than defcriptionے
of these wonderful machines, whose invention & useے
had acquired so much glory & a great name, that he loved forے
a man endowed not with human consciousness, but with all divine Divinity.ے
Difm, s-le fans deguifer, la feule experience onlyے
fervent imitators, who are over the topے
chofese, & having only reffource in the collection of their por ?ے
te-feuille, give like blind in the false for themے
projects, execution, & the toif‚.ے
Plutarquein vit11ے
Maml / i,ے
I would say, however, that fans want to promote ignorance, that a Satis ?.. v bu12.ےٹ is ,,;, ..
Engineer must limit himself to the study of what can be useful for the detur fecif-
practice, fans fe indulge in vain curiosities, lest in-Jife '' 1
1
..Œ ex.ے,.ےb
mgu 1sے
framed by 1 primer of the discoveries pla1Gr, plus capa les Do‚lri, —sے
to flatter fa vanity than to lead it to a greater pe :: r-rr..f0_: "ے
fe‚t: ion des Arts, it was not crazy wind diftrait & tempted to neglect NE..ea: umr cl ْ ْ 1 d ْ rے
ْے
r ْ, 1 r lid "‚ &, l med1ocrictr.ion evo1.r; 1 oit 1es premier ioms aa 10 1t ْ aa propre-habeinoras,
t of the Works with which he is responsible, & avoid the pitfall of contempt eafiJue? u ..
I hr ?.ےr.ے, d.ےrrec..JJrue that es autes 1c1ences 1111p1rent for es occupations which smokes adAr-
make within reach of the most limited efiprits;ےhe just had to be cl, ire‚lu-
firam, ut zے
able to hear & use the works of the Sea-quid of hfr & d A die.ےd S.ے.ے1, rebu.r & vans es ca mies es c1ences, qm que que rapport Artib.ےjudi ?
at the Arts n‚ceffaires at the conftruaion of Places, presenting the ca.re & pro ?
d Hے
.ےbare opus‚tu es to yvers & other cems of 101 ..! ir that laiffe the fuerit, nave of the King.ےd .. {li! umur
.ےvel defic1at,
Among the connoiffances which make us born! Fa1res, that of Vitr.ے1: ?!
Cut of the Stones, although one of the most neilig‚es, is not c.ے11
bے


x SPEECHESے
ے
one of the least important.ےI recognized by my own experience ?
rience that it was therefore indefenably indefensible to an In.ے
genicur than an Architeete, because H can be sent asے
me in distant colonies, & ml: me in provincesے
where there is a lack of workers capable of executing certainے
parts of the Fortifications, ot1 intelligence is required in the apparatus.ے
The test that I had just made of it on my second returnے
of America, gave me the idea of ??understanding it, of making a Treaty;ے
invited to this cntreprife, first by the extreme rarity denے
Books on this matter, especially in the imperfect mannerے
which she has been treated to as much as possible.ےI get it
project, when I learned that an Architeete was going to publish one,ے
indeed, a few months later, that of M. de LA RuE appeared;ے
but as it did not, like that of Fr. DERAND,ے
(which was so to say the feul) that to lead the handے
fans enlighten the efpric, I recognized that it was not affcz Methodicalے
to fulfill the expectation of the audience, which fouhaicoic sinceے
long-tcms a more Geometric Work;ےI was convinced
when the people to whom I communicated my plan,ے
hired me to work on it & fuivre it, because the diff ?ے
rence in eft fi great, that we can say, that it is not multi ..ے
fold the same ef peces of Books.ےThe ones I just mentioned
made for the Workers, & this one for the people whoے
must drive.ےlike Engineers & Architcaes, that
one must fuppofer initiates in Geometry.ے
ے
I made routine and a certain natural geometryے
act as a substitute for fitters in ordinary cases;ے
but I felt that it became useless to them in those whoے
do not enunciate in the Lines, as I will point outے
when it will do that, and that they will stop everythingے
short, if the Engineer was in a state to suppress it.ےHe must therefore
pfevenir la hontcufe n‚ceOEc‚ de fc deliver to the ignorancc of the mostے
experienced, who only come to grips with it by forceے
to demolish several times, finished .ffam finally by some deformityے
or dfSolidity fault.ےThese cases are not rare for fc ima1
ے
ے


PRELIMIN .AIR E. xjے
ے
gine, pu if they make me happen;ےnor is it extraordinary
to find the vestiges, non-feulement in the racordernensے
old works with works, but still inے
those who flee.ے
ے
I fuppofcrai,! If you want, that Entrepreneurs supplyے
good Fitters;ےdoes he not believe in the dignity of an Engineer,
to be in a state of knowledge & to examine what they are doing,ے
to order & decide on the best confiruetion, & notے
provide faults that they can mischievously, or forے
to fervor waste stones, or to spare a little moreے
hay?ےBesides, this matter is interesting enough to deserve
the attention of a curiofپ‚ jufte;ےwe can judge by this
fleeing.ے
ے
SECONDDISCOUR S.ے
ے
Expofition & division of the subject in question.ے
ے
L
L
'IDE'E that we attached to the name of the Pier Cup: ._ے
rts, do not be what prefers the spirit first;ےthis word
"does not specifically mean the Artifan book which cuts theے
Pierre, but the Science of the Mathematician who leads him inے
the deffein it has to form a vault, or a body of a cer ..ے
taine figure by the assembly of several small parts.ےIt is necessary
indeed more industry than one thinks, so that they faithے
do so that, although unequal figures & sizes,ے
they each compete in particular to form exaaementے
a regular or regularly irregular furface, & that theyے
are scattered in such a way that they screw up in the area, inے
leaning on each other, fans otherے
] iaifon than that of their own loser;ےbecause the links of
mortar or cement should always be counted for nothing.ے
This shows that this Science holds its principles, first of allے
of Geometry, for the connoifance of lines & furfacesے
curves & straight lines & solid bodies that must beے
divided.ے
ے
b ijے
ے
\ے
ے
ے


