## The First Six Books with Notes |

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Page 6

3. equal to AF ( 1 ) , and

3. equal to AF ( 1 ) , and

**join**FC , GB . . 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 ... Page 7

3 . to AC ( 1 ) , and

3 . to AC ( 1 ) , and

**join**CD . Then in the triangles DBC , and ACB , the sides DB , BC are equal to the sides AC , CB , and the angles DBC and ACB are also equal ( 2 ) ; therefore the triangles themselves DBC and ACB , are equal ... Page 8

Let the vertex Dof one triangle be within the other , produce the sides AC and AD and

Let the vertex Dof one triangle be within the other , produce the sides AC and AD and

**join**CD . Because the sides AC and AD of the triangle CAD ( 6 ) hypotk . are equal ( 6 ) , the angles ECD and FDCare equal ( 7 ) ; 1 ( 7 ) prop 5. but ... Page 9

1 . mote from A. The right line

1 . mote from A. The right line

**joining**the points A and F , bisects the given angle BAC . 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 ... Page 12

3. produce it until EF be equal to BE ( 2 ) and

3. produce it until EF be equal to BE ( 2 ) and

**join**FC . The triangles CEF and AEB have the sides CE ( 3 ) Constr . and EF equal to the sides AE and EB ( 3 ) and the ( 4 ) Prop , 15. angle CEF equal to AEB ( 4 ) , therefore the angles ...### 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.