## The First Six Books with Notes |

### From inside the book

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Page 1

The

The

**vertex**of an angle is the point in which the sides meet one another . An angle is expressed either by one letter placed at the**vertex**, or by three letters , of which the middle one is at the**vertex**, the others any where along the ... Page 7

18 . and first let the

18 . and first let the

**vertex**of each of the triangles be without the other triangle , and draw CD . , Because the sides AD and AC of the triangle CAD ( 1 ) hypoth . are equal ( 1 ) , the angles ACD and ADC are equal ( 2 ) prop . 5 . Page 8

19 o F 110 right line cannot have their conterminous sides equal , when the

19 o F 110 right line cannot have their conterminous sides equal , when the

**vertex**of each of the triangles is without the other . Fig . 19 . Secondly . Let the**vertex**Dof one triangle be within the other , produce the sides AC and AD ... Page 18

In an isosceles triangle ABC the right line BD , drawn from the

In an isosceles triangle ABC the right line BD , drawn from the

**vertex**perpendicular to the base , bisects the base and the vertical angle . For in the triangles ABD , CBD , the angles A and ADB are respectively equal to the angles C ... Page 25

For if the right line AD which joins the

For if the right line AD which joins the

**vertices**of the triangles be not parallel to BC , draw through the point ... cutting a side BD of the triangle BDC , or the side produced , in a point E different from the**vertex**, and draw CE .### 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.