Elements of Geometry

Cover Elements of Geometry
Elements of Geometry
John Playfair, Euclid
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In dififerent circles, similar arcSf sectors, and segments, are those of which the arcs subtend equal angles at the centre. Two equal figures are always similar ; but two similar figures may be very unequal.
2. Two sides of one figure fure said to be reciprocally proportional to two sides of another, when one of the, sides of the first is to one of the sides of the second, as the remaining side of the second is to the re- maining side of the first.
3. A straight lin6 is said to be cut in extrem
...e and mean ratio, when the whole is to the greater segment, as the greater segment is to the less.
4. The altitude of a triangle is the straight line drawn from its vertex perpendicular to the base.
The altitude of a parallelogram is the perpendicu- lar which measures the distance of two oppo- site sides, taken as bases. And the altitude of a trapezoid is the perpendicular drawn between its two parallel sides.
PROP. I. THEOR.
Triangles and parallelograms, of the same altitude, are one to another as their bases.


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