## 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 7

circle BCD , AC is equal to AB . [ Definition 15 . And because the point B is the

centre of the circle ACE , BC is equal to BĂ . [ Definition 15 . But it has been

shewn that ...

**ABC**shall be an equilateral**triangle**. Because the point A is the centre of thecircle BCD , AC is equal to AB . [ Definition 15 . And because the point B is the

centre of the circle ACE , BC is equal to BĂ . [ Definition 15 . But it has been

shewn that ...

Side 9

Let ABC , DEFbe two triangles which have the two sides AB , AC equal to the two

sides DE , DF , each to each ... EDF : the base BC shall be equal to the base EF ,

and the

Let ABC , DEFbe two triangles which have the two sides AB , AC equal to the two

sides DE , DF , each to each ... EDF : the base BC shall be equal to the base EF ,

and the

**triangle ABC**to the triangle DEF , and the other angles shall be equal ... Side 10

For if the

on the point D , and the straight line AB on the straight line DE , the point B will

coincide with the point E , because AB is equal to DE . [ Hyp . And , AB coinciding

...

For if the

**triangle ABC**be applied to the triangle DEF , 80 that the point A may beon the point D , and the straight line AB on the straight line DE , the point B will

coincide with the point E , because AB is equal to DE . [ Hyp . And , AB coinciding

...

Side 11

... each to each ; and they contain the angle FAG common to the two triangles

AFC , AGB ; therefore the base FC is equal ... the remaining angle ABC is equal

to the remaining angle ACB , which are the angles at the base of the

.

... each to each ; and they contain the angle FAG common to the two triangles

AFC , AGB ; therefore the base FC is equal ... the remaining angle ABC is equal

to the remaining angle ACB , which are the angles at the base of the

**triangle ABC**.

Side 12

If two angles of a

or are opposite to , the equal angles , shall be equal to one another . Let

a

If two angles of a

**triangle**be equal to one another , the sides also which subtend ,or are opposite to , the equal angles , shall be equal to one another . Let

**ABC**bea

**triangle**, having the angle**ABC**equal to the angle ACB : the side AC shall be ...### Hva folk mener - Skriv en omtale

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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.