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p 215
Pro. 21
313
Upon
a given
strait
line
F.G,
to make
a figure
similar
to a
given
figure
ABC
DE
Join
AC,
AD,
make
the
angle
FGH
equal
to A
BC,
FH
G equal
to A
CD,
HI
J equal
to G
AD
by
problem 9
and
the
thing
is done
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p 216
Pro. 22
314
To
make
a figure
similar
to
a given
figure
AB
CD, &
in the
given
ratio
to it of
M to
N.
Produce
BA to
E, find
AE a
fourth
proportional
to M,
N, and
BA,
by problem
15, upon
the
diameter
EB
describe
the
semicircle
EFB,
draw
AE at
right
angles
to EB,
make
AG
equal
to A
F, and
the
figure
AGH
I similar
to A
BGI,
by
problem
21.
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p 217
Pro. 23
315
Upon
a given
strait
line
AB,
to describe
the
segment
of a
circle,
that
shall
contain
an
angle
equal
to a
given
angle
C.
Make
the
angle
BAD
equal
to the
given
angle
C, draw
AE at
right
angles
to AD,
bisect
AB
in F,
draw
FE,
perpendicular
to A
B, and
about
the
center
E, with
the
radius
E
A or
EB,
describe
the
segment
AG
B.
+
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p 219
Pro. 24
316
The
base
of a
triangle,
the
verticle
angle,
and
the
ratio
of the
sides,
are given —
to make
the triangle
Make
the
Angle
ACB
equal
to the
given
angle,
and
CD
to CE
in the
given
ratio
of m
to n,
join
ED,
and
continue
it
to F,
draw
FA, parallel
to CB,
and
AB
parallel
to
FE.
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p 220
Pro. 25
317
The angles
at the
base
of a
triangle,
&
a line
joining
the
vertex
and
middle
of the
base,
are
given
— to
make
the
triangle
In the
strait
line
AB
assume
DE,
DF
equal
to each
other
make
the
angles
FEG,
EFG
equal
to the
given
angles
at
the
base
each
to each,
join
DG
and
continue
it to
C,
make
D.C equal
to the
given
line,
and
draw
CA,
CB,
parallel
to
GE,
GF.
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p. 221
Pro. 26
318
The
verticle
angle,
a line
joining
the
vertex
and
middle
of the
base,
and
the
angle
made
by the
said
line
and
base,
are
given —
to
make
the
rectangle.
In
the
strait
line
AB
take
DE,
DF equal
to each
other,
make
the angle
B
DC, equal
to the
given
angle
and D
C equal
to the
given
line,
upon
EF,
describe
the segment
of a
circle
that
will
contain
the vertical
angle,
by problem
13, cutting
DC in
G, join
EG, D
F, and
draw
GA, G
B, parallel
Pro 26
conclu.
to G
E, G
F
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p 222
Pro 27
319
The
base
of a
triangle
AB,
the altitude
AD,
and
the ratio
of
its sides
AC, C
B are
given
as M
to N,
to make
the triangle
Divide
the base
in the
given
ratio
of the
sides
at E,
by problem
13, make
EF
equal
to EB,
produce
AB
to G,
find
EG as
fourth
proportional
to AF,
FE, A
E, by
problem
15, about
the
center
G, with
the radius
GE,
describe
the
circle
EGH,
draw
DG
parallel
to A
G, and
join
AC,
CB.
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p 223
Pro 28
320
The
angles
at the
base
of a
triangle,
and
the
sum
of its
three
sides
are
given
— to
make
the
triangle
Let
DE
be the
given
sum
of the
sides;
make
the
angles
DEC,
EDC,
equal
to half
the
given
angles
at the
base
respectively,
by
problems
48, 9
make
the
angle
DCA,
equal
to CD
E, and
the
angle
ECB
equal
to C
ED.
---page break---
p 224
Pro 29
321
To
inscribe
a triangle
ABC,
in a
given
triangle
DEF,
and
make
it equiangular
to another
given
triangle
G
HI.
Make
the
angles
FDK,
DEK
equal
to the
acute
angles
G and
H, each
to each,
join
KE
cutting
DF in
C, draw
CA
parallel
to K
D, CB
parallel
to K
F and
join
AB.
---page break---
p 225
Pro. 30
322
To
inscribe
a triangle
in
a square
A
BCD
and
make
it equiangular
to a
given
triangle
E
FG.
Make
the
angles
BA
H, A
BH
equal
to the
two
least
angles
of
the
given
triangle
E & F,
each
to each
draw
HI
parallel
to
AD,
IK
parallel
to H
A, IL
parallel
to H
B, and
join
KL.
---page break---
p 226
Pro 31
323
To
inscribe
a square
in a
given
triangle
ABC
Let
fall
the
perpendicular
C
D, draw
CE
parallel
to A
B, make
CE
equal
to CD,
join
AE
cutting
BC
in F,
draw
FG
parallel
to B
A, &
GH,
FI,
parallel
to C
D.
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Identifier: | JB/135/083/003"JB/" can not be assigned to a declared number type with value 135. |
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135 |
posology |
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083 |
geometry iii |
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003 |
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copy/fair copy sheet |
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recto |
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46201 |
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