## The First Six Books with Notes |

### From inside the book

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Page 6

And in the same triangles , the angle FCB is equal to the angle GBC ( 4 ) , and taking away these from the equals FCA and GBA , the

And in the same triangles , the angle FCB is equal to the angle GBC ( 4 ) , and taking away these from the equals FCA and GBA , the

**remaining**angles ACB ( 5 ) Ax , 3 . and ABC are equal ( 5 ) , but these are the angles at the base BC of ... Page 8

It is evident that the

It is evident that the

**remaining**angles A and E , C and D , opposite to the equal sides , are equal , and also that the triangles themselves are equal . ; IAA PROP . IX . PROB . Page 11

... together with the angle BED , is equal to two right angles ( 1 ) ; therefore AEC and CEB ( 2 ) Ax 3 . together are equal to CEB and BED , take away the common angle CEB , and the

... together with the angle BED , is equal to two right angles ( 1 ) ; therefore AEC and CEB ( 2 ) Ax 3 . together are equal to CEB and BED , take away the common angle CEB , and the

**remaining**angle A EC is equal to BED ( 2 ) . PROP . Page 17

... ( BA to DE ) to those equal angles , the

... ( BA to DE ) to those equal angles , the

**remaining**sides and angles are respectively equal to ones another . re First let the equal sides be BC and DF which are adjacent to the equal angles , then the side BA is equal to the side DĖ . Page 21

If two triangles have two angles equal to two , the

If two triangles have two angles equal to two , the

**remaining**angles are also equal . Cor . 3. In a right angled isosceles triangle , each angle at the base is half a right angle . Cor . 4. Each angle of an equilateral triangle is equal ...### 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.