## The First Six Books with Notes |

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Page 64

From this proposition is immediately deduced a method of drawing a

From this proposition is immediately deduced a method of drawing a

**tangent**through any given point B in the circumference of a circle : draw through that point a diameter AB , and erect at the extremity of it a perpendicular BF . Fig . Page 65

24 . to draw a right line which shall be a

24 . to draw a right line which shall be a

**tangent**to the circle . Let C bc the centre of the given circle , and from the centre C with the radius CA , describe a circle CAE ; draw CA which meets the circle in the point F , and draw ... Page 66

If a right line ( BC ) be a

If a right line ( BC ) be a

**tangent**to a circle , the right line ( BA ) drawn perpendicular to it from the point of contact , passes through the centre of the circle . For , if it be possible , let the centre Z be without the line BA ... Page 72

Hence also can be drawn a

Hence also can be drawn a

**tangent**to a circle from a given point without it : draw a right line 1 from the given point to the centre of the circle -- Elements of Euclid . 72. Page 73

If a right line ( EF ) be a

If a right line ( EF ) be a

**tangent**to a circle and Fig . 44 , from the point of contact a right line ( AC ) be drawn cutting the circle , the angle ( FAC ) made by this line with the**tangent**is equal to the angle ( ABC ) in the ...### 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.