: tJJے
''ے
SPEECHے
ے
Secondly from Mechanics & Statics, for met4ے
be the balance between the portions of the folids that make up theے
vaults, force them to fuck each other fur supportے
that we fix them.ے
ے
Our delfein is not here to confide the vaults as aے
clusters of p‚fan bodies, which make different efforts the ones fur lesے
others: this Theory, although very curious & very-useful, canے
be reduced for practice to the small number of propofitionsے
demonstrated by Mrs.ےFROM H1RE, PARENT, COUPLET & BELII
..OR, touching the arches of vaults, to which we can add ْے
ter some obfervatioos fur the buildings which fubfiftent sinceے
for a long time, although a little outside the rules of calculation, should beے
the good quality of the materials that make up the body,ے
give the time of fc to bind, or by the different loser ofے
those of the vaults and their piers, to which it is necessary to have regardے
in calculations;ےbecause fi one efl: from a light stone & the other from a
more puffing, the puffiness increases or decreases with regard toے
corners.ے
ے
So here we confidate the Stone Cup, that com,ے
relating to Geometry, fuppofant howling that a bodyے
conical, piramidal, or wedge-shaped, cannot feے
through a hole, which is not big to my small holeے
that the baff e of the body that we introduce into it.ےThis foppof‚ this
fcience fe will summarize:ے
ے
1 ّ.ےTo curate the curved lines formed by the divifion
mad, concave & convex eyelashes cut by flat furfaccs,ے
or by curved furfaces;ےc'eH: what we might call
from a word of Greek origin, Tomomorphy, or Figureے
derfe‚iions, if it were allowed to forge new wordsے
to avoid periphers.ے
ے
2 9 ?ے
To describe these curved lines as flat faces, lorf ..ے
that it is poffible & necessary, or fur curved furfaccs lorfqu'ellcsے
cannot adapt to a plan in their full extent,ے
what we might call Tomography, or deflے
riptianے
fleliom ..ے
ے
ے


PRELI M. INAIR E. x.iij
ے
3 ّ.ےFind easy ways to represent the folidcs
& their differences as flat faces, as far as it is possibleے
to do ;ےas they can only be expressed very imperfectly
, these means fe reduifente, 1 ّ.ےto the projection
made on a plan by cut lines paralleled between them,ے
& perpendicular to the plan of the description, what weے
is called a horifontal plane, [clmography, & a verti
ے
ے
ّ
ے
cal, Spelling.ے2nd.ےWhen the furfaces are tidily stored away
& in their full extent for a plan, what is calledے
development, & which we could call Epipedography.ے
3ے
ّے
.ےAt the definition of the angles of any planes or furfaces
crazy entr'ellese., what one could call the Gonio-_ے
spelling, Dejٹription of angles.ے
ے
4 ّے
.ےTo make use of all these strong representations,
to achieve a suitable body fetish to the confiructiot1ے
vaults, applying the angles & angles modelsے
furuses furious of the most foolish made in parallelepipedes,ے
to cut them & reduce them to the required ligures, cutting downے
the excess parts, which efi properly the Art ofے
Cut of Stones & Woods, that is to say, that of making these fections,ے
that we could call Tomotechnics.ے
ے
So by refuting these imagined words to give an ideaے
clear & fپnple of the fujet in question, we deal in the pre ..ے
first part of this Book, of Science, & in the feconde,ے
of the Art of Stereotomy, that is to say, fe‚lions des foli
ے
ے
?
ے
of.ے
ے
We divide the first part into two Books, one of theے
Tomomorphy, or figures of fe‚lions, the other of Tomography,ے
or defcription of fairies.ے
ے
The feconde auffi in two Books, dom one efl: Stereography,ے
or description of the mad, and the other of Tomotechnics, or! 'Artے
to make fe‚lions.ے
ے
Such are the Subjects of the four Books of this Book, fleeingے
the order that seemed most simple and natural to us;ےthis
that we will try to explain & prove by demons
ے
ے
b Djے
ے
ے


} jV SPEECHے
ے
rrations, which do not fuppofent other connoiffance of panics di.:sے
Mathematics than that of Elementary Geometry, suchے
that she was in Euclid & the Authors who fled her.ے
ے
I said that today Linear Geometry is no longer a warے
fashionable, & that to give an air of Science, you have toے
fafre parade of Anal yfo;ےhowever, the ancient Geometry,
ے
.. Fon- ,, (says a S‡avant) * although less fublime, less piquanr1:
......: 0_ ,, this, even less pleasant, is more likely to be born!ے
&ے
.. J: iJm,ے
,, p! usflnfiblmum useful;ےit is the fire that provides the news
ے
lt1em.ےof
ے
the .. Fi.rnd.ے,, crazy foundations, especially in the matter of which
it is, where the Algebraic calculation could only be useful betweenے
the hands of those who are more advanced there than ordinarily doے
most of the people who are involved in the architecture,ے
for whom we have undertaken this work.ےBesides she drives
more naturally to the practice of cutting featuresے
crazy people, & makes me more memorable in my memoryے
, where furfaces & fe lines carve deeperے
than the precepts of Algebraic formulas.ےThe S‡avans did not
no need for a small work, which would only be a game forے
them;ےdriven by the ambition of the glory of discoveries, they
take care only of the chofes d1ffici_les, fans get crazy about theirے
utility in the Arts;ےwhat did Mr. de FONTENELLE do this
Judicial hifloire remark, that the Geometry is quite extended, butے
ے
of the A.cad.ے
ے
that, she doesn't, ft 1 ْ r.ے0r p ْ mlqu ? ْ 1 1 sn, have
ے
not auezrr app 1qu ‚e to the magi.ےr
ے
not treated our mackerel, I make it f erv ice to those whoے
are curious, to give them the principles in a collectionے
included in the first volume, which is sufficient to spare themے
the long, boring & less intrusive: the big kidsے
Folio volumes, where it is more muddled ْ in detailے
of practice only by the bottom of the difficulty;ےthey will be able to
to wax the folution of Problems which are calledے
Features of the Stone Cup;ےhowever in favor of those
who like the works made, we added their conftru‚l: ionے
in the fourth part, which will contain a lotے
more material in less volume than the books of P. Di
ے
ے


,ے
ے
p RELIMINAIR E. XVے
ے
R.AND & de M. DEI.A RuE;ےI hope so that the le‚ture will make
more pleasant, because we will find the demonstrations, whichے
will only apply Theorl: mes & Pro blˆmesے
contained in the first three Books.ےBy the way, I did not research
other approval in the diaion than that of raifo11 ..ے
ment.ےIn this kind of writing we have to be more busy with
nothing but words;ےa le8: eur raifonnable requires only the ْ
sharpness & an intelligible diet;ےthat's what I'm running for
more attached.ےPerhaps I will not always have reuffered, in a
long Work it always glides some fault;ےi beg him so
to forgive those of the impreffion, which was not made madے
my eyes.ے
ے
He refuses to give me anything to curiofity that we canے
touching on the origin of the Cup of Stones, at whichے
I will expofer my conj‚8: ures to conclude this Pre Difcours
ے
ے
.ےarea.
ے
THIRD SPEECH.ے
ے
From the origin of the Stone Cup, & from the ufag ..ے
ے
that we have to do.ے
ے
Lے
L
E Wood is the most natural and convenient materialے
for the confruaion of New Buildings in the habi ..ے
tation of men;ےbut the challenge common to all those who do
edible buildings, to establish the duration for a longterns,ے
the idea that 01: 1woods are fujets to fall intoے
decay by decay, & the fear that they will be ravagedے
by fires, made the Stones rather than Wood, ot1 we haveے
pt1 fobfiituer them.ےIn this view we spared neither pain
nor the great outbursts to tear them from the aid of theے
; earth, Jes tranf carry & carve them.ے
ے
The neccffit‚ auffi forced the men in several regions,ے
to use Stones instead of Wood, because the 11.:turcے
ے
ے


