## 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).1846 |

### Common terms and phrases

absurd added appears arch assumed base becomes bisected Book called centre changed circle circumference co-efficient common Const construct contained contained oftener denominator describe difference divided Division divisor double draw drawn equal angles equal by Prop equation equi-submultiples equiangular equilateral evident example extremity fall four fourth fraction given given line greater half indices inscribed internal less magnitudes means meet multiplying namely opposite parallel parallelogram pass perpendicular possible PROBLEM produced proportional PROPOSITION quantities quotient ratio rectangle rectilineal figure remaining right angles right line root RULE Schol segment side AC sides similar square squares of AC stand submultiple Subtraction taken term THEOREM third touches triangle BAC unknown whole

### Popular passages

Page 20 - If two triangles have two sides of the one equal to two sides of the...

Page 30 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.

Page 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.

Page 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.

Page 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.

Page 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.

Page 129 - In any proportion, the product of the means is equal to the product of the extremes.

Page 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.

Page 215 - ... are to one another in the duplicate ratio of their homologous sides.

Page 160 - PROPOSITION XV. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. Let ABCDEF be the given circle.