Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added Elements of Plane and Spherical TrigonometryG. Long, 1819 - 333 sider |
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Side 163
... equilateral , the sides about the equal angles are proportion- als ; the polygon ABCD is therefore similar to the polygon GHIKLM ( def . 1. 6. ) . And because similar polygons are as the squares of their homologous sides ( 20. 6 ...
... equilateral , the sides about the equal angles are proportion- als ; the polygon ABCD is therefore similar to the polygon GHIKLM ( def . 1. 6. ) . And because similar polygons are as the squares of their homologous sides ( 20. 6 ...
Side 164
... polygon ABCDEF is to the polygon GHIKLM as the square of AD to the square of GK ; and they have also been shewn to be similar . Therefore , & c . Q. E. D. COR . Every equilateral polygon inscribed in a circle is also equi- angular : For ...
... polygon ABCDEF is to the polygon GHIKLM as the square of AD to the square of GK ; and they have also been shewn to be similar . Therefore , & c . Q. E. D. COR . Every equilateral polygon inscribed in a circle is also equi- angular : For ...
Side 165
... polygon , an equilateral polygon may be described about the circle , the sides of which will each be equal to KL , and will be equal in number to the sides of the inscribed polygon . Therefore , KL is the side of an equilateral polygon ...
... polygon , an equilateral polygon may be described about the circle , the sides of which will each be equal to KL , and will be equal in number to the sides of the inscribed polygon . Therefore , KL is the side of an equilateral polygon ...
Side 166
... equilateral polygon inscribed in the circle ABC . Wherefore also , HL is the side of an equilateral polygon , of the same number of sides , described about ABC ( 3. 1. Sup . ) . Let the polygon described about the circle be called M , and ...
... equilateral polygon inscribed in the circle ABC . Wherefore also , HL is the side of an equilateral polygon , of the same number of sides , described about ABC ( 3. 1. Sup . ) . Let the polygon described about the circle be called M , and ...
Side 167
... polygon M to the difference of the polygons ; therefore , since the square of AC is greater than M , the square of AF is greater than the difference of the polygons ( 14.5 ... equilateral polygon inscribed OF GEOMETRY . BOOK 1 . 167.
... polygon M to the difference of the polygons ; therefore , since the square of AC is greater than M , the square of AF is greater than the difference of the polygons ( 14.5 ... equilateral polygon inscribed OF GEOMETRY . BOOK 1 . 167.
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Vanlige uttrykk og setninger
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle square straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Populære avsnitt
Side 56 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Side 19 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.
Side 62 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Side 62 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...
Side 130 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 76 - THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which...
Side 36 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Side 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Side 55 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.