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p 191
Prob. 1
293
Upon
a given
strait
line
A.B,
to
make
an equilateral
triangle.
About
the
center
A
with
the
radius
A
B, describe
the
circle
B.C.D
by
article
60, also
about
the
center
B, with
the
radius
B
A, describe
the
circle
A & C
and
join
A.C,
CB
---page break---
p. 192
Prob. 2
294
From
a given
point
A, to
draw
a line
that
shall
be equal
to a
given
strait
line
B.C.
Join
AB,
and
upon
it
make
the
equilateral
triangle
AB
D, produce
the
sides
DA,
DB,
to E
& F,
about
the
center
B,
with
the
radius
BC,
describe
the
arch
CF,
and
about
the
center
D, with
the radius
DF,
describe
the
arch
F.E.
---page break---
p 193
Pro. 3.
295
Two
unequal
strait
lines
A.B.
and
CD,
being
given
to
take
a part
of the
greater
that
shall
be equal
to the
lesser.
From
the
point
A draw
the
line
AE,
equal
to the
line
C.D,
by
2, and
about
the
center
A, with
the radius
A.E,
describe
a circle
cutting
AB,
in F.
---page break---
P 194
Pro. 4
296
To divide
a given angle
A.B.C
into
two
equal
parts,
or to
bisect
it.
On
the
center
B. at
any
distance
BA
describe
the
arch
AC,
on the
centers
A &
C, with
the
distances
A.B,
C.B,
describe
arches
cutting
each
other
in D,
and
draw
B.D.
---page break---
p. 195
Pro. 5
297
To
divide
a given
finite
strait
line
A.B,
into
two
equal
parts,
or to
bisect
it.
About
the
centers
A &
B, with
any
radius
greater
than
half
the
line,
describe
circles
cutting
one
another
in C
& G,
and
draw
CG,
cutting
AB,
in E.
---page break---
p 196
Pro. 6
298
To erect
a perpendicular
to a
given
strait
line
A.B,
at a
given
point
in it
C.
About
the
center
C, at
any
distance
describe
a circle
cutting
the
given
line
in D
& E,
about
the
centers
D & E,
with
any
radius
greater
than
CD
describe
circles
cutting
in F,
and
draw
C.F.
Otherwise
Above
the
center C
describe
a circle
AD
& B,
on
the
cen-
---page break---
p. 197
Pro. 6
298
center
A
cut
the
circle
in D,
on
the
center
D
describe
the
arch
F.E,
and
on E
cut
that
arch
in F,
all
with
the
same
radius,
and
draw
C.F.
---page break---
p 198
Pro. 7
299
From
a given
point
A, to
let
fall
a perpendicular
upon
an
infinite
strait
line
B.D.
About
the
center
A, describe
a circle
at
pleasure
cutting
the
given
line
in C
& E,
about
the
centers
C & E
with
the
same
radius
describe
circles
cutting
one
another
in
F, &
draw
A.F
cutting
B.D
in G.
+
---page break---
p. 200
Pro. 8
300
To
make
a triangle,
whose
sides
shall
be equal
to three
given
strait
lines
AB,
B.C,
CD;
provided
any
two
of
them
taken
together
be
greater
than
the
third
About
the
center
B, with
the
radius
B.
A, describe
the
circle
A.E.
F, on
the
center
C, with
the
radius
C
G, describe
the
circle
D.G.F
and
draw
BF,
FG.
---page break---
p. 201
Pro. 9.
301
At a
given
point
A, in
a given
strait
line
AB,
to
make
an
angle
equal
to a
given
Angle
C, D, E.
Make
A B
equal
to
D
C, by
problem
3, erect
B
F, CE,
perpendicular
to, AB,
DC,
each
to each
by problem
6, make
BF,
equal
to CF,
and
draw
A.F.
+
---page break---
p. 203
Pro. 10
302
Through
a given
point
A, to
draw
a line
parallel
to a
given
strait
line
B.C.
In
the
given
line
take
the
point
D at
pleasure,
and
join
AD,
make
the
angle
DAF
equal
to the
angle
ADE
by
problem
9,
and
the
thing
is
done.
+
---page break---
p 205
Pro. 11
303
To
describe
or
make
a
square
upon
a
given
strait
line
AB.
Draw
AD
at
right
angles
to
AB,
by
prob
6,
make
AD
equal
to
AB
draw
D.C.
parallel
to
AB,
and
BC
parallel
to
AD
by
problem
10.
---page break---
p. 206
Pro. 12
304
To
divide
a
given
strait
line
AB,
into
a
proposed
number
of
equal
parts
Draw
AC
at pleasure,
and
BD
parallel
to B.
C, by
Problem
10, in
AC.
BD,
take
the
proposed
number
of equal
parts
of any
length
namely
A
E, E
F, F
C, B
G, G
H, H
D, all
equal
to one
another,
and
draw
EH,
FG,
cutting
the
given
line
in
J & L
---page break---
p 207
Pro. 13
305
To
divide
a
given
strait
line
AB,
in a
given
ratio
Let
the
given
ratio
be
that
of M
to N,
draw
AC
at
pleasure,
and
in it
take
AD
equal
to M,
and
DC
equal
to N,
join
B.C,
draw
DE
parallel
to C
B, &
E will
be the
point
required.
---page break---
p. 208
Pro. 14
306
To
find
a
third
proportional
to
two
given
strait
lines,
AB,
BC.
Let
AB
and
BC
make
a
strait
line,
draw
AE,
at
pleasure,
and
in it
take
AD
equal
to
BC,
by
problem
3, join
BD,
draw
CE,
parallel
to
BD,
and
DE,
will
be the
line
required.
---page break---
p 209
Pro. 15
307
To
find
a
fourth
proportional
to
three
given
strait
lines
AB,
BC,
CD.
Let
AB
and
BC,
make
a
strait
line,
draw
AF
at
pleasure,
and
in
AF
take
AE,
equal
to
CD,
join
BE,
draw
CF,
parallel
to
B.E,
and
EF
will
be
the
line
required.
---page break---
210
Pro. 16
308
To
find
a
mean
proportional
between
two
given
strait
lines
AB,
BC.
Let
AB
and
BC
make
a
strait
line,
divide
AC
equally
in
D, by
problem
5, about
the
center
D,
with
the
radius
DA
or
DC
describe
a
semicircle
ABC
and
draw
BE
perpendicular
to AC,
by
problem
6
---page break---
p. 211
Pro. 17
309
To
make
a
square
equal
to a
given
rectangle,
A,
B
CB
Produce
AB
to E,
make
BE
equal
to
BC,
bisect
AE
in
F about
the
center
F describe
the
circle
AG
E, continue
EC
to G
and
upon
EG,
describe
the
square
BG
HI.
---page break---
p. 212
Pro. 18
310
To
make
a rectangle
upon
a
given
strait
line
GH,
that
shall
be equal
to a
given
triangle
AB
C.
Produce
AB
to D,
make
BD
equal
to the
given
line,
bisect
A
B in
E, erect
EF at
right
angles
to A
B,
draw
B.G
FH
parallel
to E
F, &
LCI
parallel
to
AD
cutting
HG in
K, join
DK,
which
continue
to
and
draw
FH
parallel
to
ED,
then
GH
Prob
18
concl
is the
angle
required.
---page break---
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posology |
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083 |
geometry iii |
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