# Elements of Plane Geometry According to Euclid

W. and R. Chambers, 1837 - 240 من الصفحات

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### المحتويات

 القسم 1 2 القسم 2 37 القسم 3 44 القسم 4 94 القسم 5 171 القسم 6 187 القسم 7 189 القسم 8 190
 القسم 11 201 القسم 12 213 القسم 13 215 القسم 14 216 القسم 15 220 القسم 16 222 القسم 17 233 القسم 18 235

 القسم 9 198 القسم 10 200
 القسم 19 240 القسم 20

### مقاطع مشهورة

الصفحة 1 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals the wholes are equal. 3. If equals be taken from equals the remainders are equal. 4. If equals be added to unequals the wholes are unequal. 5. If equals be taken from unequals the remainders are unequal. 6. Things which are double of the same thing are equal to one another.
الصفحة 73 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
الصفحة 9 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.
الصفحة 4 - If two triangles have two sides of the one equal to two sides of the...
الصفحة 139 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. Let BC, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (2.
الصفحة 23 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
الصفحة 129 - 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 80 - A circle is said to be described about a rectilineal figure, when the circumference of the circle passes through all the angular points of the figure about which it is described. 7. A straight line is said to be placed in a circle, when the extremities of it are in the circumference of the circle.
الصفحة 27 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.
الصفحة 44 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.