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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a given angle and from each of them segments be cut off having
23
of chords be drawn the locus of their points of bisection will be
24
to the concave part of the circumference making equal angles with
25
If on the radius of a given semicircle another semicircle
30
line given in position a line which shall be equal and parallel to
36
parts
40
of intersection a circle be described cutting them the points where
42
necessary of the squares described upon the legs they will cut
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
angles formed by these lines will be equal
53
being in the circumference of the other and any line be drawn from
58
greater may be double the part intercepted by the circumference
60
line which shall make with the circumference an angle less than
63
from which a tangent drawn to the circumference shall be equal
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be drawn perpendicular to the base and from the greater segment
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to meet the tangents drawn from the extremities of the bisecting line
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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
a given ratio
87
To divide a given trapezium whose opposite sides are
133
If the sides of an equilateral and equiangular pentagon
134
perpendiculars be let fall on every side the sum of the squares
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triangle and the extremities of the adjacent sides be joined
146
sides of a rightangled triangle perpendiculars be let fall upon
147
mine a third such that its distances from the extremities may
154
contained by the whole and one of the parts may be equal to
158
a point in the circumference from which lines drawn to the
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the other
165
sides
172
a given ratio so that the difference of the squares of the remainders
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mainders may have a given ratio and the sum of the squares of
179
to a given square and have the difference of its adjacent sides equal
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two right angles a circle may be described about
191
In a given segment of a circle to inscribe a rectangular
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through a given point and touch a circle in a given point the
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two circles given in magnitude and position
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will be in the same straight line
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of the diameter of a semicircle from which if a line be drawn to
373

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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...
Miles Bland
Uten tilgangsbegrensning - 1821
Geometrical problems deducible from the first six books of Euclid, arranged ...
Miles Bland
Uten tilgangsbegrensning - 1819
Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...
Miles Bland
Uten tilgangsbegrensning - 1819
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Vanlige uttrykk og setninger

ABCD base centre chord circle circle ABC circles cut circumference common describe describe a circle 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 Hence inscribed intercepted Join Join AE less Let ABC let fall line joining lines be drawn lines drawn manner mean proportional meeting opposite sides parallel parallel to BC parallelogram pass pendicular perpendicular point of contact point of intersection produced quadrant radius right angles segments semicircle shewn sides similar square straight line tangent trapezium triangle triangle ABC whence

Populære avsnitt

Side 124 - If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those sides produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight '.line which joint the points of section, shall be parallel to the remaining side of the triangle.
Vises i 107 bøker fra 1806-2008
Side 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.
Vises i 133 bøker fra 1806-1996
Side 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...
Vises i 139 bøker fra 1762-2004
Side 160 - Upon a given straight line, to describe a segment of a circle, containing an angle equal to a given angle. Let AB be the given straight line, and C the given angle ; it is required to.
Vises i 33 bøker fra 1819-1935
Side 230 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Vises i 202 bøker fra 1806-2005
Side 157 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Vises i 232 bøker fra 1762-2007
Side 33 - FC ; (ax. 1.) and FA, FB, 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.
Vises i 41 bøker fra 1806-2001
Side xxv - ... the squares of the diagonals, is equal to the sum of the squares of the bisected sides together with four times the square of the line joining those points of bisection.
Vises i 35 bøker fra 1819-2006
Side 248 - If an equilateral triangle be inscribed in a circle, and the adjacent arcs cut off by two of its sides be bisected, the line joining the points of bisection shall be trisected by the sides.
Vises i 31 bøker fra 1819-1897
Side 355 - The sine of an angle is equal to the sine of its supplement. The sine rule Consider fig.
Vises i 58 bøker fra 1811-2002

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TittelGeometrical 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
Utgave2
UtgiverJ. Smith, 1819
Lengde377 sider
  
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