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 - 377 sider
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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

Andre udgaver - Se alle

Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...
Miles Bland
Fuld visning - 1821
Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...
Miles Bland
Fuld visning - 1819
Geometrical problems deducible from the first six books of Euclid, arranged ...
Miles Bland
Fuld visning - 1819
Se alle »

Almindelige termer og sætninger

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

Populære passager

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Bibliografiske oplysninger

QR code for Geometrical Problems Deducible from the First Six Books of Euclid, Arranged and Solved
TitelGeometrical Problems Deducible from the First Six Books of Euclid, Arranged and Solved: To which is Added an Appendix Containing the Elements of Plane Trigonometry ...
ForfatterMiles Bland
Udgave2
UdgiverJ. Smith, 1819
Oprindeligt fraUniversity of Michigan
Digitaliseret11. jun 2007
Længde377 sider
  
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