## 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

Resultat 6-10 av 68

Side 37

... and the diameter bisects the parallelogram , that is , divides it into two equal

parts . Note . A parallelogram is a

are parallel ; and a diameter is the straight line joining two of its opposite angleg .

... and the diameter bisects the parallelogram , that is , divides it into two equal

parts . Note . A parallelogram is a

**four**- sided figure of which the opposite sidesare parallel ; and a diameter is the straight line joining two of its opposite angleg .

Side 49

Therefore the

the parallelogram ADEB is equilateral . [ Axiom 1 . Likewise all its angles are right

angles . For since the straight line AD meets the parallels AB , DE , the angles ...

Therefore the

**four**straight lines BA , AD , DE , EB are equal to one another , andthe parallelogram ADEB is equilateral . [ Axiom 1 . Likewise all its angles are right

angles . For since the straight line AD meets the parallels AB , DE , the angles ...

Side 56

Therefore the

together with twice the rectangle AC , CB . But HF , CK , AG , GE make up the

whole figure ADEB , which is the square on AB . Therefore the square on AB is ...

Therefore the

**four**figures HF , CK , AG , GE are equal to the squares on AC , CB ,together with twice the rectangle AC , CB . But HF , CK , AG , GE make up the

whole figure ADEB , which is the square on AB . Therefore the square on AB is ...

Side 60

If a straight line be divided into any two parts ,

by the whole line and one of the parts , together with the square on the other part

, is equal to the square on the straight line which is made up of the whole and ...

If a straight line be divided into any two parts ,

**four**times the rectangle containedby the whole line and one of the parts , together with the square on the other part

, is equal to the square on the straight line which is made up of the whole and ...

Side 61

Therefore the

the

, GR and RN are quadruple of CK ; therefore the eight rectangles which make ...

Therefore the

**four**rectangles AG , MP , PL , RF are equal to one another , and sothe

**four**are quadruple of one of them AG . And it was shewn that the**four**CK , BN, GR and RN are quadruple of CK ; therefore the eight rectangles which make ...

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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.