## 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 28

The opposite sides and angles of parallelograms are equal to one another , and

the

parallelogram is a four - sided figure , of which the opposite sides are parallel ;

and ...

The opposite sides and angles of parallelograms are equal to one another , and

the

**diameter**bisects them , that is , divides them in two equal parts . N. B. - Aparallelogram is a four - sided figure , of which the opposite sides are parallel ;

and ...

Side 31

and the triangle DBC is the half of the parallelogram DBCF , because the

therefore the triangle ABC is equal to the triangle DBC . Wherefore triangles , & c

. Q . E . D ...

and the triangle DBC is the half of the parallelogram DBCF , because the

**diameter**DC bisects it : But the halves of equal things are equal ( Ax . 7 . ) ;therefore the triangle ABC is equal to the triangle DBC . Wherefore triangles , & c

. Q . E . D ...

Side 34

The complements of the parallelogram which are about the

parallelogram , are equal to one another . Let ABCD be a parallelogram , of

which the

is ...

The complements of the parallelogram which are about the

**diameter**of anyparallelogram , are equal to one another . Let ABCD be a parallelogram , of

which the

**diameter**is AC , and EH , Fg the parallelograms about A H D AC , thatis ...

Side 58

If any point be taken in the

straight lines which can be drawn from it ... part of that

of any others , that which is nearer to the line which passes through the centre is

...

If any point be taken in the

**diameter**of a circle which is not the centre , of all thestraight lines which can be drawn from it ... part of that

**diameter**is the least ; and ,of any others , that which is nearer to the line which passes through the centre is

...

Side 66

Let ABC be a circle , the centre of which is D , and the

line drawn at right angles to A B from its extremity A , shall fall without the circle .

For , if it does not , let it fall , if possible , within the circle , as AC , and draw DC to

...

Let ABC be a circle , the centre of which is D , and the

**diameter**AB : the straightline drawn at right angles to A B from its extremity A , shall fall without the circle .

For , if it does not , let it fall , if possible , within the circle , as AC , and draw DC to

...

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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.