XV) VISCOURSے
furnace has supplied more Carrieres than Forfts.ےHowever the
manierc de blhir with 2rl- .. ٹs a 1 aru fi n: itm: el1e, that we haveے
looked like a beauty in, tatil "ln of this firm: mr.ے
from where we came the Ufagc des Colonnes dans l'Architectureے
a1 c.que, & that of the round pillars & Poles in the_ے
Gcthique.ے
ے
To make this imitation more perfect, the Elders do
ے
ے
foient 1 - :. m, Cclonnes, as much as they can: em
ے
ے
this, as .. make the trunks of the trees;ےthey in ufoi1..r, t of ml! me
for their ArchitraYcs, which they use for the main beamsے
that the columns were to carry.ےHe celebrates the vestiges of
buildings of the Egyptians, the Greeks, & the Romans, which makeے
see that they used stones of enormous size there.ے
ے
In the last fiecles we abandoned these manicres ofے
to build, too difficult to do. ".. r l‹m.g.1enfited with the weights that had to be transported, &ے
by the outpouring of the extraordinary women whom they consume;ے
we preferred to them the collection of several stonesے
a more manoeuvrable gro.ffeur, & fans depart from the taste of the Ancients,ے
we continued to imitate tree trunks by columns,ے
but we made them out of drums, that is to say, out of trapsے
cylinder.ےThe beams were likewise imitated by Architraves;
but we made them of keyboards>. ْ, who screw themselves up in the air,ے
as if the whole was only one continuous piece.ےHowever
like this fituation is too forced, & that the puff in eftے
large, the Architeaes supported them by arcades, whichے
seemed to them more foolish;ے& although by this confiruaion the
columns & architraves become useless, they emr them,
always rent for ornament.ےThis goC1t is the taste today
dominant in Europe, imitated by some monuments of Antiquityے
Romaine, which we used as a model after a longے
interval of a completely different architectural GoC1t.ے
ے
The proportions of the Ancient columns had appeared in theے
Gauls & in other places of Europe, too maffive & tooے
short, we fubfپtuoit them ..groups of extreme poles ..
long and petite, and the difficulty of imitating withے
ے
Stonesے
ے
ے


PRELIMINAIR E. xvij
ے
ْ Stones! The horifoutale situation of the beams had caused the architraves to reject, in place of which we can paffer with an oppof ected peach, foolish stone arches crazy for lesevoutese, which crisscross & coalesce in different ways,ے
imitating in this way the barrel arbors, which are made <the branches of trees folded in a circle from one side to the other.
ے
The very outline of the cylindrical cradles having seemed too childish to them, that is to say, making too much effort to spread the walls, the Archiceeles of these times make their ceimres by two arcs of equal circles, but of different centers, in the center deffein to keep the slopes faster, & by this means to reduce this effort by making them thinner & lighter: they still cross them by other parts of vau..etes, which form quantity of bankrupt angles, whose stops were hidden & fortified by ribs of warheads, archesے
doubleaux, tiercerons, & formingets, of which they formed an infinite number of compartments, aboutiffans fouvent to butts of fuf lamps hung in the air.ےAll these intertwined naiffances, and the interferences of the moldings required great intelligence
in the Art of the Cup of Prides;ےwhere I guess,
that it is to the Gothic Architecture that we must relateے
the origin, or at least the adolescence of this Art.ےMy spoke
ے
ے
However, apart from the fact that it does not refute from ancient Monuments and where it was put into use, only for very simple features; it is only in the enumeration that VITRUVE makes connoiffa..these records to an Archicette , he does not speak of that of the Cupے
der Pierres;ےindeed, the noble limplicity of the Architecture of the Elders did not exercise much the skill of the Appareillers,
who preferred only cylindrical or peripheral vaults to drive.ےThe formation, on the contrary, of a large number of bifarre & difficult figures, who preferred to be at least in the Gothic Arch, gave them reason to imagine others, to take advantage of the irregularity of the locations.
Buildings, or fupple on lack of space.ےLesein, gles, for example,.ے.which doesn?t go away!
ے
VSے
ے
ے


