II
I I
(
DOM
288
D 0 0
(15) a = 225( 10 )'- = 100
325 ( 18.02 the radius of the circle.
28)225
224
3602).
10000
7204
.2796
Say then, that the diameter is 36 feet, omitting the very-small fractional part .02.
Then 36 X 3.1416 = 113.976 the circumference of agreat circle.
Therefore 113.976 X 5 = 569.880 feet, the superficialcontent of the dome.
Figure 2.—In order to show the truth of the above rule,for finding the above diameter of a circle, from the two chords,and the distance between them being given ;
Let y — fi, the height of the lesser segment;h = f b, the distance between the chords ;x = b d, the distance from the nearest chord A G, tothe centre i;
C=ab, half the greater chord ag;c = e F, half the lesser chord ;
Then, by the property of the circle, we have
F K = E F a = C 1
and
But
and
also
and
B I X BK = BA 1 =C
vi — y
FK — y + 2x + 2 hbi =y + hbk = y + A + 2 x.
Therefore y X(y + 2a:+2/^) = c , first equation ;
(y + /t) X (y + h + 2 x) — C 2 the second equation;y* 2 x y + 2 h y ■= c' 1 , the first actually multiplied ;y 2 + hy + 2 xy + hy + A 2 + 2 hx = c a , the secondmultiplied.
Then by putting n in the place of x + A in each of theseequations,
the first becomes y 2 + 2 n y — c a
and the second y‘ + 2ny + 2hxz z c 2 — A»
V 1 + 2 n y + ra 2 = c 2 + n 2 by completingthe square of the first. Therefore
first value of y zz (c 2 + » 2 )l — n
y 2 + 2 » y = c 2 — h? — 2 hx second trans-posed ;
therefore y 2 + 2 » y + w 2 = c j — A 2 — 2 h x + n?
y
+ n = (c a — A 2 — 2 h X + W ! )i; the
second
value of y — (°* — “ 2 h x + w 2 )^ — n.
Then by making the first and second value of y equal toeach other, and by taking away the negative quantity— n,which is common to both sides, and squaring the equation,we obtain
c 2 + » 2 = C a — A 2 — 2i* + » !or c 2 z= C 2 — A 2 — 2 h xor 2 h x zz C a — c a — A 2
and consequently x =
‘ — c 2 — A 2 c a — (A 2 -f c 2 )
2 A
2 A
which expression agrees with the rule.
The second rule for finding the radius of the circ t ^oto find the hypothenuse of a right-angled triangle • ^ ^ th 0sides containing the right angle being given, the sq pfOhypothenuse is equal to the sum of the squares osides by the 47th Proposition of Euclid. , of
DOMESTIC ARCHITECTURE, that de P art “r„ g[e irart which relates especially to the design and erec th° s ®fices adapted to private purposes as distinguished ^ flreerected for public uses, more particularly ofployed as private dwellings. Although holding branch 00 ",position in the scale when compared with other ^ D ce ^the art, domestic architecture is of sufficient pro^ 8
the present day to merit the greatest attention ol ^ e ld ^sional man. Amongst the ancients this depart^ 1 j D g ei®
very low position, all the energies of the archite^^
an®
G^tbeir
ployed on the public buildings and temples.would scarcely have been understood amongst tn ng ,'tEgyptians, and but little amongst the earlier ,o°fbuii d !Sprivate dwellings scarcely deserving the name ^ jndiAs luxury increased at Rome , the houses of pr* j n ac c ° gSduals increased in size and magnificence, as wenmodation, and the country-residences of the n'o . flit 1 ?seem to have been buildings of some l m P ortan r0 und'^° Ill jvilla contained thirty-seven apartments on the S uBJ # ,Specimens of Roman houses exist at Hercu ^ ^ yiP^Pompeii, as well as some few elsewhere. Th TJco^
• littl*.
in
area 630 feet in 1 a "a v contains 74 rooms, an'
Of English T) 335 feet in breadth.
this placed tilt meStlC architecture, we needbuildings erected^™ Can scarce ty be applied to any j aflthe buifdi, ^ C of t ,re :r US t0 the reiga of Henryof the style Inf a 6 wil1 be dilated upon w he ” ’-jy, “ 3the Tudor style WI l’ fdfer the name of the reigning s . pre-vailed, all the I Up t0 the P eriod in which tins st t T 0 eimore w less % g6r resi,lenc « in England were ^we refer to’ “ acooun tof the earlier of these p,bet MS - al «o House, Tudor ot^yc.
DOMIPT? C ^ UEE ’ VlLLA > Eoman AncniTBcr^general thn ’i ° r HotnctLij ( domicilium , a 1119,15 fyodW’a more r p a ? e of residence of an individual or Ja time. CS ncted sense, where a person reside ^
VALH, or IIJO J ill
usually raised on a natural or artificial 11101111 a
I
as
most court or hnli;. —_ „ris<
and it Wag Da lower part was vsea d ,e
m0 £ooKc m t'nngeonf ^ the don j° n ' kee P-
serted in stones? 1,^, W00c! ’ about nine inches in
i s 0 f tb " h.mk WaJJ the is used i„ b o'
® Une m Port with the London tem/**’
^or
wood bricks.
, of
a ho 09 "’
passag?£’J Sa xon dor \ the gate
Tile ^ apartment, &c. .rinto
branches, viz.^i’^f f doors Rurally divides ite aper tu^°r opening, which f atlon and proportion of ‘ JtsoO
bricklayer; and ft uter waiIs » beloD Z t0 e tr wh' icb
entrance is to hp min S' of the gate or Jeaf ’ ^Lrte 1111t0 be secured, together with its »PP ur
tment.
,ic 0 -
cor dh*
which appertains to the joiner’s department ^ pe “"id b 0The proportion of the aperture mustto the size and intention of the bull 1 o’ j n g el1 g d 0 "^ 1attended to above every other con8 i deratl °wo, for l 9l ° ^dimensions may be in the ratio of one to 'and from three to seven in those of ^ es3 , S „ a tes- ^,heEntrances are of two kinds ; doors an f o0 t!are used only for the passage of persons for
admit horsemen and carriages. Doors a