## 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

respect of quantity . 4 . Magnitudes are said to have a

the less can be multiplied so as to exceed the other . " 5 . The first of four ...

**Ratio**is a mutual relation of two magnitudes of the same kind to one another inrespect of quantity . 4 . Magnitudes are said to have a

**ratio**to one another , whenthe less can be multiplied so as to exceed the other . " 5 . The first of four ...

Side 135

Analogy , or proportion , is the similitude of

terms at least . 10 . When three magnitudes are proportionals , the first is said to

have to the third the duplicate

Analogy , or proportion , is the similitude of

**ratios**. 9 . Proportion consists in threeterms at least . 10 . When three magnitudes are proportionals , the first is said to

have to the third the duplicate

**ratio**of that which it has to the second . Side 136

And the same thing is to be understood when it is more briefly expressed by

saying , A has to D the

L . In like manner , the same things being supposed , if M has to N the same

that ...

And the same thing is to be understood when it is more briefly expressed by

saying , A has to D the

**ratio**compounded of the**ratios**of E to F , G to H , and K toL . In like manner , the same things being supposed , if M has to N the same

**ratio**that ...

Side 140

... the first & c . Q . E . D . PROPOSITION 4 . THEOREM . If the first have the same

equimultiples whatever of the first and the third , and also 140 EUCLID ' S

ELEMENTS .

... the first & c . Q . E . D . PROPOSITION 4 . THEOREM . If the first have the same

**ratio**to the second that the third has to the fourth , and if there be taken anyequimultiples whatever of the first and the third , and also 140 EUCLID ' S

ELEMENTS .

Side 141

multiples whatever of the first and the third , and also any equimultiples whatever

of the second and the fourth , then the multiple of the first shall have the same

of ...

multiples whatever of the first and the third , and also any equimultiples whatever

of the second and the fourth , then the multiple of the first shall have the same

**ratio**to the multiple of the second , that the multiple of the third has to the multipleof ...

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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.