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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.
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.
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
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 AGE, continue EC to G and upon EG, describe the square BG HI.
p. 212
Pro. 18
310
To make a rectangle upon a given strait line GH, that shall be equal to a given triangle ABC.
Produce AB to D, make BD equal to the given line, bisect AB in E, erect EF at right angles to AB, draw B.G FH parallel to E F, & LCIparallel to AD cutting HG in K, join DK, which continue to and draw FH parallel to ED, then GH LK
Prob 18 concl'd
is the angle required.
p. 213
Pro. 19
311
To make a triangle equal to a given quadrangle, ABCD.
Produce AB to E, join DB, draw CE parallel to DE and join DE.
p. 214
Pro. 20
312
To make a triangle equal to a given pentagon ABCDE
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
p 215
Pro. 21
313
Upon a given strait line F.G, to make a figure similar to a given figure ABCDE
Join AC, AD, make the angle FGH equal to ABC, FHG equal to ACD,
HI J equal to GAD by problem 9 and
the thing is done
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posology |
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geometry iii |
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copy/fair copy sheet |
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46201 |
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