## 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 |

### Inni boken

Side 52

... or

parallelograms about a diameter , together with the two complements , is called a

Gnomon .

... or

**rectangle**, is said to be**contained**by any two of the straight lines which**contain**one of the right angles . 2 . In every parallelogram , any of theparallelograms about a diameter , together with the two complements , is called a

Gnomon .

Side 53

If there be two straight lines , one of which is divided into any number of parts ,

the

and BC ...

If there be two straight lines , one of which is divided into any number of parts ,

the

**rectangle contained**by the tico straight lines is equal to the**rectangles****contained**by the undicided line , and the several parts of the divided line . Let Aand BC ...

Side 54

If a straight line be divided into any two parts , the

whole and each of the parts , are ... Let the straight line AB be divided into any

two parts at the point C : the

If a straight line be divided into any two parts , the

**rectangles contained**by thewhole and each of the parts , are ... Let the straight line AB be divided into any

two parts at the point C : the

**rectangle contained**by AB , BC , together with the ... Side 55

Then the rectangle AE is equal to the rectangles AD , CE . But AE is the

and AD is contained by AC , CB , for CD is equal to CB ; and CE is the square ...

Then the rectangle AE is equal to the rectangles AD , CE . But AE is the

**rectangle****contained**by AB , BC , for it is contained by AB , BE , of which BE is equal to BC ;and AD is contained by AC , CB , for CD is equal to CB ; and CE is the square ...

Side 56

Therefore CGKB is rectangular ; and it has been shewn to be equilateral ;

therefore it is a square , and it is on the side CB . ... And because the complement

AG is equal to the complement GE ; [ I . 43 . and that AG is the

Therefore CGKB is rectangular ; and it has been shewn to be equilateral ;

therefore it is a square , and it is on the side CB . ... And because the complement

AG is equal to the complement GE ; [ I . 43 . and that AG is the

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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.