## The First Six Books with Notes |

### From inside the book

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Page 5

... by those sides also equal to one another ( D to B ) ; their

... by those sides also equal to one another ( D to B ) ; their

**bases**( EF and AC ) are equal , and the angles at the**bases**, which are opposite to the equal sides , are equal ( E to Å and F to C ) ; and also the triangles themselves . Page 6

A In an isosceles triangle ( B.1C ) the angles at the

A In an isosceles triangle ( B.1C ) the angles at the

**base**( ABC and ACB ) are equal to one another ; and if the equal sides be produced , the angles below the**base**( FBC and GCB ) shall also be equal . B Take any point F in the side ... Page 7

Hence every equiangular triangle is also equilateral ; for whatever side is taken for the

Hence every equiangular triangle is also equilateral ; for whatever side is taken for the

**base**, the angles adjacent to it are equal , and therefore the sides F which subtend them . PROP . VII . THEOR . 1 33 On the same right line ( AB ) ... Page 8

For if the equal

For if the equal

**bases**AC and ED be so applied to one another , that the equal sides A B and EF , CB and DF , may be conterminous , the vertex B must fall ( 1 ) prop . 7. upon F ( 1 ) , and the equal sides A B and EF , CB and ( 2 ) ax ... Page 9

Because the sides AD and AE are equal ( 3 ) , and ( 3 ) constr . the side AF is common to the triangles FAD , and FAE , and the

Because the sides AD and AE are equal ( 3 ) , and ( 3 ) constr . the side AF is common to the triangles FAD , and FAE , and the

**base**FD is also equal to FE ( 3 ) , the angles DAF and EAF are equal ( 4 ) , and therefore ( 4 ) prop .### 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.