## 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

... therefore the angle GCB is equal to the angle DFE ; but DfE is , by the

hypothesis , equal to the angle BCA ; wherefore aso the angle BCG is equal to

the angle BCA , the less to the greater , which is

unequal to ...

... therefore the angle GCB is equal to the angle DFE ; but DfE is , by the

hypothesis , equal to the angle BCA ; wherefore aso the angle BCG is equal to

the angle BCA , the less to the greater , which is

**impossible**; therefore AB is notunequal to ...

Side 32

therefore also the triangle BDC is equal to the triangle EBC , the greater to the

less , which is

manner , it can be demonstrated that no other line but ad is parallel to BC ; Ad is ...

therefore also the triangle BDC is equal to the triangle EBC , the greater to the

less , which is

**impossible**: Therefore a E is not parallel to BC . B с In the samemanner , it can be demonstrated that no other line but ad is parallel to BC ; Ad is ...

Side 57

angles ; wherefore FEB is a right angle : And FEA was shown to be a right angle ;

therefore FEA is equal to the angle FEB , the less to the greater , which is

circle , & c ...

angles ; wherefore FEB is a right angle : And FEA was shown to be a right angle ;

therefore FEA is equal to the angle FEB , the less to the greater , which is

**impossible**: Therefore AC , BD do not bisect one another . Wherefore , if in acircle , & c ...

Side 61

which is

manner it may be demonstrated that no other point but d is the centre ; D

therefore is the centre . Wherefore , if a point be taken , & c . Q. E. D. PROP . X.

THEOR .

which is

**impossible**: Therefore È is not the centre of the circle ABC : In likemanner it may be demonstrated that no other point but d is the centre ; D

therefore is the centre . Wherefore , if a point be taken , & c . Q. E. D. PROP . X.

THEOR .

Side 62

the centre of the circle DEF : But K is also the centre of the с circle ABC : therefore

the same point is the centre of two circles that cut one another , which is

in ...

the centre of the circle DEF : But K is also the centre of the с circle ABC : therefore

the same point is the centre of two circles that cut one another , which is

**impossible**( 111. 5. ) . Therefore one circumference of a circle cannot cut anotherin ...

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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.