# 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 Trigonometry

G. Long, 1819 - 333 من الصفحات

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### المحتوى

 القسم 1 17 القسم 2 19 القسم 3 53 القسم 4 66 القسم 5 97 القسم 6 107 القسم 7 124 القسم 8 152
 القسم 14 167 القسم 15 168 القسم 16 180 القسم 17 192 القسم 18 209 القسم 19 215 القسم 20 221 القسم 21 229

 القسم 9 153 القسم 10 156 القسم 11 158 القسم 12 161 القسم 13 163
 القسم 22 246 القسم 23 265 القسم 24 289 القسم 25 304 القسم 26 330

### مقاطع مشهورة

الصفحة 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.
الصفحة 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.
الصفحة 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.
الصفحة 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...
الصفحة 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...
الصفحة 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.
الصفحة 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...
الصفحة 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.
الصفحة 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.
الصفحة 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.