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, Printer to the University; and sold by Nicholson & Son, Deighton & Sons, Thorpe, and Newby, Cambridge; and J. Mawman, and F. C. & J. Rivington, London., 1819 - 377 sider

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Resultater 1-5 af 81

Side v
... touch a circle , and be parallel to a chord ; the point of contact will be the middle point of the arc cut off by that chord . COR . 1. Parallel lines placed in a circle cut off equal parts of the circumference . COR . 2. The two ...
Side viii
... circle whose diameter is the common chord of the equal circles . 32. If two circles touch each other externally or internally ; any straight line drawn through the point of contact will cut off similar segments . 33. If two circles touch ...
Side ix
... circles ; this diameter and the lines joining the points of intersection and contact are in continued proportion . 41. If a common tangent be drawn to any number of circles which touch each other internally , and from any point in this ...
Side x
... circle tangents be drawn ; any other tangent to the circle , terminated by them , is so divided at the point of contact , that the radius of the circle is a mean proportional between its segments . 54. Two circles being given in ...
Side xiii
... circle a per- pendicular be drawn to the diameter which passes through one extremity ; it will bisect the segment of ... touches and the other cuts the circle ; a line drawn from the same point in any direction , equal to the tangent ...

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Udvalgte sider

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points of intersection to the extremities of the diameter cutting each
36
of intersection a circle be described cutting them the points where
42
If from the angular points of the squares described upon
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
line which shall make with the circumference an angle less than
63
If the diagonals of a quadrilateral figure inscribed in a circle
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
If two circles cut each other and any two points be taken
87
From a given point in the diameter of a semicircle produced
91
the other two sides
92
drawn to the opposite sides making equal angles with the base
97
If two exterior angles of a triangle be bisected and from
103
The three straight lines which bisect the three angles of
109
secting that which joins the vertex and the bisection of the base
114
If the opposite sides or opposite angles of a quadrilateral
120
of any four lines which can be drawn to the four angles from
126
If the sides of an equilateral and equiangular pentagon
134
To draw a line parallel to a given line which shall be termi
171
Between two lines given in position to draw a line equal
177
mainders may have given ratio and the sum of the squares of
179
to a given square and have its adjacent sides together equal to
185
If the opposite angles of a quadrilateral figure be equal
191
triangle to describe on the other sides segments similar to that
193
In a given triangle to inscribe a parallelogram similar to
199
points and touch a given straight line
203
and touch a given circle and a given straight line
209
line both given in position and have its centre also in a given
212
On the base of a given triangle to describe a quadrilateral
218
be drawn to cut one another the greater segments will be equal
220
cut each other at right angles the rectangles contained by the oppo
226
a circle is greater or less than a right angle by the angle contained
232
from its extremity the line intercepted between the vertex and
237
described on the sides of a rightangled triangle is in the middle
244
adjacent to the angles is equal to the square of either line drawn
249
In any triangle if perpendiculars be drawn from the angles
255
be drawn to any point in the circumference meeting a diameter per
273
other two sides to construct the triangle I
295
taining it and the difference of the segments of the base made
301

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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
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Almindelige termer og sætninger

ABCD angle ABC angles at F base centre chord circle ABC circles cut circles touch circumference describe a circle divided draw a line Draw the diameter drawn parallel duplicate ratio equal angles equiangular Eucl extremities given angle given circle given in position given line given point given ratio given square given straight line given triangle intercepted isosceles triangle Join AE Join BD Let AB Let ABC let fall line given line joining line required lines be drawn lines drawn mean proportional opposite side parallel to BC parallelogram pendicular perpen point of bisection point of contact point of intersection point required radius rectangle rectangle contained right angles segments semicircle shewn tangent touches the circle trapezium triangle ABC

Bibliografiske oplysninger

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
UdgiverJ. Smith, Printer to the University; and sold by Nicholson & Son, Deighton & Sons, Thorpe, and Newby, Cambridge; and J. Mawman, and F. C. & J. Rivington, London., 1819
Oprindeligt fraOxford University
Digitaliseret29. jul 2008
Længde377 sider
  
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