: xviij SPEECHESے
to practice doors there, did not prevent that there was vaultedے
fan paffas smother them, which seems at first sightے
contrary to solidity;ےwe had cabinetry rairly worn
horns to make up a free space behind;ےwe screwed
efcaliers in endless ways, & we imagined so manyے
of chofes unknown to the ancients, which we found very matterے
to compile Books.ے
PtttLIBERT DE LORME, Chaplain of Henri II, is said to beے
the first who heard of it, not expressly, but by occafionے
clans fon Treaty of Architecel: ure, which he published in 1567;ےwe see
that this date is not very old;ےMATHURIN JoussE produifit
some Traits in my Book titled Secrets d'Archite‚fore,ے
printed at La Fleche in 1642. Father DERAND, the following yearے
, put this Art in all ful exten <hle for the Workers;ے
BossE, (the same year) gave a completely different fifteme, which heے
tenoit of DESARGt: Es, which, for its obscurity & noveltyے
of my language, was not tasted.ےFinally M. DE LA RuE, in
'J 728, restored some of the features of Fr. DERAND, with someے
other new ones.ےAll these Authors have produced only one
simple practice devoid of all evidence.ےFather DECHALLES
in 1672 was the first, & was the feudal until preferred, whoے
added demos;ےbut the Treaty of Lapidumfec-
1ione, inferred from my great course in Latin mathematics,ے
only prefers an extract from Father Derand, which he sometimes hasے
copied until mistakes, as we will see in fonے
location.ےHe seems to have completely ignored the Theory of
curves with double curvature, which very often repulseے
the meeting of the furfaces of various vaults, with the stops ofے
their straddles.ے
After seeing all these differences or swimming, it seemed to me thatے
still has some more n, games to do.ے
First, that it was about giving a connoiffanceے
exatl: c of the nature of the curved lines which fe formem at the edgesے
arches, both on their faces and at the interface of the does,ے
of those that make up several parties.ےwho cross,
: xviij SPEECHESے
to practice doors there, did not prevent that there was vaultedے
fan paffas smother them, which seems at first sightے
contrary to solidity;ےwe had cabinetry rairly worn
horns to make up a free space behind;ےwe screwed
efcaliers in endless ways, & we imagined so manyے
of chofes unknown to the ancients, which we found very matterے
to compile Books.ے
PtttLIBERT DE LORME, Chaplain of Henri II, is said to beے
the first who heard of it, not expressly, but by occafionے
clans fon Treaty of Architecel: ure, which he published in 1567;ےwe see
that this date is not very old;ےMATHURIN JoussE produifit
some Traits in my Book titled Secrets d'Archite‚fore,ے
printed at La Fleche in 1642. Father DERAND, the following yearے
, put this Art in all ful exten <hle for the Workers;ے
BossE, (the same year) gave a completely different fifteme, which heے
tenoit of DESARGt: Es, which, for its obscurity & noveltyے
of my language, was not tasted.ےFinally M. DE LA RuE, in
'J 728, restored some of the features of Fr. DERAND, with someے
other new ones.ےAll these Authors have produced only one
simple practice devoid of all evidence.ےFather DECHALLES
in 1672 was the first, & was the feudal until preferred, whoے
added demos;ےbut the Treaty of Lapidumfec-
1ione, inferred from my great course in Latin mathematics,ے
only prefers an extract from Father Derand, which he sometimes hasے
copied until mistakes, as we will see in fonے
location.ےHe seems to have completely ignored the Theory of
curves with double curvature, which very often repulseے
the meeting of the furfaces of various vaults, with the stops ofے
their straddles.ے
After seeing all these differences or swimming, it seemed to me thatے
still has some more n, games to do.ے
First, that it was about giving a connoiffanceے
exatl: c of the nature of the curved lines which fe formem at the edgesے
arches, both on their faces and at the interface of the does,ے
of those that make up several parties.ےwho cross,


PRELIMINAIR E. xixے
ے
to f‡avoir draw them fur plans when it e .. poffible, or fu_re
ے
_
ے
curved furfaces, when these ltgnes do double curl, ure,ے
how confused: the first novelty of this Treaty.ے
ے
The faconde will make the corre‚lion of the mistakes of several years ?ے
cie ns traits.ے
ے
The third, that of the conftruel: ion of several chan--ے
aged, & some who have not yet appeared.ے
ے
I can count for the fourth novelty, @ ‚monfira ?ے
traits, because Fr. DECHALLES only preceded meے
Latinے
but not in Fran‡ois, strong only to fervor meے
ے
,ے
ے
of the experience of JoussE, the Secrets d'Archite‚lurc do everything ?ے
fully disclosed.ے
ے
The novelty of this Art & the difficulties it contains, engageے
the Archite‚l: es of the last two fiecles to look forے
occafions to parade their science, perfuad‚ querien could not better make them commendable, than theseے
Bold works where you can't help but admire theے
Cup of Stones;ےstrong they are keen to do even
fans ignored.ےI have vC1 the third of a square tower, that we can
to make carry bottom, foutenue by the cut fire of a platform. creeping strip, which raised an angle in the air, & muchے
feminable temerities.ے
ے
The Archite‚l: es of our time no longer finding so many ..aifonے
to be admired by a knowledge that has become more common,ے
or perhaps become fainter, banished all these boldness.
bifarres, which have no other beam than that of their exe
ے
ے
''ے
ے
cution, & which non-feulement contribute nothing to the decorationے
buildings, but still make them harmful, inے
what they increase the efforts & the load;ے..in effect
not suitable for implementing the overhang lines, such asے
the fallopian tubes, which are forced to abolish them, orے
for some clearance, or to avoid depenfe & in
ے
ے
..modity to take the place from the foundations.ے
I would add again, that it is rather necessary to confuse the good tasteے
than to be scarce and difficult in <?. uvragcs,ے
ے
C lJ.ے
ے
ے


: xx SPEECHESے
ے
what are our Archite‚l leaning towards? Modern, runningے
new: The meeting & integration of differentے
vaults do not always have a good effect.ےA cloister arch
, for example, of a slightly concave circular painter,ے
glasses, & stuffed with a cul-de-four, as seen inے
a Chapel of the Eglifc of St. Sulpice, is worseے
than a less compacted vault.ےCylindrical glasses which
cross a portion of a fheroid vault, or vault of a furbaiified oven,ے
do not prefer very closely, because the ordersے
overhang paroiffent droerfles, that is to say, leaning toے
right & left, as can be seen at the sameے
Church of St. Sulpice;ےthis deformity decreases, when the telescope
is seen from above, and further away, as in St.ے
Roch;ےbut it has not been completely removed, and we cannot
the nature of the curve, which is not in a plane, as weے
will see it in the course of the first Book.ے
ے
Finally we can still notice, that the circular vaultsے
crossed by two cradles that fe cross, on a nude air &ے
imperfect, fi they do not divide by a horifontal cornice,ے
which subtracts the fegment from fphere, & puts it, soے
say, apart from plumes;ےwe see the need for it at the Novitiate
of the Jefuites, in Paris.ےIt would take too long to search for
double vaulting competitions, which never failے
eye fans the fecours of some correaif, although do it folidelyے
& in the rules of good con! l: ru‚lion.ے
ے
These remarks are more useful to the Archite‚l: ure Civil than to theے
Military, where we neglect beauty for the sake of solidity;ےhe
It would not, however, be bad for the Engineers toے
study of the Civic Architecture;ےshe efi necessary to the conftruaion
of military buildings, which they are responsible for inے
Towns of War, such as Cafernes, Magafins, Hospitals, Lo ..ے
gems of the General Staff, & even: sometimes Eglifes,ے
Forts & Citadels, which are the same as the Buildingsے
Civilians, of which Hs differs only in name.ےThey can even,
when the Court sees fit, take the Bƒ "'.'ے
ے
ے
ے


