## The First Six Books with Notes |

### From inside the book

Results 1-5 of 26

Page 90

A greater magnitude is called a

A greater magnitude is called a

**multiple**of a less , when the greater is measured by the less . 3. Ratio is a mutual relation of two magnitudes of the same kind , with respect to quantity . 4. Magnitudes are said to have a ratio to each ... Page 92

Equi -

Equi -

**multiples**of the same or of equal magnitudes are equal : 2. Those magnitudes of which the same or equal magnitudes are equi -**multiples**or equi - submultiples , are equal , 3. A**multiple**or submultiple of a greater magnitude is ... Page 93

First , let one of the given magnitudes BC be a

First , let one of the given magnitudes BC be a

**multiple**of A , and A is not oftener contained in one of them than in ... E remain , BC and Dm are therefore equi -**multiples**of B. 1 . the same A , and therefore BC is equal to Dm ( 1 ) ... Page 94

Hence it is evident , that if either of the given magnitudes be a

Hence it is evident , that if either of the given magnitudes be a

**multiple**of A , the other is also an equi -**multiple**of A. Cor . 2. If two magnitudes be equal , as often as one of them is contained in any third , so often is the other ... Page 95

+ let A be taken away from CD as often as B is contained in EF , and let md be the remainder ; because Cm and EF are equi -

+ let A be taken away from CD as often as B is contained in EF , and let md be the remainder ; because Cm and EF are equi -

**multiples**of A and B ( 1 ) , and A is ( 1 ) Chatr . greater than B ( 2 ) , Cm is greater than EF ( 3 ) , but EF ...### 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.