JB/135/083/002

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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

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 ABD, 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.

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 Problem 2, and about the center A, with the radius A.E, describe a circle cutting AB, in F.

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.

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.

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-

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.

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. +

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.

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 BF, CE, perpendicular to AB, DC, each to each by problem 6, make BF equal to CF and draw AF.+

p. 203
Pro. 10
302
Through a given point A, to draw a line parallel to a given straight 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. +

p 205
Pro. 11
303
To describe or make a square upon a given straight 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.

p. 206
Pro. 12
304
To divide a given straight line AB, into a proposed number of equal parts.
divide
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 Ae, EF, FC, BG, GH, HD, all equal to one another, and draw EH, FG, cutting the given line in J & L

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 CB, & E will be the point required.

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---

p. 213
Pro. 19
311

To
make
a
triangle
equal
to
a given
quadrangle,
AB
CD.

Produce
AB
to E,
join
DB,
draw
CE
parallel
to DE
and
join
DE.

---page break---

p. 214
Pro. 20
312

To
make
a
triangle
equal
to
a given
pentagon
AB
CDE

Produce
the
base
AB
both
ways
to F
and
G, join
DA, D
to, draw
EF parallel
to DA

parallel
to
DB,
and
join
FD,
DG

---page break---

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

Identifier: | JB/135/083/002"JB/" can not be assigned to a declared number type with value 135.
Date_1		Marginal Summary Numbering
Box	135	Main Headings	posology
Folio number	083	Info in main headings field	geometry iii
Image	002	Titles
Category	copy/fair copy sheet	Number of Pages	3
Recto/Verso	recto	Page Numbering
Penner		Watermarks
Marginals		Paper Producer
Corrections		Paper Produced in Year
Notes public		ID Number	46201
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