p RELIM l NA l R E. XX)ے
public civilians;ےbut they should never fe m..ler
those of Individuals, of whatever quality they may be.ے
Firstly because being King's officers, both in Annuale rest and in work; * it is fairness that they are different,
make the loifir they may have to get into the Cabinet of: ::; ..
u ,, ..: dt :;
S..iences q..i neceffai..es, .. Hi..oriques des des;: u; "ce; =
Seats, which can provide them with ideas to put them f..s, mih:ے
‚ dr ْ ْ t 'd Lr {d fi' ? E rd 11a ftmejlrien cat e 1ervir ut1 aement a werentes e mations. n 1econ folidum reے
place, because nothing so slanders the Engineers, as these for-flip7ndiun;
d ْ ْ lrrd, d 'i ˆ & accipere .tes occupations which are 1ont 1oup <ioneer e views mter t, Tite-Liv-c,ے
compromise them with Workers or Paymen, who re-1 ? 1 ? 0 ? s,ے
throw out the faults emanating from their ignorance, orے
the whim of the Owner;ےthe frequent examples that we see
should correct people who are too informal.ےFinally because!
mHant of Civil Archite‚lure, they appear to be fortifying from the Mid-
litaire & nourish disdain;ےthat the sword people have for those
which mix J \ ll‚chaniques Arts.ےIt is not that there is
in the fervice of noble occupations: the Infant Officer
terie must defend small hay from the cleanliness of wild
dats & cafernes, that of Cavalry to that of the stablesے
& horses, Marine?s refit & conftru‚lionے
Vaiifeaux, that of Arcillerie with wheelwrights; gcs & forgese,ے
&! Engineer in all the Arts which are related to that of ba-
shoot ;ےthese functions would have by themselves some sort of ْ
v. it being against the prejudice of the world, fi it was not agreed inے
the rules of honor, that there is nothing abjeel of all thatے
concerns the fervice of the King in the Military State: the Engineersے
must enclose in these terminals, and let the Architeetureے
Civil to those who make it profeflion ..ے
El iijے
p RELIM l NA l R E. XX)ے
public civilians;ےbut they should never fe m..ler
those of Individuals, of whatever quality they may be.ے
Firstly because being King's officers, both in Annuale rest and in work; * it is fairness that they are different,
make the loifir they may have to get into the Cabinet of: ::; ..
u ,, ..: dt :;
S..iences q..i neceffai..es, .. Hi..oriques des des;: u; "ce; =
Seats, which can provide them with ideas to put them f..s, mih:ے
‚ dr ْ ْ t 'd Lr {d fi' ? E rd 11a ftmejlrien cat e 1ervir ut1 aement a werentes e mations. n 1econ folidum reے
place, because nothing so slanders the Engineers, as these for-flip7ndiun;
d ْ ْ lrrd, d 'i ˆ & accipere .tes occupations which are 1ont 1oup <ioneer e views mter t, Tite-Liv-c,ے
compromise them with Workers or Paymen, who re-1 ? 1 ? 0 ? s,ے
throw out the faults emanating from their ignorance, orے
the whim of the Owner;ےthe frequent examples that we see
should correct people who are too informal.ےFinally because!
mHant of Civil Archite‚lure, they appear to be fortifying from the Mid-
litaire & nourish disdain;ےthat the sword people have for those
which mix J \ ll‚chaniques Arts.ےIt is not that there is
in the fervice of noble occupations: the Infant Officer
terie must defend small hay from the cleanliness of wild
dats & cafernes, that of Cavalry to that of the stablesے
& horses, Marine?s refit & conftru‚lionے
Vaiifeaux, that of Arcillerie with wheelwrights; gcs & forgese,ے
&! Engineer in all the Arts which are related to that of ba-
shoot ;ےthese functions would have by themselves some sort of ْ
v. it being against the prejudice of the world, fi it was not agreed inے
the rules of honor, that there is nothing abjeel of all thatے
concerns the fervice of the King in the Military State: the Engineersے
must enclose in these terminals, and let the Architeetureے
Civil to those who make it profeflion ..ے
El iijے


xxŒŒے
ے
t ...!ے
'fLJ..ffJ' .. l'R'b? "ti..l''IJ..lQJ,. (PR \, Z:.ے
ے
ے
ee, r,: .. & .......... Eoe..fi / 1 .. .. .... s .......... 136 .. <? -e .... Gے
ے
.. = ...... پtJ ............ f: پ!)ے
ے
TITLE TABLE 1ے
RESے
ے
DUPREMIERTOM E.ے
ے
DISCOURSPRELIMINAIRE S.ے
ے
ّ
ے
1. UR.ےthe usefulness of Theory in Rela-S Arts
tifs at Archite‚ture.ےPage j
.2 ّ.ےThe expofition of the fu jet in question.ےjx
ے
3 ّ.ےFrom the origin of the Cup of stones, & of the use
ے
that we should do.ے.xپj
ے
BOOK I.ے
ے
From the figure of the fe‚lions of the bodies cut byے
planes, or penetrated by madmen.ےWhy the connoiffance
is necessary in Architecture.ے1
ے
ے
From the figure of vaults in general compared to that ofے
ے
regular bodies.ے4
ے
From accidental variations to vaults, compared toے
those of the bodies.ے
ے
FIRST PART.ے
ے
CHAP.ے
ے
Fe‚lions of bodies by plans.ے
ے
I.ے
ے
Sections of the .fphere.ےS
ے
CHAP.ے/
ے
II.ےSections of cones cut by plans.ے10
Definitions of remarkable points & lines inے
ے
the fe‚l: conical ions.ے1 Œ
ے
Expofition of some properties of the led linesے
inside & outside the corneque fe‚Hons,ے
ے
abfciffes & ordinates.ے16
ے
Particular properties in rellipfe.ے1
: 3ے
ے
Tangents of conical fe‚Hons.ے19
ے
Pe some differences of pofپion of the fe‚ٹions coni
ے
ے
ques in these cones fcalenes.ے: 20
ے
ے
ے


