## The First Six Books with Notes |

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Page 3

A square is a quadrilateral figure , which has all its sides

A square is a quadrilateral figure , which has all its sides

**equal**, and all its angles right angles . 32. Rectilineal figures , which have more than four sides , are called polygons . O Postulates . 1. Let it be granted that a right ... Page 4

It is evident that ACB is a triangle constructed upon the given line ; but it is also equilateral , for the right line AC is

It is evident that ACB is a triangle constructed upon the given line ; but it is also equilateral , for the right line AC is

**equal**to AB , as they are radii of the ( 3 ) Def . 13. same circle DCB ( 3 ) ; and the right line BC is**equal**... Page 5

to the same BG , are

to the same BG , are

**equal**to one another ( 7 ) . ( 7 ) Ar . 1 . Therefore from the given point A a right line AL has been drawn**equal**to the given right line BC . Schol . The position of the right line AL varies according to the ... Page 6

And as the sides of the angles E and F coincide with the sides of the angles A and C , the angles themselves ( 3 ) Ax . 8 . must coincide , and are therefore

And as the sides of the angles E and F coincide with the sides of the angles A and C , the angles themselves ( 3 ) Ax . 8 . must coincide , and are therefore

**equal**( 3 ) . And if the right lines which bound the triangle EDF coincide ... Page 7

17 .

17 .

**equal**, the sides opposite to them , ( AC und AB ) are He also**equal**. B For if the sides be not**equal**, let one of them AB be greater than the other , and from it cut off DB**equal**( 1 ) prop . 3 . to AC ( 1 ) , and join CD .### What people are saying - Write a review

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### Common terms and phrases

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

### Popular passages

Page 145 - 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 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 : 16.

Page 28 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

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 118 - A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less.

Page 146 - 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 168 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...

Page 3 - Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one another.

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

Page 3 - A rhombus is that which has all its sides equal, but its angles are not right angles.