## 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

ABC shall be an equilateral triangle . Because the point A is the centre of the

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

ABC shall be an equilateral triangle . Because the point A is the centre of the

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 ... Side 8

But it has been

them equal to BG . But things which are equal to the same thing are equal to one

another . [ Axiom 1 . Therefore AL is equal to BC . Wherefore from the given point

...

But it has been

**shewn**that BC is equal to BG ; therefore AL and BC are each ofthem equal to BG . But things which are equal to the same thing are equal to one

another . [ Axiom 1 . Therefore AL is equal to BC . Wherefore from the given point

...

Side 10

But the point B was

coincide with the base EF ; because , B coinciding with E and C with F , if the

base BC does not coincide with the base EF , two straight lines will enclose a ...

But the point B was

**shewn**to coincide with the point E , therefore the base BC willcoincide with the base EF ; because , B coinciding with E and C with F , if the

base BC does not coincide with the base EF , two straight lines will enclose a ...

Side 11

And because the whole AF is equal to the whole AG , of which the parts AB , AC

are equal , ( Hypothesis . the remainder BF is equal to the remainder CG . [ Axiom

3 . And FC was

And because the whole AF is equal to the whole AG , of which the parts AB , AC

are equal , ( Hypothesis . the remainder BF is equal to the remainder CG . [ Axiom

3 . And FC was

**shewn**to be equal to GB ; therefore the two sides BF , FC are ... Side 13

But it has been

vertices as D , be within the other triangle ACB , produce AC , AD to E , F . Then

because AC is equal to AD , in the triangle ACD , [ Hyp . the angles ECD , FDC ,

on the ...

But it has been

**shewn**to be greater ; which is impossible . But if one of thevertices as D , be within the other triangle ACB , produce AC , AD to E , F . Then

because AC is equal to AD , in the triangle ACD , [ Hyp . the angles ECD , FDC ,

on 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.