TITLES.ے: Xxپj
ے
THEOREM I. The plane elliptical f ettion.ےmade in
the interval of two concentric cones & f embla ..ے
bleeds, as heard by the concave & convex fur / aces of aے
hollow cone of equal equalizer, and a compact crownے
by two circumferences of elپpfes which are not equidifting, & which cannot be concentricے
that in fcalenes cones, when the fairy isے
perpendicular to the axis.ے.2
2ے
ے
ے
THEOR.ےHe.ےA given conical fe‚lion can be cel
ے
ے
the of an infinity of different cones.ے2>
ے
CHAP.ےDesfe‚lions of cylinders cut by planes.ے28
ے
THEOR.ےIII.ےThe feerion hovers of cylinder efpeces
ے
III.ے
ے
which have for bafe a parabola or a hyperbola,ے
ے
is a conical feltion with the same effect.ے3
1ے
ے
ے
THEOR.ےIV.ےThe fe‚ٹion of a hollow cylinder whose ..
pa! feur eft: equal everywhere, cut by a plane which is not parallel to fa bafe, eil: a crown of ellipfeے
comprified by two concentric and adjustable femalesے
, but not equidifting, except theے
counterfeit f eaion in f calenes cylinders, whereے
it is a crown of a circle.ے3 3
ے
Flat fe‚lrons of quefquer body regularly
ے
.CHAP.ے
ے
irregular.ے3>
ے
IV.ے
ے
THEOR.ےV. The fairy tale of a fheroid & a conoid
regular, cut by a plane perpendicular to fonے
axis, is a circle;ے& if it is parallel or oblique,
she is an ellipf.ے3 6
ے
THEOR.ےVI.ےThe feerion of an annular cylindrical body,
whose axis is curved in the shape of a circumference.ے
circle rcnce, & which: eft: cut by a perpendicular planeے
to whoever hooks by the curved axis, eftے
a fourth-order oval.ے39
ے
ے
Fairies of the corner-conoid cut by plans.ے42
ے
TH EOR.ےVII.ےIf the corner-corner is cut by a plan perpendicular to that of the parallelogram by
the axis, & parallel to one of its sides, the fairy willے
a re-angle triangle.ے1 ْ 4
ے
T1-moR.ےVIII.ےIf the plane cutting the corner conoid is
perpendicular to the parallelogram by the axis, & paralldeے
all corner head circle, the fora fe‚tionے
ے
ے


xxjv TABLEے
an ellipfo.
Application to use, & remark for a faultے
similar in the line of a modern Author.ے
44ے
from ap-
54ے
SECOND PART OF THE FIRST BOOK.ے
FEEL: ions made at the forface of bodies by the penetration of other bodies.ے5 7
:.ے, Of the nature of the feral fe‚rions by the mutual penetration of the pheres, cones & cylinders.ے5 8
CHAP.ےDes J: ‚liom Jol, des des Jpheres, & first of all
V. their variations.ے63
Notet..eTHEOR.ےVII.ےThe reveling curve of the f..ite fe‚lion
if there is by the furfaces of two spheres that feے
{auNoے
d41d penetrate, eft the circumference of a circle.ے64
c: s de..x ee / eTHEOR, VIII.ےThe fe‚lion made by the meeting of the fur'Di
ei) dreams.ےfaces of a sphere & a straight cylinder, whose axis
paOEe by the center of the sphere, is a circle.ے6>
THEOR, IX.ےThe fe‚lion made by the meeting of a
fphere & a fcalene cylinder, whose axis pa! fe parے
the center of the sphere is an elliptical.ے66THEOR.ےX. The fe‚tion made by the meeting of the furfaces
a sphere & a right cylinder which penetrates itے
of any circumference, & whose axis doesے
paOEe not through the center of the sphere, eft an ellipfimbre.ے
71 Note for the difference in cases which may
worm in fcalenes cylinders.ے77THEOR.ےXI.ےThe fe‚l: ion made by the penetration of a
cylinder which enters the sphere only in one par.ے
tie circumference, is an el, Iimimim compo ?
fairy.ے78
From the meeting of the furfaces of the spheres with that of the cones.
THEOR.ےXII.ےThe fe‚tion made by the meeting of the furfaces
a sphere & a right hand dom raxeے
paffe through the center of the sphere, is a circle.ے82THEoR.ےXIII.ےThe fe‚l-ion made by the meeting of
furfaces of a sphere & a cone fcalene of whichے
the axis pa! fe by the center of the sphere, is an elliے
pfo‹dimbre 1xxjv TABLEے
an ellipfo.
Application to use, & remark for a faultے
similar in the line of a modern Author.ے
44ے
from ap-
54ے
SECOND PART OF THE FIRST BOOK.ے
FEEL: ions made at the forface of bodies by the penetration of other bodies.ے5 7
:.ے, Of the nature of the feral fe‚rions by the mutual penetration of the pheres, cones & cylinders.ے5 8
CHAP.ےDes J: ‚liom Jol, des des Jpheres, & first of all
V. their variations.ے63
Notet..eTHEOR.ےVII.ےThe reveling curve of the f..ite fe‚lion
if there is by the furfaces of two spheres that feے
{auNoے
d41d penetrate, eft the circumference of a circle.ے64
c: s de..x ee / eTHEOR, VIII.ےThe fe‚lion made by the meeting of the fur'Di
ei) dreams.ےfaces of a sphere & a straight cylinder, whose axis
paOEe by the center of the sphere, is a circle.ے6>
THEOR, IX.ےThe fe‚lion made by the meeting of a
fphere & a fcalene cylinder, whose axis pa! fe parے
the center of the sphere is an elliptical.ے66THEOR.ےX. The fe‚tion made by the meeting of the furfaces
a sphere & a right cylinder which penetrates itے
of any circumference, & whose axis doesے
paOEe not through the center of the sphere, eft an ellipfimbre.ے
71 Note for the difference in cases which may
worm in fcalenes cylinders.ے77THEOR.ےXI.ےThe fe‚l: ion made by the penetration of a
cylinder which enters the sphere only in one par.ے
tie circumference, is an el, Iimimim compo ?
fairy.ے78
From the meeting of the furfaces of the spheres with that of the cones.
THEOR.ےXII.ےThe fe‚tion made by the meeting of the furfaces
a sphere & a right hand dom raxeے
paffe through the center of the sphere, is a circle.ے82THEoR.ےXIII.ےThe fe‚l-ion made by the meeting of
furfaces of a sphere & a cone fcalene of whichے
the axis pa! fe by the center of the sphere, is an elliے
pfoidimbre 1


