## 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

The first of four magnitudes is said to have the same ratio to the second , that the

third has to the fourth , when any

being taken , and any

...

The first of four magnitudes is said to have the same ratio to the second , that the

third has to the fourth , when any

**equimultiples**whatever of the first and the thirdbeing taken , and any

**equimultiples**whatever of the second and the fourth , if the...

Side 135

When of the

multiple of the first is greater than the multiple of the second , but the multiple of

the third is not greater than the multiple of the fourth , then the first is said to have

...

When of the

**equimultiples**of four magnitudes , taken as in the fifth definition , themultiple of the first is greater than the multiple of the second , but the multiple of

the third is not greater than the multiple of the fourth , then the first is said to have

...

Side 137

Those magnitudes , of which the same or equal magnitudes are

are equal to one another . 3 . A multiple of a greater magnitude is greater than ...

**Equimultiples**of the same , or of equal magnitudes , are equal to one another . 2 .Those magnitudes , of which the same or equal magnitudes are

**equimultiples**,are equal to one another . 3 . A multiple of a greater magnitude is greater than ...

Side 138

If any number of magnitudes be

whatever multiple any one of them is of its part , the same multiple shall all the

first magniLet any number of magnitudes AB , CD be

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 the

first magniLet any number of magnitudes AB , CD be

**equimultiples**of as manyothers E , F ...

Side 139

If the first be the same multiple of the second that the third is of the fourth , and if

of the first and the third there be taken

be the same ...

If the first be the same multiple of the second that the third is of the fourth , and if

of the first and the third there be taken

**equimultiples**, these shall be**equimultiples**, the one of the second , and the other of the fourth . Let A the firstbe 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.