## 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 7

But it has been

them equal to BG ; and things that are equal to the same are equal to one

another ; therefore the straight line Al is equal to BC . Wherefore from the given

point A a ...

But it has been

**shown**that bc is equal to BG ; wherefore AL and BC are each ofthem equal to BG ; and things that are equal to the same are equal to one

another ; therefore the straight line Al is equal to BC . Wherefore from the given

point A a ...

Side 57

angles ; wherefore FEB is a right angle : And FEA was

therefore FEA is equal to the angle FEB , the less to the greater , which is

impossible : Therefore AC , BD do not bisect one another . Wherefore , if in a

circle , & c ...

angles ; wherefore FEB is a right angle : And FEA was

**shown**to be a right angle ;therefore FEA is equal to the angle FEB , the less to the greater , which is

impossible : Therefore AC , BD do not bisect one another . Wherefore , if in a

circle , & c ...

Side 60

than the base FD : In like manner it may be

Therefore DA is the greatest ; and DE greater than DF , and DF than DC : And

because MK , KD are greater than MD , and C MK is equal to MG , the remainder

KD is ...

than the base FD : In like manner it may be

**shown**that rd is greater than cD :Therefore DA is the greatest ; and DE greater than DF , and DF than DC : And

because MK , KD are greater than MD , and C MK is equal to MG , the remainder

KD is ...

Side 86

... one another ; but Ed has been

therefore A E , EF , FB are equal to one another . 3. Through a given point to draw

a straight line which shall make equal angles with two straight lines given in

position .

... one another ; but Ed has been

**shown**to be equal to A E , and FD to FB ,therefore A E , EF , FB are equal to one another . 3. Through a given point to draw

a straight line which shall make equal angles with two straight lines given in

position .

Side 95

But since Pg is greater than GQ , the triangle APG is greater than AGQ , and the

triangle God is greater than GQP ; therefore , the whole triangle DPA is greater

than the whole triangle DQA ; but it has been

equal ...

But since Pg is greater than GQ , the triangle APG is greater than AGQ , and the

triangle God is greater than GQP ; therefore , the whole triangle DPA is greater

than the whole triangle DQA ; but it has been

**shown**that the triangle DPA isequal ...

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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.