## The First Six Books with Notes |

### From inside the book

Results 1-5 of 42

Page 32

71 . pendicular be let fall upon the opposite side , the difference between the squares of the sides AB and BC which contain that angle , shall be equal to the difference between the squares of the

71 . pendicular be let fall upon the opposite side , the difference between the squares of the sides AB and BC which contain that angle , shall be equal to the difference between the squares of the

**segments**AD and DC of the side on ... Page 39

If two equal right lines be so divided that the rectangle under the

If two equal right lines be so divided that the rectangle under the

**segments**of one be equal to the su rectangle under the**segments**of the other , their segThe ments shall be equal . Se sa If one of the right lines be bisected ... Page 40

For the difference between the squares of the sides AB and AC is equal to the difference between the squares of the

For the difference between the squares of the sides AB and AC is equal to the difference between the squares of the

**segments**, BF and FC , of the side upon ( 1 ) Cor . 4. which the perpendicular falls ( 1 ) , and , therefore , when ... Page 41

... isosceles triangle to the base , the rectangle unG der the

... isosceles triangle to the base , the rectangle unG der the

**segments**of the base AE and EC is Book the Second . 41. Page 42

der the

der the

**segments**of the base AE and EC is equal to the difference between the square of this line BE and the square ... If a right line ( AB ) be divided into any two parts , the squares of the whole line ( AB ) and either**segment**( CB ) ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### 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.