## The First Six Books with Notes |

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Page 4

Since then oth the lines A and BC are equal to ( 4 ) Ax . 1. the same AB , they must be equal to one another ( 4 ) , and therefore the triangle ACB is equilateral . Schol . Draw the lines AG and GB and in the same

Since then oth the lines A and BC are equal to ( 4 ) Ax . 1. the same AB , they must be equal to one another ( 4 ) , and therefore the triangle ACB is equilateral . Schol . Draw the lines AG and GB and in the same

**manner**it can be ... Page 10

In the same

In the same

**manner**a perpendicular can be erected at one extremity of a given line , by first producing the line . 2,5 D B PROP . XII . PROB . X Fig . 25 . See N. To draw a perpendicular to a given indefinite right line ( AB ) from a ... Page 11

Therefore BE is not the continuation of CB ; and in the same

Therefore BE is not the continuation of CB ; and in the same

**manner**it can be proved that no other line , except BD , is the continuation of it ; therefore BD forms with BC one continued right line . Page 12

ECF and A are equal ( 5 ) , and therefore ACĎ is greater than A. In like

ECF and A are equal ( 5 ) , and therefore ACĎ is greater than A. In like

**manner**it can be shewn , that if AC be produced , the external angle BCG is greater than the angle B , and therefore that the angle ACD , which is equal to BCG ( 4 ) ... Page 13

In the same

In the same

**manner**, if CB be produced ( 2 ) Prop . 13 . from the point B , it can be demonstrated that the angle ABC together with the angle A , is less than two right angles : therefore any two angles of the triangle are less than two ...### 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.