## Euclid's Elements of Geometry |

### Other editions - View all

Euclid's Elements of Geometry: Translated From the Latin of ... Thomas ... Thomas Elrington No preview available - 2018 |

Euclid's Elements of Geometry: Translated From the Latin of ... Thomas ... Thomas Elrington No preview available - 2022 |

Euclid's Elements of Geometry: Translated from the Latin of ... Thomas ... Thomas Elrington No preview available - 2015 |

### Common terms and phrases

absurd AC and CB AC by Prop AC is equal angle ABC angles by Prop arch base bisected centre circumference co-efficient Const contained in CD contained oftener divided divisor double draw drawn equal angles equal by Constr equal by Hypoth equal by Prop equal to twice equation equi equi-multiples equi-submultiples equiangular equilateral external angle fore four magnitudes proportional given angle given circle given line given right line given triangle gonal half a right inscribed less multiplying oftener contained opposite parallel parallelogram perpendicular PROPOSITION quantities rectangle under AC rectilineal figure remaining angles remaining side right angles right line AC Schol segment side AC similar similarly demonstrated squares of AC submultiple subtract THEOREM tiple touches the circle triangle BAC twice the rectangle

### 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.