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

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Side 67

From this it is manifest that the straight line which is drawn at right angles to the

diameter of a circle from the extremity of it ,

it only in one point , because , if it did meet the circle in two , it would fall within it ...

From this it is manifest that the straight line which is drawn at right angles to the

diameter of a circle from the extremity of it ,

**touches the circle**; and that it touchesit only in one point , because , if it did meet the circle in two , it would fall within it ...

Side 68

Therefore the angle EBA is equal to the angle EDF : But EDF is a right angle ,

wherefore EBA is a right angle : And EB is drawn from the centre : but a straight

line drawn from the extremity of a diameter , at right angles to it ,

Therefore the angle EBA is equal to the angle EDF : But EDF is a right angle ,

wherefore EBA is a right angle : And EB is drawn from the centre : but a straight

line drawn from the extremity of a diameter , at right angles to it ,

**touches the****circle**... Side 69

If a straight line

drawn at right angles to the touching line , the centre of the circle shall be in that

line . Let the straight line DE touch the circle ABC in • c , and from c let ca be

drawn ...

If a straight line

**touches a circle**, and from the point of contact a straight line bedrawn at right angles to the touching line , the centre of the circle shall be in that

line . Let the straight line DE touch the circle ABC in • c , and from c let ca be

drawn ...

Side 78

If a straight line

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

circle ...

If a straight line

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

Side 84

Let any point d be taken without the circle ABC , and from it let two straight lines

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

11.

Let any point d be taken without the circle ABC , and from it let two straight lines

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.

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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.