CHAP.ے
YI.ے
D ES TITLE S. nvے
l: pfo‹dimbre, or a cerde fi elle ell: crazy-contrary.ے
81ے
THEOR.ےXIV.ےThe fe‚tion made by the meeting of fur-
.faces of a sphere & a concnui l‚nctre deے
tome fa circumference, & of which 1 axis does not p: iffeplr the center of ia f phere, eft an ellipfoidimbre.ےYes
the .cone c! l: fcalene, it can be a circle.ے8>
THF—R.ےX V. The fairy made by the meeting of
furl2ces of the sphere & a cone of which 1 axis does notے
pa.lٹ not through the center of this sphere, - & which only 1aے
pe: ietre p: is of any circumference, efi a curveے
Compofee of two portfolios of elipip‹dimbresے
or other curves of the same kind, belongingے
to the circle, to the parabola, or to the hyperbola.ے90
Fe‚lions made by the pen: tntior1 drs cyl, ndres entre 'ے
& with IrJ coner.ے
THEOR.ےXVI.ےThe fe‚tion made by the penetration of
cylinders <the same nature, equal or unequal, of whichے
the axes are equal in length, & parallel in ..ے
tr'eux, eft a parallelograf! lmC, 94'.THEOR.ےXVU.ےThe fe‚tion made by the meeting of
furfaces of two equal or unequal cylinders, of whichے
the axes fe cut perpendicularly or obliquely,ے
& which have an equal & femblable diameter ..ے
ment for a plane by their axes, and an ellipfe;ے
& fi one of the cylinders is straight & the other fcalene,ے
or both fcalenes & equal bafes, sheے
can be a circle.ے9>
THE OR, XVIII.ےThe celebration made by the meeting of
furfaces of two uneven straight cylinders, whoseے
axes fe cut perpendicularly, and is a cycloidimbre.ے
97THEOR.ے_XIX.ےThe fe‚tion made by the meeting of
furfaces of two unequal cylinders, of which the axesے
fe cut obliquely & that fe penetrate, strongے
that one enters the other in any circumference,ے
is a ellipfimbre.ے102.THE: GOLD.ےXX.ےThe fe‚tion made by the meeting of the furfaces
of two cylinders, one of which penetrates the other of any circumference) _perpendicularly ouob ..ے
..ے
CHAP.ے
YI.ے
D ES TITLE S. nvے
l: pfo‹dimbre, or a cerde fi elle ell: crazy-contrary.ے
81ے
THEOR.ےXIV.ےThe fe‚tion made by the meeting of fur-
.faces of a sphere & a concnui l‚nctre deے
tome fa circumference, & of which 1 axis does not p: iffeplr the center of ia f phere, eft an ellipfoidimbre.ےYes
the .cone c! l: fcalene, it can be a circle.ے8>
THF—R.ےX V. The fairy made by the meeting of
furl2ces of the sphere & a cone of which 1 axis does notے
pa.lٹ not through the center of this sphere, - & which only 1aے
pe: ietre p: is of any circumference, efi a curveے
Compofee of two portfolios of elipip‹dimbresے
or other curves of the same kind, belongingے
to the circle, to the parabola, or to the hyperbola.ے90
Fe‚lions made by the pen: tntior1 drs cyl, ndres entre 'ے
& with IrJ coner.ے
THEOR.ےXVI.ےThe fe‚tion made by the penetration of
cylinders <the same nature, equal or unequal, of whichے
the axes are equal in length, & parallel in ..ے
tr'eux, eft a parallelograf! lmC, 94'.THEOR.ےXVU.ےThe fe‚tion made by the meeting of
furfaces of two equal or unequal cylinders, of whichے
the axes fe cut perpendicularly or obliquely,ے
& which have an equal & femblable diameter ..ے
ment for a plane by their axes, and an ellipfe;ے
& fi one of the cylinders is straight & the other fcalene,ے
or both fcalenes & equal bafes, sheے
can be a circle.ے9>
THE OR, XVIII.ےThe celebration made by the meeting of
furfaces of two uneven straight cylinders, whoseے
axes fe cut perpendicularly, and is a cycloidimbre.ے
97THEOR.ے_XIX.ےThe fe‚tion made by the meeting of
furfaces of two unequal cylinders, of which the axesے
fe cut obliquely & that fe penetrate, strongے
that one enters the other in any circumference,ے
is a ellipfimbre.ے102.THE: GOLD.ےXX.ےThe fe‚tion made by the meeting of the furfaces
of two cylinders, one of which penetrates the other of any circumference) _perpendicularly ouob ..ے
..ے


the other ْ fcalene, & whose axes fe the other ْ fcalene, & whose axes feے
', txvj TA BLEے
ے
ے
only at the sides, fans that their axes fe rencon .;ے
ے
trent, efl: an ellipfoidimbre.ے1 OS '
ے
ے
THEOR.ےXXI.ےThe fe‚lion made by the meeting of
furfaces of two cylinders, one of which does not penetrateے
the other than a part of the circumference, & of whichے
the axes are not parallel, and is a compacted ellipfimbr.ے.ے110
ے
ے
Fe‚lions made by the meeting of farfaces of cones-s &ے
ے
cylinders that penetrate.ےI 1 2
ے
ے
.THEOR.ےXXII.ےThe feaion made by the meeting of
furfaces of a cone & a straight cylinder, or a co ..ے
ne & of a fcalene cylinder of ْ same obliquity as ْے
their bafes, whose axes are confused, is a cer
ے
ے
key.ے113
ے
_THEOR, XXIII.ےThe fe‚lion made pat the meeting of
f urfaces of a cylinder & a cone which do notے
of the same nature, that is to say, of which-I'w1 is right &ے
ے
confuse, eftے
ے
114ے
ے
ے
THEOR.ےXXIV.ےThe feetion made by the penetration of a
cylinder & of a cone, whose axes fe coupentobliquement, can be in a feul case an ellipfeplane.ے116
ے
ے
, 'f.HEOR.ےXXV.ےThe fairy made by the meeting of
furfaces of a cone & of a cylinder which penetrate,ے
strong that the axes of these two fe bodies crossے
or are parallel to each other, is a EuJJimbre.ے118
ے
THEOR.ےXXVI.ےThe fe‚l: ion made by the penetration of \ m ?
cone in a cylinder, is an ellipfoidimbre.ے121CHAP.
F‚‚liom made by the penetration of cones emreux.ے12“
YI I. THEOR.ےXXVII.ےThe fe‚lions made by the penetrat ...
two unequal cones (if they are straight) where the sidesے
femblab1es (if they are fcalenes) fe cut at diftancesے
equal of their fommet, make fe‚tions pla .:ے
don't .. 127ے
ے
THEOR.ےXXVIII.ےThe feaion made by the penetration of unequal straight cones, whose axes fe confuse,
or unequal fcalenes cones, whose axesے
fe confused & also inclined to their bafes,ے
is a circle ... ...! 8,ے
ے


