## The First Six Books of the Elements of Euclid: With Notes |

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absurd acute added alternate angle ABC arches base bisected centre circle circumference common Constr constructed contained contained in CD definition demonstrated described diameter difference divided draw drawn equal angles equi-multiples equi-submultiples equiangular equilateral Euclid evident external angle extremity fall figure fore four magnitudes fourth given circle given line gles greater half Hence Hypoth inscribed internal intersect join less line AC magnitudes manner mean meet multiple oftener opposite parallel parallelogram pass perpendicular placed possible PROB produced Prop proportional proposition proved radius ratio rectangle rectilineal figure remaining right angles Schol segment side AC similar squares of AC stand submultiple taken tangent THEOR third triangle ABC twice vertex whole

### Popular passages

Page 147 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.

Page 3 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.

Page 22 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 16 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.

Page 148 - A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.

Page 2 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Page 92 - F) a ratio compounded of the ratios which the first has to the second, the second to the third, the third to the fourth (A to D, D to C, and C to F) ; and so on to the last.

Page 93 - AXIOMS. 1. Equimultiples of the same, or of equal magnitudes, are equal to one another. 2. Those magnitudes, of which the same or equal magnitudes are equimultiples, are equal to one another. 3. A multiple of a greater magnitude is greater than the same multiple of a less. 4. That magnitude, of which a multiple is greater than the same multiple of another, is greater than that other magnitude.

Page 25 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.

Page 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.