## The First Six Books with Notes |

### From inside the book

Results 1-5 of 63

Page 6

In the triangles FAC and GAB , the sides FA and ( 2 ) Constr • AC are equal to the sides GA and AB ( 2 ) , and the &

In the triangles FAC and GAB , the sides FA and ( 2 ) Constr • AC are equal to the sides GA and AB ( 2 ) , and the &

**hypoth**. angle A is common to both , therefore the angle ACF is equal to ABG , and the angle AFC to AGB ; and ( 3 ) ... Page 7

... therefore the triangles themselves DBC and ACB , are equal , a part ( 2 )

... therefore the triangles themselves DBC and ACB , are equal , a part ( 2 )

**hypoth**. equal to the whole , which is absurd : therefore neither of the sides AB or AC is greater than the other ; they are therefore equal to one another . Page 16

Since the right lines AG and AC are equal ( 3 ) , the &

Since the right lines AG and AC are equal ( 3 ) , the &

**hypoth**. angles ACG and AGC are equal ( 4 ) ; but the angle < ( 4 ) Prop.s. BĞC is greater than AGC , therefore greater than ACG , and therefore greater than BCG . Page 17

4 . also equal to DFE ( 4 ) , therefore the angle BCG is ( 4 )

4 . also equal to DFE ( 4 ) , therefore the angle BCG is ( 4 )

**hypoth**. equal to BCA ( 5 ) , which is absurd : neither of the ( 5 ) ax , 1 . sides BA and DE , therefore , is greater than the other , therefore they are equal ; and also ... Page 18

4. and EFD are equal ( 10 ) , but the angle C is also equal ( in

4. and EFD are equal ( 10 ) , but the angle C is also equal ( in

**hypoth**. to EFD ( 11 ) , therefore AHB and C are equal ( 12 ) , ( 12 ) Ar . ! . which is absurd ( 13 ) ; neither , therefore , of the sides ( 13 ) prop .### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### 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.