## The Elements of Euclid, the parts read in the University of Cambridge [book 1-6 and parts of book 11,12] with geometrical problems, by J.W. Colenso |

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Page 153

A greater magnitude is said to be a

A greater magnitude is said to be a

**multiple**of a less , when the greater is measured by the less , that is , when the greater contains the less a certain number of times exactly . 111. Ratio is a mutual relation of two magnitudes of ... Page 154

When of the equimultiples of four magnitudes ( taken as in the fifth definition ) , the

When of the equimultiples of four magnitudes ( taken as in the fifth definition ) , the

**multiple**of the first is greater than that of the second , but the**multiple**of the third is not greater than the**multiple**of the fourth ; then the ... Page 156

Those magnitudes , of which the same or equal magnitudes are equimultiples , are equal to one another . 11. A

Those magnitudes , of which the same or equal magnitudes are equimultiples , are equal to one another . 11. A

**multiple**of a greater magnitude is greater than the same**multiple**of a less . IV . That magnitude , of which a**multiple**is 156 ... Page 157

That magnitude , of which a

That magnitude , of which a

**multiple**is greater than the same**multiple**of another , is greater than that other magnitude . JA B PROP . I. THEOR . If any number of magnitudes be equimultiples of as many , each of each , whatever**multiple**... Page 158

If the first magnitude be the same

If the first magnitude be the same

**multiple**of the second that the third is of the fourth , and the fifth the same**multiple**of the second that the sixth is of the fourth , then shall the first together with the fifth be the same ...### What people are saying - Write a review

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The Elements of Euclid, the Parts Read in the University of Cambridge [Book ... Euclides No preview available - 2016 |

### Common terms and phrases

ABCD angle ABC angle ACB angle BAC base base BC BC is equal bisected centre chord circle circle ABC circumference common described diameter difference divided double draw drawn equal equal angles equiangular equimultiples extremities fall figure fore four fourth given circle given line given point given straight line greater half inscribed intersection join less Let ABC lines be drawn lines drawn magnitudes manner meet multiple opposite sides parallel parallelogram pass perpendicular plane polygon PROB produced PROP proportionals Q.E.D. PROP rectangle rectangle contained rectilineal figure right angles segment semicircle shew shewn sides similar square square of AC straight lines &c Take taken THEOR third touches the circle triangle ABC Wherefore whole

### Popular passages

Page 42 - 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 4 - Let it be granted that a straight line may be drawn from any one point to any other point.

Page 33 - F, which is the common vertex of the triangles: that is », together with four right angles. Therefore all the angles of the figure, together with four right angles are equal to twice as many right angles as the figure has sides.

Page 62 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Page 22 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.

Page 58 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.

Page 146 - ... may be demonstrated from what has been said of the pentagon : and likewise a circle may be inscribed in a given equilateral and equiangular hexagon, and circumscribed about it, by a method like to that used for the pentagon.

Page 194 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

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 69 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.