# Euclid's Elements of geometry, the first three books (the fourth, fifth, and sixth books) tr. from the Lat. To which is added, A compendium of algebra (A compendium of trigonometry).

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### المحتويات

 Dedication iii 3 Additional Definitions 41 Subtraction of Algebra 63 Multiplication of Algebra 99 Division 105 Division 106 Fractions 113
 Involution 122 Equations of the First Degree 129 Numerical Proof of Euclids Second Book 142 Fourth Book 147 Fifth Book 163 Sixth Book 195 Trigonometry 229

### مقاطع مشهورة

الصفحة 20 - If two triangles have two sides of the one equal to two sides of the...
الصفحة 30 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
الصفحة 209 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
الصفحة 218 - 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 114 - To reduce fractions of different denominators to equivalent fractions having a common denominator. RULE.! Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
الصفحة 90 - 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 129 - In any proportion, the product of the means is equal to the product of the extremes.
الصفحة 163 - Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order.
الصفحة 215 - ... are to one another in the duplicate ratio of their homologous sides.
الصفحة 160 - PROPOSITION XV. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. Let ABCDEF be the given circle.