## 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 56

If a straight line drawn through the centre of a circle bisect a straight line in it

which does not

cuts it at right angles , it shall bisect it . Let ABC be a circle , and let CD , a straight

line ...

If a straight line drawn through the centre of a circle bisect a straight line in it

which does not

**pass**through the centre , it shall cut it at right angles ; and , if itcuts it at right angles , it shall bisect it . Let ABC be a circle , and let CD , a straight

line ...

Side 57

If in a circle two straight lines cut one another which do not both

centre , they do not bisect each the other . Let ABCD be a circle , and AC , BD two

straight lines in it which cut one another in the point E , and do not both

If in a circle two straight lines cut one another which do not both

**pass**through thecentre , they do not bisect each the other . Let ABCD be a circle , and AC , BD two

straight lines in it which cut one another in the point E , and do not both

**pass**... Side 63

If two circles touch each other externally , the straight line which joins their

centres shall

touch each other externally in the point A : and let F be the centre of the circle

ABC , and G ...

If two circles touch each other externally , the straight line which joins their

centres shall

**pass**through the point of contact . Let the two circles ABC , ADEtouch each other externally in the point A : and let F be the centre of the circle

ABC , and G ...

Side 81

If AC , BD

evident , that AE , EC , BE , ED , being all equal , the rectangle AE , EC is likewise

equal to the B rectangle BE , ED . But let one of them bo

...

If AC , BD

**pass**each of them through the centre , so that E is the centre ; it isevident , that AE , EC , BE , ED , being all equal , the rectangle AE , EC is likewise

equal to the B rectangle BE , ED . But let one of them bo

**pass**through the centre...

Side 102

To describe a circle which shall

line in another given point . 11. To describe a circle which shall

given point , and touch a given circle in another given point . 12. To describe a

circle ...

To describe a circle which shall

**pass**through a given point , and touch a givenline in another given point . 11. To describe a circle which shall

**pass**through agiven point , and touch a given circle in another given point . 12. To describe a

circle ...

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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.