## The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books : with Notes, an Appendix, and Exercises |

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Side 134

A greater magnitude is said to be a

measured by the less ; that is , when the greater contains the less a certain

number of times exactly . 3 . Ratio is a mutual relation of two magnitudes of the

same kind to ...

A greater magnitude is said to be a

**multiple**of a less , when the greater ismeasured by the less ; that is , when the greater contains the less a certain

number of times exactly . 3 . Ratio is a mutual relation of two magnitudes of the

same kind to ...

Side 135

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

the third is not greater than the

...

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

**multiple**of the first is greater than the**multiple**of the second , but the**multiple**ofthe third is not greater than the

**multiple**of the fourth , then the first is said to have...

Side 137

A

That magnitude , of which a

is greater than that other magnitude . PROPOSITION 1 . THEOREM .

A

**multiple**of a greater magnitude is greater than the same**multiple**of a less . 4 .That magnitude , of which a

**multiple**is greater than the same**multiple**of another ,is greater than that other magnitude . PROPOSITION 1 . THEOREM .

Side 138

If any number of magnitudes be equimultiples of as many , each of each ;

whatever

first magniLet any number of magnitudes AB , CD be equimultiples of as many

others E , F ...

If any number of magnitudes be equimultiples of as many , each of each ;

whatever

**multiple**any one of them is of its part , the same**multiple**shall all thefirst magniLet any number of magnitudes AB , CD be equimultiples of as many

others E , F ...

Side 139

Let AB the first be the same

fourth , and let BG the fifth be the same

of F the fourth : AG , the first together with the fifth , shall be the same

Let AB the first be the same

**multiple**of C the second , that DE the third is of F thefourth , and let BG the fifth be the same

**multiple**of the second , that EH the sixth isof F the fourth : AG , the first together with the fifth , shall be the same

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The Elements of Euclid for the Use of Schools and Colleges Isaac Todhunter Uten tilgangsbegrensning - 1872 |

The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ... Isaac Todhunter Uten tilgangsbegrensning - 1880 |

The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... Euclid,Isaac Todhunter Uten tilgangsbegrensning - 1867 |

### Vanlige uttrykk og setninger

ABCD AC is equal angle ABC angle BAC Axiom base bisected Book centre chord circle ABC circumference common Construction Corollary Definition demonstration describe a circle described diameter difference divided double draw drawn equal equal angles equiangular equilateral equimultiples Euclid extremities fall figure fixed formed four fourth given circle given point given straight line greater half Hypothesis inscribed intersect join less Let ABC magnitudes manner meet middle point multiple namely opposite sides parallel parallelogram pass perpendicular plane polygon PROBLEM produced proportionals Q.E.D. PROPOSITION quadrilateral radius ratio reason rectangle contained rectilineal figure remaining respectively right angles segment shew shewn sides similar square straight line drawn suppose taken tangent THEOREM third triangle ABC twice Wherefore whole

### Populære avsnitt

Side 264 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Side 73 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a Right Angle; and the straight line which stands on the other is called a Perpendicular to it.

Side 264 - To draw a straight line at right angles to a given straight line, from a given point in the same. Let AB be...

Side 184 - 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.

Side 10 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.

Side 300 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.

Side 60 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Side 62 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts in the point D ; The squares on AD and DB shall be together double of AD»+DB

Side 244 - Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so at length to become greater than AB.

Side 6 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.