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

### Inni boken

Resultat 1-5 av 5

Side 8

whence AE and c are each of them equal to AD ; wherefore the

equal to c ( Ax . 1. ) , and from ... Let ABC , DEF be two triangles which have the

two sides A B ,

whence AE and c are each of them equal to AD ; wherefore the

**straight line**AE isequal to c ( Ax . 1. ) , and from ... Let ABC , DEF be two triangles which have the

two sides A B ,

**AC**equal to the two sides DE , DF , each to each , viz . AB to DE ... Side 28

Let A B , CD be equal and parallel

parts by the straight A lines

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

angles ...

Let A B , CD be equal and parallel

**straight lines**, and joined towards the sameparts by the straight A lines

**AC**, BD ;**AC**, BD are also equal and parallel . JoinBC ; and because AB is parallel to CD , and BC meets them , the alternate С

angles ...

Side 40

L A into any parts in the points D , E ; the rectangle contained by the

A , BC is equal to the B D E С rectangle ... contained by AB , с в BC , together with

the rectangle * AB ,

L A into any parts in the points D , E ; the rectangle contained by the

**straight lines**A , BC is equal to the B D E С rectangle ... contained by AB , с в BC , together with

the rectangle * AB ,

**AC**, shall be equal to the square of Upon A B describe ( 1. Side 64

the circle ACK : And the circle ACK is without the circle ABC and therefore the

circumference of the circle ABC , the

the circle ACK : And the circle ACK is without the circle ABC and therefore the

**straight line ac**is without this last circle ; but , because the points A , C are in thecircumference of the circle ABC , the

**straight line AC**must be within ( iu . 2. ) ... Side 82

Lastly , Let neither of the

centre F , and through E , the intersection of the

diameter GEFH : And because the rectangle A E , EC is equal , as has been ...

Lastly , Let neither of the

**straight lines AC**, BD pass through the centre : Take thecentre F , and through E , the intersection of the

**straight lines AC**, DB , draw thediameter GEFH : And because the rectangle A E , EC is equal , as has been ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### 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 to FB equilateral exterior angle extremity figure fore four given point given straight line greater half impossible interior isosceles triangle join less Let ABC Let the straight likewise 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 side bc sides squares of AC straight lines 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.