Geometrical Problems Deducible from the First Six Books of Euclid, Arranged and Solved: To which is Added an Appendix Containing the Elements of Plane Trigonometry ...

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J. Smith, 1819 - Euclid's Elements - 377 pages
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Contents

From the circumference of a given circle to draw to a straight
22
a given angle and from each of them segments be cut off having
23
to the concave part of the circumference making equal angles with
25
circle
28
If from the extremities of the diameter of a semicircle per
34
line given in position a line which shall be equal and parallel to
36
given line
37
of intersection a circle be described cutting them the points where
42
triangles equiangular and equal to the given triangle
43
pendiculars to their common diameter be produced to cut the cir
47
other extremity of the diameter the part without the circle may
52
being in the circumference of the other and any line be drawn from
58
To determine a point in the arc of a quadrant from which
63
parts
65
be drawn perpendicular to the base and from the greater segment
69
to meet the tangents drawn from the extremities of the bisecting line
75
in the circumference of one of them through which lines are drawn
80
which are perpendicular to each other in such a manner that
86
the whole line and one of the parts as diameters semicircles
87
From a given point in the diameter of a semicircle produced
91
the other two sides
92
triangle to describe on the other sides segments similar to that
94
drawn to the opposite sides making equal angles with the base
97
If two exterior angles of a triangle be bisected and from
103
triangle meet in the same point
109
To draw a line from one of the angles at the base of a tri
115
To bisect a parallelogram by a line drawn from a point in
121
of any four lines which can be drawn to the four angles from
126
If the sides of an equilateral and equiangular pentagon
134
perpendiculars be let fall on every side the sum of the squares
140
Between two lines given in position to draw a line equal
177
mainders may have a given ratio and the sum of the squares of
179
To describe a rectangular parallelogram which shall be equal
185
two right angles a circle may be described about
191
If an equilateral triangle be inscribed in a circle the square
193
given parallelogram
199
points and touch a given straight line
202
touching a given circle
208
Through two given points within a given circle to describe
213
A trapezium being given two of whose sides are parallel
219
be drawn to cut one another the greater segments will be equal
220
drawn parallel to the other intersecting the adjacent side of
225
circle be produced till they meet the three points of intersection
231
a circle is greater or less than a right angle by the angle contained
232
If a triangle be inscribed in a semicircle and a perpen
238
described on the sides of a rightangled triangle is in the middle
244
Those segments are also in the duplicate ratio of
250
through the points where they meet that line and the point in
256
drawn to any point in the circumference and meeting the perpen
261
If the exterior angle of a triangle be bisected by a straight
262
from the centre the sum of the squares of the two lines drawn from
264
angles the length of which is the double of a mean proportional
268
be drawn to any point in the circumference meeting a diameter per
273
arc of a circle two parallel lines be drawn the former terminated
278
described with radii equal the former to the side and the latter
283
the point of contact another be described with the same radius
289
other two sides to construct the triangle
295
bisecting the vertical angle
312
by the perpendicular the sum of the squares of the sides and
319

Other editions - View all

Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...
Miles Bland
Full view - 1821
Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...
Miles Bland
Full view - 1819
Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...
Miles Bland
Full view - 1819
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Common terms and phrases

ABCD base centre chord circle circle ABC circumference common contained determine diameter difference distance divided double draw draw any line equal equiangular Eucl extremities figure given angle given circle given in position given line given point given ratio greater half intercepted Join AE less Let ABC let fall line given line joining line required lines be drawn lines drawn manner mean proportional meet opposite sides parallel to BC parallelogram passes pendicular perpendicular point of contact point of intersection points of bisection produced radius rectangle right angles segments semicircle shewn similar squares straight line tangent trapezium triangle ABC whence

Popular passages

Page 14 - IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Appears in 144 books from 1806-2001
Page xiii - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle,. shall be equal to the square of the line which touches it.
Appears in 135 books from 1806-1996
Page 230 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Appears in 204 books from 1806-2005
Page 327 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Appears in 281 books from 1732-1996
Page 158 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other...
Appears in 140 books from 1762-2004
Page 212 - FC are equal to one another : wherefore the circle described from the centre F, at the distance of one of them, will pass through the extremities of the other two, and be described about the triangle ABC.
Appears in 46 books from 1806-2001
Page 123 - If from a point, without a parallelogram, there be drawn two straight lines to the extremities of the two opposite sides, between which, when produced, the point does not lie, the difference of the triangles thus formed is equal to half the parallelogram. Ex. 2. The two triangles, formed by drawing straight lines from any point within a parallelogram to the extremities of its opposite sides, are together half of the parallelogram.
Appears in 51 books from 1817-1893
Page 305 - Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex ; construct the triangle.
Appears in 69 books from 1800-1923
Page 247 - The perpendicular from the vertex on the base of an equilateral triangle is equal to the side of an equilateral triangle inscribed in a circle, whose diameter is the base.
Appears in 36 books from 1813-1899
Page 299 - AB be equal to the given bisecting line ; and upon it describe a segment of a circle containing an angle equal to the given angle.
Appears in 55 books from 1806-1945

Bibliographic information

QR code for Geometrical Problems Deducible from the First Six Books of Euclid, Arranged and Solved
TitleGeometrical Problems Deducible from the First Six Books of Euclid, Arranged and Solved: To which is Added an Appendix Containing the Elements of Plane Trigonometry ...
AuthorMiles Bland
Edition2
PublisherJ. Smith, 1819
Original fromthe University of Michigan
Digitized11 Jun 2007
Length377 pages
  
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