## 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 17

than the с

therefore the angles ACD , ACB are greater than the angles ABC , ACB ; but ACD

, ACB are together equal ( 1 . 13. ) to two right angles ; therefore the angles ...

than the с

**interior**and opposite angle ABC ; to each of these add the angle ACB ;therefore the angles ACD , ACB are greater than the angles ABC , ACB ; but ACD

, ACB are together equal ( 1 . 13. ) to two right angles ; therefore the angles ...

Side 24

than the

which is impossible : therefore A B and co being pro- C F duced do not meet

towards B , D. In like mannerit may be demonstrated that they do not meet

towards AC ...

than the

**interior**and opposite angle EFG ; but it is also equal A. B toit ( Hyp . ) ,which is impossible : therefore A B and co being pro- C F duced do not meet

towards B , D. In like mannerit may be demonstrated that they do not meet

towards AC ...

Side 25

If a straight line fall upon two parallel straight lines , it makes the alternate angles

equal to one another ; and the exterior angle equal to the

upon the same side ; and likewise the two

If a straight line fall upon two parallel straight lines , it makes the alternate angles

equal to one another ; and the exterior angle equal to the

**interior**and oppositeupon the same side ; and likewise the two

**interior**angles upon the same side ... Side 26

If a side of any triangle be produced , the exterior angle is equal to the two

and opposite angles ; and the three

two right angles . Let ABC be a triangle , and let one of its sides Bc be produced ...

If a side of any triangle be produced , the exterior angle is equal to the two

**interior**and opposite angles ; and the three

**interior**angles of every triangle are equal totwo right angles . Let ABC be a triangle , and let one of its sides Bc be produced ...

Side 27

Again , é because AB is parallel to CE , and BD B falls upon them , the exterior

angle ECD is equal to the

was shown to be equal to the angle BAC ; therefore the whole exterior angle

ACD is ...

Again , é because AB is parallel to CE , and BD B falls upon them , the exterior

angle ECD is equal to the

**interior**and opposite angle ABC ; but the angle ACEwas shown to be equal to the angle BAC ; therefore the whole exterior angle

ACD is ...

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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.