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XXX. Given tt'-s'; 1; L.

(0-0). (

st); (st):-(sms'); and

A-C. XXXII. a—¢; rad. of O through A, C and

centre of in. O; and 6x rad. of O

touching b and a, c produced. XXXIII B; dist. of centres of in. and cir. Os;

and their distances from where I

meets b. XXXIV. a=c;sms'; bp a max, XXXV. atc;

B; and a line from A to cut a

XXXVI. 28; 2-C; and bp a max.

Pia’----?; and distance of centre of

O from b. XXXVIII. b; B; matnc. Or b; B; ma--nc. XXXIX. A, B, C; and mb+na+rc. XL. B; dif. of lines to 6 par. to a and c

from centre of in 0; and dif. be

tween the sum of these parallels and b. XLI.

; P ;

and sum of lines from A and

C to the middle points of a and C. XLII. the a formed by joining centre of grav.

with centres of in. and cr. Os. XLIII.

bp; A; and bis, of b. XLIV. S-; A; bp. XLV. a-ciA-Cand the dif. of As formed



by l.




b; bis. of b; and A-Ca maximum.
b; B; and (atcxl.
B; atc; 6X (-a).
b; B; ns+mp is given or a max.
B;r; and rect. of lines from A and

C to, centre of inscribed 0,,
b; 3a+4c?; and B a max.
B; 2S ; ac (6+2R).
B; segment of l. between B and cen-

tre of O touching b, and a and c pro-
duced; and ratio of lines fron) A and

C to centre of this O and ins. O. The lines from A, B, C to centre of O

touching b and sides a and c produced.

." LIV.


LV. Given b; B; bis. of 6—(a–c).
LVI. b; B; -m2 : 02-1?. Pr. where

ma, na are given O’s. LVII. b; A; and point where 2R from B

meets b. LVIII. B; p; and distance from middle point

of 6 to where p meets cr. O. LIX. b; B : bis. of bx (sms) a max. LX. ac ; A-C; c= (

ss). LXI. 2R; bp a max; ratio of the parts of

2R perpendicular to y below b and

above the parallel to b through B. LXII. 2R; (a? +c298; and bp a max. LXIII. a-C; 0–6 and ptr. LXIV. segment between the perpendiculars on

1 from A, C; arc; r: (u—). LXV. B; bp; b=2r X2R. LXVI. b; B; v.vot.t'. LXVII. perpendicular from centre of in. O on

its prolongation to meet bis. of b;

1-4 (atc-6). LXVIII. bis, of b;r; R' LXIX.

a ;

; and sm-Es'm' when mm' are

given lines.
LXX. B; atc; b-bis. of b.
LXXI. b; ptatc; and B a max.

A--C;1; K-r.
LXXIII. bis. of b; its distance from the foot of

p+b; p2b3 a max. LXXIV. a+c; (s.s) ; and p? = 's's LXXV. (ss).(t—v); (a--c). (ss)-(a--c)).

A--C. LXXVI. a'+c;r; and segment of cr. O be

low b. LXXVII. B; 2S; b+p. LXXVIII.

B; atc; 1 Ep2.
LXXIX. atc; 6+p; and B a max.

LXXX. L;r; A-C..
LXXXI. vo v ; RXp; and distance from cen-

tre of 'cr, Ó to intersection of
I with b.


LXXXII. Given 2S; bpi d-c. LXXXIII. R; a--C; s. s

a max. LXXXIV. 262—(bis. of 6); P; axbxc.

LXXXV. b; B; and a+p= b. LXXXVI, (a-c) A-C; 6+m when m : 2R,

Pr. LXXXVII. b; B; (ac). 2R a max. LXXXVIII. (a+c); (P+6); B, and when deter

minable. LXXXIX. 28 ; prolongation of bis. of 6 to

cir. of cr. O; a2 +62 +c. XC.

b; A-C; m?. -na a max. when

mand n are the lines from A and

C to middles of a and c.
XCI. B; a£c; błm, when m is a line

from B, making any < with b. XCII. B; 25; and line from B to divide

6 Pr.

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

b; A; and axca max. B being

obtuse. XCV.

1 ; l' the bisector of supplement of

vertical ; cd. XCVI.

b; B; l. (s—s)? a max. XCVII.

2S; B; axc. XCVIII.

b; A-C; bis. of b. XCIX.

axc+mXn, or a Xc; mXn, when m, n are the lines from A and C to the centre of

insc. O. C. b+c; b-a; bp either given, or a

B; 19;



a, b, c to pass through three points.
B; R; p.
b; a line from B to a given point


in b; B a max.
A-C; bis. of b; 2SX (a +246) X

pa max.
2S; B; bp a max.
a; c; bis. of 6 Xb a max.
b; A: 1.
l; and


from A, C on it.



CIX. Given B; side of inscr. O'; axm when

m is the portion a between the

corner of o’ and b. CX.

b; amc; segment of a between B

and perp. from A. CXI.

B; b-a :- and mtn, when m is

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


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