Page images
PDF
EPUB

XXX. Given tt'-ss'; ; L-l.

XXXI.

XXXII.

XXXIII

XXXIV.
XXXV.

XXXVI. XXXVII.

XXXVIII.

XXXIX.

XL.

XLI.

XLII.

XLIII.

XLIV.

XLV.

XLVI. XLVII. XLVIII,

A XLIX.

L.

LI.

LII.
LIII.

... LIV.

(v—v′) · (s—t); (s—t)÷(s—s'); and

A-C.

a-c; rad. of O through A, C and centre of in. O; and bx rad. of O touching b and a, c produced.

B, dist. of centres of in. and cir. Os; and their distances from where meets b.

a-c; s-s'; bp a max,

atc; B; and a line from A to cut a Pr.

2S; a-c; and bp a max.

p;

a2-c2; and distance of centre of cr. O from b.

b; B; ma+nc. Or b; B; ma―nc.
A, B, C; and mb+na+rc.

B; dif. of lines to b par. to a and c
from centre of in ; and dif. be-
tween the sum of these parallels and b.
b; p; and sum of lines from A and

C to the middle points of a and c. the ▲ formed by joining centre of grav. with centres of in. and cr. Os. bp; A; and bis. of b.

5-5; A; bp.

a-c; A-C and the dif. of As formed by l.

b; bis. of b; and A-Ca maximum. b; B; and (a+c)xl.

B; a+c; bx (c—a).

B

b; B; ns+mp is given or a max.
; r; and rect. of lines from A and
C to centre of inscribed O.,
b; 3a2+4c2; and B a max.
B; 2S; ac (b+2R).

B; segment of 7. between B and cen-
tre of touching b, and a and c pro-
duced; and ratio of lines from 4 and
C to centre of this and ins. O.
The lines from A, B, C to centre of O
touching band sides a and c pro-
duced.

LV. Given b; B; bis. of b-(a–c).

LVI.

LVII.

LVIII.

LIX.

LX.
LXI.

LXII. LXIII. LXIV.

LXV.

LXVI.

LXVII.

LXVIII.

LXIX.

LXX.

LXXI.

LXXII.

LXXIII.

LXXIV.

LXXV.

b; B; a2-m2 : c2—n2. Pr. where

[ocr errors]

m2, n2 are given 2s.

b; A; and point where 2R from B
meets b.

B; p; and distance from middle point
of b to where p meets cr. O.
b; B: bis. of b× (s-s) a max.
ac; A-C; c2(s—s').

2R; bp a max; ratio of the parts of
2R perpendicular to b below 6 and
above the parallel to b through B.
2R; (a2+c2); and bp a max.
a-c; v-and pr.

segment between the perpendiculars on
i from A, C; a ÷ c; r ÷ (v-t).
B; bp; b2=2rx 2R.

b; B; v. vt. t.

perpendicular from centre of in. O on b; its prolongation to meet bis. of b ; b-1 (a+c—b).

bis. of b; r; R'

a; e; and sms'm' when m, m' are given lines.

B; atc; b-bis. of b.

b; p+a+c; and B a max.

A-C; 1; R'—r.

bis. of b; its distance from the foot of p÷b; p2b a max.

a+c; (s. s2)3; and p2 = s s

(s—s′) . (t—v) ; (a—c). ((s—s')— (a——c)). A--C.

LXXVI. Dadi sa2+c2;r; and segment of cr. O be

[blocks in formation]

LXXXI. XIC v. v; RXp; and distance from cen

tre of cr. to intersection of Z with b.

LXXXII. Given 2S; bp: a-c.

LXXXIII.

LXXXIV.

LXXXV.

LXXXVI.

LXXXVII.

LXXXVIII.

LXXXIX.

XC.

R; ac; s. s' a max.
40-(bis. of b)2; p; axb×c.
b; B; and a+p = b.

(a—c) A—C; b+m when m: 2R,
Pr.

b; B; (a-c). 2R a max.

(a+c); (p+b); B, and when deter-
minable.

28; prolongation of bis. of b to
cir. of cr. ; a2+b2+c2.
b; A-C; m2-n2 a max. when
m and n are the lines from A and
C to middles of a and c.
B; a±c; b±+m, when m is a line
from B, making any with b.
B; 2S; and line from B to divide
b Pr.

R; x'; and A-C a max.

XCI.

XCII.

XCIII.

XCIV.

b

XCV.

XCVI.

XCVII.

XCVIII.

XCIX.

C.

CI.

CII.

CIII.

CIV.

CV.

CVI.

CVII.

CVIII.

[blocks in formation]
[merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

CIX. Given B; side of inscr. 2; axm when m is the portion a between the corner of2 and b.

CX.

CXI.

b; a-c; segment of a between B and perp. from A.

B; b-a; and m+n,

when m is

the perp. from C on c, and n the portion of c towards A.

FINIS.

[merged small][ocr errors]
« PreviousContinue »