## 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 17

Any two angles of a triangle are together

any triangle ; any two of A its angles together are

Produce BC to D ; and because ACD is the exterior angle of the triangle B ABC ,

ACD ...

Any two angles of a triangle are together

**less**than two right angles . Let ABC beany triangle ; any two of A its angles together are

**less**than two right angles .Produce BC to D ; and because ACD is the exterior angle of the triangle B ABC ,

ACD ...

Side 60

and the diameter ; and of the rest , that which is nearer to the least is always

than one more remote : And only two equal straight lines can be drawn from the

same point to the circumference , one upon each side of the least line . Let ABC ...

and the diameter ; and of the rest , that which is nearer to the least is always

**less**than one more remote : And only two equal straight lines can be drawn from the

same point to the circumference , one upon each side of the least line . Let ABC ...

Side 66

preceding , Bc is double of bH , and Fg double of FK , and the squares of EH , BH

are equal to the squares of EK , KF , of which the square of Ez is

square of EK , because En is

preceding , Bc is double of bH , and Fg double of FK , and the squares of EH , BH

are equal to the squares of EK , KF , of which the square of Ez is

**less**than thesquare of EK , because En is

**less**than EK ; therefore the square of Bh is greater ... Side 75

In equal circles , equal straight lines cut off equal circumferences , the greater

equal to the greater , and the

and BC , EF equal straight lines in them , which cut off the two greater

circumferences ...

In equal circles , equal straight lines cut off equal circumferences , the greater

equal to the greater , and the

**less**to the**less**. Let ABC , DEF be equal circles ,and BC , EF equal straight lines in them , which cut off the two greater

circumferences ...

Side 77

F In a circle , the angle in a semicircle is a right angle ; but the angle in a segment

greater than a semicircle is

F In a circle , the angle in a semicircle is a right angle ; but the angle in a segment

greater than a semicircle is

**less**than a right angle ; and the angle in a segment**less**than a semicircle is greater than a right angle . Let ABCD be a circle , of ...### Hva folk mener - Skriv en omtale

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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.