## Euclid's Elements of Geometry |

### From inside the book

Page 161

Ratio is a mutual relation of two magnitudes of the same kind ,

Ratio is a mutual relation of two magnitudes of the same kind ,

**in respect of quantity . 4. Magnitudes are said to have a ratio to one another , when the less can be**multiplied so as to exceed the greater . 5. Magnitudes are said to be ...### What people are saying - Write a review

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### Common terms and phrases

absurd added appears arch assumed base becomes bisected called centre circle circumference common Const construct contained contained oftener describe difference divided double draw drawn equal angles equal by Prop equation equi-submultiples equiangular equilateral evident example external angle extremity fall figure fore fourth fraction given line given right line greater half Hypoth inscribed internal joining less mean meeting multiplying opposite parallel parallelogram pass perpendicular possible PROBLEM produced proportional PROPOSITION quantities ratio rectangle rectilineal figure right angles right line root RULE segment side AC similar similarly similarly demonstrated squares of AC stand submultiple subtract taken term THEOREM third touches triangle BAC twice the rectangle whole

### Popular passages

Page 18 - If two triangles have two sides of the one equal to two sides of the...

Page 28 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.

Page 207 - ... 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 216 - 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 127 - In any proportion, the product of the means is equal to the product of the extremes.

Page 161 - 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 112 - 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 213 - ... are to one another in the duplicate ratio of their homologous sides.

Page 163 - Convertendo ; when it is .concluded, that if there be four magnitudes proportional, the first is to the sum or difference of the first and second, as the third is to the sum or difference of the third and fourth.

Page 88 - 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.