## The First Six Books with Notes |

### From inside the book

Results 1-5 of 16

Page 52

An angle is said to stand upon the part of the circumference , or the

An angle is said to stand upon the part of the circumference , or the

**arch**, intercepted between the right lines that contain the angle . 9. A sector of a circle is the figure contained ... Page 67

If two equal angles stand upon the same

If two equal angles stand upon the same

**arch**Fig . 32 . BD and the vertex of one of them BAD be in the circumference of the circle , the vertex of the other shall be in the same circumference , For , if it be possible , let the vertex ... Page 69

37 . and DĀF , ABC and DEF ) , whether they be at the centres or at the circumferences , stand upon equal

37 . and DĀF , ABC and DEF ) , whether they be at the centres or at the circumferences , stand upon equal

**arches**, First let the given angles AOC and DHF be at the centres , draw to any points B and E in the circumferences the lines AB ... Page 70

equal circles , and the remaining segments are equal , and therefore the

equal circles , and the remaining segments are equal , and therefore the

**arches**AGC and DKF are equal . In the same manner it can be demonstrated that the**arches**AGC and DKF are equal if the given angles at the circumferences ABC and ... Page 71

8 .

8 .

**arch**DHF ( 3 ) ; and since the circles are equal , take ( 3 ) Prop.26 away these equal**arches**from them , and the remain - B . 3 . ing**arches**ABC and DEF are equal . PROP . XXIX . THEOR . In equal circles ( ABC , DEF ) the right ...### 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.