## The first three books of Euclid's Elements of geometry, with theorems and problems, by T. Tate |

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Resultat 1-5 av 5

Side 23

If a straight line falling upon two other straight lines makes the

equal to one another , these two straight lines shall be parallel . Let the straight

line EF , which falls upon the two straight lines AB , CD , make the

angles ...

If a straight line falling upon two other straight lines makes the

**alternate**anglesequal to one another , these two straight lines shall be parallel . Let the straight

line EF , which falls upon the two straight lines AB , CD , make the

**alternate**angles ...

Side 24

lines AB , CD , make the

parallel to CD . For , if it be not parallel , AB and cd being produced , shall meet

either towards B , D , or towards A , C ; let them be produced and meet towards B

...

lines AB , CD , make the

**alternate**angles A EF , EFD equal to one another ; AB isparallel to CD . For , if it be not parallel , AB and cd being produced , shall meet

either towards B , D , or towards A , C ; let them be produced and meet towards B

...

Side 26

to the angle GKD ; and it was shown that the angle AGK is equal to the angle GhF

; therefore also AGK is equal to GKD ; and they are

A B is parallel ( I. 27. ) to CD . ' Wherefore straight lines , & c . Q.E.D. K F PROP .

to the angle GKD ; and it was shown that the angle AGK is equal to the angle GhF

; therefore also AGK is equal to GKD ; and they are

**alternate**angles ; thereforeA B is parallel ( I. 27. ) to CD . ' Wherefore straight lines , & c . Q.E.D. K F PROP .

Side 28

Let A B , CD be equal and parallel straight lines , and joined towards the same

parts by the straight A lines AC , BD ; AC , BD are also equal and parallel . Join

BC ; and because AB is parallel to CD , and BC meets them , the

angles ...

Let A B , CD be equal and parallel straight lines , and joined towards the same

parts by the straight A lines AC , BD ; AC , BD are also equal and parallel . Join

BC ; and because AB is parallel to CD , and BC meets them , the

**alternate**Сangles ...

Side 78

... straight line touches a circle , and from the point of contact a straight line be

drawn cutting the circle , the angles made by this line with the line touching the

circle , shall be equal to the angles which are in the

circle .

... straight line touches a circle , and from the point of contact a straight line be

drawn cutting the circle , the angles made by this line with the line touching the

circle , shall be equal to the angles which are in the

**alternate**segments of thecircle .

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### Andre utgaver - Vis alle

The first three books of Euclid's Elements of geometry, with theorems and ... Euclides Uten tilgangsbegrensning - 1851 |

The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Ingen forhåndsvisning tilgjengelig - 2014 |

The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Ingen forhåndsvisning tilgjengelig - 2014 |

### Vanlige uttrykk og setninger

ABCD alternate angle ABC angle ACB angle BAC angle equal base BC BC is equal bisect centre circle ABC circumference coincide common construct demonstrated describe diameter divided double draw equal angles equal to FB equilateral exterior angle extremity figure fore four given point given straight line gnomon greater impossible interior isosceles triangle join less Let ABC likewise line be drawn meet opposite angles opposite sides parallel parallelogram pass perpendicular PROB produced PROP Q. E. D. PROP rectangle contained remaining angle right angles segment semicircle shown sides squares of AC straight line AC Take taken THEOR third touch touches the circle triangle ABC twice the rectangle vertex wherefore whole

### Populære avsnitt

Side 6 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Side 5 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 20 - If two triangles have two sides of the one equal to two sides of the...

Side 30 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.

Side 17 - Any two angles of a triangle are together less than two right angles. Let ABC be any triangle ; any two of its angles together are less than two right angles.

Side 84 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square of the line which meets it, the line which meets it shall touch the circle.

Side 82 - If from any point without a circle two straight lines be drawn, one of -which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 11 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.

Side 19 - To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third, (i.

Side 7 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.