, CHAP.ے
ے
YIII.ے
ے
''ے
ے
DEST 1 TRE S .-- it.xvij
ے
THEOR, XXIX.ےThe fe‚lion made by the penetration of two unequal but femblable cones, therefore the
axes & sides are parallel to each other, and a paraboloid,ے
Page 129ے
ے
ے
THEOR.ےXXX.ےThe feaion made by the meeting of
furfaces of two cones which fe penetrate, whoseے
axes are parallel, & whose sides of one of the trianglesے
on the axis, meet that of the other (extended ? ege if necessary) and is a ellipfo‹di1ubre.ے1 30
ے
THEOR, XXXI.ےThe fairy made by the meeting of
furfaces of two cones whose axes .. fe intersectے
perpendicularly or obliquely, in strong that the extended sides of one or the other, do not ren ?ے
not counter beyond us & beyond the fommet of aے
of them 'is an ellietoidimbre.ے13
Iے
ے
ے
TH1 ::: 0R, XXXII.ےThe feai“n made by the meeting of
fur faces of two cones, whose axes fe coupentobliquement, & including one side of pn triangles byے
the axis meets the two of the other .. triangle, which isے
in the same plane, where im sides' being extendedے
beyond the fus de fon fommet, is a hyperboloidimbred in one and the other cone.ے132
ے
ے
..HEOR.ےXXXIII.ےThe fe‚tion made by the meeting of
f urfaces of two cones whose axes are cross-sectionally, & one of the sides of the triangles by the axis ell: parallel to one of the sides of the other triangular of the feaion by the axis of the other cone, is a courtyard ?ے
be equivalently different in each cone;
f‡avoir, a hyperbo1oidimbre in one of the e-ones,ے
& a parabolo-imimbre in the other, according to which oneے
of the two cones furpatre or is furpaff‚ by the otherے
in line with these sides, 13 3ے
Fe‚Jionr j…ites at the fur / ace of .fPhlroides penetrated by spheres, canes or cylinders.ے1 Hr ?
THEoR.ےXXXIV.ےThe feaion made by the meeting of
furfaces of a fheroid with that of a fphere,
of a cylinder & a cone, which penetrate it or whichے
make it penetrated, so that the axes of theseے
bodies are confused, and is a circle.ے1 5 ,;
ے
ے
THEOR, XXXV.ےThe fe.‚t..on made by the meeting of uni
d ij_ے
ے
ے


TABLE..ے
ے
fpl-iete &.ےa spheroid do11t the axis ne ْ pafl "e paii'par ْ
the center of the sphere, is a kind of ellipfo ? tdimbreے
, that is, a double curvature curve,ے
which we can mark, er some confident report to aے
ellipfe.ے1 36
ے
THEOR.ےXXXVI.ےThe fe‚l: ion made by the meeting of ?
furfaces of, a right cylinder & a fpheroid whoseے
the axis is perpendicular to that of a cylinder, dl: aے
cycloimbre.ے1 39
ے
ے
.THEOR, XXXVIIf Fe‚l: ion made pa: t the meetingے
furfaces of a cylinder & a fheroid, includingے
les axes ne fe rencoi; itre.nt pas, eft une efpece d'el
ے
ے
'.,.ے'lipfimbre \ & can' be "ellipfe da-os certain cases.
ے
141ے
ے
.THEOR .. XXXVIII.ےLa fٹ‚l: 1011 meets pat
ے
furfa'ces of a fheroid & a cone whose axisے
meets that of the f-pheroid- ْ perpendicularly orے
obliquely takes in a double curveے
curvature., tell‚ that efttellipfo‹dimbre;ےbut in 1
ے
cenains ْ case-it can be a eupfe ptanٹ.ے142.
ے
''ے
ے
- 'ے
ے
BOOK .. SECON D.ے
ے
'' From the drift of the L, curved genes formed by the je‚lionے
ے
bodies.ے.ےI ff
ے
ے
p;ے'R' E "MIER: & ? p A R. T i E,
ے
ے
De la defaription deJ fe0ions planes fur des plans.ے14;
ے
ے
.CHAP.ےDe.la defcriptlon of the circle-.
ے
I.ے
ے
Pے
P
ROBLEME i.ےBy three given points draw ْ a..arc..of a circle by plufters other points found fans
the center f ecous.ے1 i7
ے
CHAP, '-Delellipfe pumierement c'on {id‚daomme being made.ے
ے
ّ
ے
II.ePROBL.ےII.ےFind 1e.ےthe center, 29. the ? diametrese
conjugates, 3 ّ.ےthe axes, 4 ّ
.ےthe homes of an ellipfe
ے
given. ْے
ے
1> Sے
P.ƒol3, III.ےP.ar iin po-in.t dom1‚, .ienet a tangent to ْ


TITLES.ے
ے
'A given ellipfe.ے
ے
Confident dlipfe like to do.ے
ے
PROBL, IV.ےAny diameter & ord.: Min
given this diameter, find its conjugate.ے
158ے
PROBLEM.ےV. The conjugate diameters being given,
ے
find the axes of the ellipfe.ے119
ے
ے
PROBLEM.ےVI.ےAn axis & a point at the circumference of
ے
the ellipfe ‚tanc given, find the other axis.ے160
ے
ے
PROBLEM.ےVII.ےThe axes of an ellipfe being given, the
describe by multiple points or by movementے
continued.ے162
PROBLEM.ےVIII.ےThe conjugate diameters being given,
tra..er the ellip.fe by several points or by a movement.ے
Continuous fans know the axes and the homes.ے
ے
170ے
ے
PROBLEM.ےIX.ےLengthen or shorten the ellipfes in such
as long as we likeے
the fe‚l: ions of the same cylinder.ے172
ے
By the '! Boleے
?ے
.
ے
,
ے
;PROBLEM.ےX. The axis of a par.aboie & a point ? to fa cir .-. Conference being given, trace it by several points & by a continuous movement.ے176
ے
Of / 'Hyperbole.ے
ے
PROBL, XI.ےThe center ْ, the fommet & a point at the con.
given the hyperbola trick, describe it by more ..ے
ے
proud points & by 'A continuous movement; n179 ْے
ے
_
ے
PROBLEM.ےXII.ےGiven the center, the fommet & u1.e
ordered at hyperbol .., .. on a first fire ... ordiameter & an order, find the af ymptotesے
ے
.ے& 1a describe by several poincs.ے, 1 8 1
ے
PROBLEM.ےXIII.ےFor five given points which do not lie in a drnite line, draw a fairy. 1: any conical ion
by a continuous movement, fans know the axes, the diameters, the centers and the foci.ے1 S 5
ے
Problem.ےXIV.ےTwo touches with the landing points
to a conical fe & ion & the ditel: ionے
of a given diameter being found,ے
points we want from this fan con curveے
noŒtr .. the center of the fe & ion) nor the grande—r of any
ے
.ے
ے
diij