## The First Six Books with Notes |

### From inside the book

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Page 3

If a right line meet two right lines , so as to make the two

If a right line meet two right lines , so as to make the two

**internal**angles on the same side of it See N. taken together less than two right angles , these right lines being continually produced , shall at length meet upon that side on ... Page 12

If one side ( BC ) of a triangle ( BAC ) be produced , the external angle ( ACD ) is greater than either of the

If one side ( BC ) of a triangle ( BAC ) be produced , the external angle ( ACD ) is greater than either of the

**internal**opposite angles ( A or B ) . O A B 30 B ( 1 ) Prop . 10 . For bisect the side AC in E ( 1 ) , draw BE and ( 2 ) ... Page 13

... than the

... than the

**internal**angle ACB ( 4 ) , therefore ABD is ( 4 ) Prop . 18 . greater than ACB , and therefore ABC is greater than ACB : but ABC is opposite the greater side AC , and ACB is opposite the less AB . PROP . XIX . THEOR . Page 14

Bisect the angle BAC by the right line AD ( 1 ) ; the external angle BDA is greater than the

Bisect the angle BAC by the right line AD ( 1 ) ; the external angle BDA is greater than the

**internal**( 2 ) Prop.16 . DAC ( 2 ) , but BAD is equal to DAC ( 3 ) , therefore ( 3 ) Constr . BDA is greater than BAD , and therefore the ... Page 15

Because the external angle BDC is greater than the

Because the external angle BDC is greater than the

**internal**DEC ( 2 ) , and for the same reason DEC ( 2 ) Prop . 18 . is greater than BAE , the angle BDC is greater than the angle BAE . PROP . XXII . PROB . Given three right lines ( A ...### 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.