## 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 55

Therefore the angle GDB is a right angle : But FDB is likewise a right angle ;

wherefore the angle FDB is equal to the angle GDB , the greater to the less ,

which is impossible : Therefore G is not the centre of the

manner ...

Therefore the angle GDB is a right angle : But FDB is likewise a right angle ;

wherefore the angle FDB is equal to the angle GDB , the greater to the less ,

which is impossible : Therefore G is not the centre of the

**circle ABC**: In the samemanner ...

Side 62

K cumference DEF in more than two А points , viz . in B , G , F ; take the centre k

of the

there is taken the point K , from which to the circumference DEF fall more than EL

...

K cumference DEF in more than two А points , viz . in B , G , F ; take the centre k

of the

**circle ABC**, and join KB , KG , D KF : And because within the circle DEFthere is taken the point K , from which to the circumference DEF fall more than EL

...

Side 64

Nor can two circles touch one another on the outside in more than one point : For

, if it be possible , let the circle ACK touch the

join ac : Therefore , because the two points A , C are in the circumference of the ...

Nor can two circles touch one another on the outside in more than one point : For

, if it be possible , let the circle ACK touch the

**circle abc**in the points A , C , andjoin ac : Therefore , because the two points A , C are in the circumference of the ...

Side 80

and because AB drawn from the point of contact A cuts the circle , the angle DAB

is equal to the angle in the alternate ... Let ABC be the given circle , and d the

given rectilineal angle ; it is required to cut off a segment from the

...

and because AB drawn from the point of contact A cuts the circle , the angle DAB

is equal to the angle in the alternate ... Let ABC be the given circle , and d the

given rectilineal angle ; it is required to cut off a segment from the

**circle ABC**that...

Side 84

Let any point d be taken without the

DCA and DB be drawn , of which DCA cuts the circle , and DB meets it ; if the

rectangle AD , DC be equal to the square of DB ; DB touches the circle . Draw (

11.

Let any point d be taken without the

**circle ABC**, and from it let two straight linesDCA and DB be drawn , of which DCA cuts the circle , and DB meets it ; if the

rectangle AD , DC be equal to the square of DB ; DB touches the circle . Draw (

11.

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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 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.