## 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 8

whence A E and c are each of them equal to AV ; wherefore the

equal to c ( Ax . 1 . ) , and from ... Let ABC , DEF be two triangles which have the

two sides A B ,

whence A E and c are each of them equal to AV ; wherefore the

**straight line**AE isequal to c ( Ax . 1 . ) , and from ... Let ABC , DEF be two triangles which have the

two sides A B ,

**AC**equal to the two sides DE , DF , each to each , viz . AB to DE ... Side 28

Let A B , CD be equal and parallel

parts by the straight A lines

BC ; and because AB is parallel to CD , and BC meets them , the alternate С

angles ...

Let A B , CD be equal and parallel

**straight lines**, and joined towards the sameparts by the straight A lines

**AC**, BD ;**AC**, BD are also equal and parallel . JoinBC ; and because AB is parallel to CD , and BC meets them , the alternate С

angles ...

Side 64

in the straight line gh which bisects BD at right angles : Therefore go passes

through the point of contact ( 111. 11. ) ... the circle ACK : And the circle ACK is

without the circle ABand therefore the

but ...

in the straight line gh which bisects BD at right angles : Therefore go passes

through the point of contact ( 111. 11. ) ... the circle ACK : And the circle ACK is

without the circle ABand therefore the

**straight line Ac**is without this last circle ;but ...

Side 82

Lastly , Let neither of the

centre F , and through E , the intersection of the IL

the diameter GEFH : And because the rectangle A E , EC is equal , as has been ...

Lastly , Let neither of the

**straight lines AC**, BD pass through the centre : Take thecentre F , and through E , the intersection of the IL

**straight lines AC**, DB , drawthe diameter GEFH : And because the rectangle A E , EC is equal , as has been ...

Side 83

to AC , and join EB , EC , ED : And because the straight line EF , which passes

through the centre , cuts the

centre , at right angles , it shall likewise bisect it ( III . 3. ) ; therefore AF is equal to

FC ...

to AC , and join EB , EC , ED : And because the straight line EF , which passes

through the centre , cuts the

**straight line Ac**, which does not pass through thecentre , at right angles , it shall likewise bisect it ( III . 3. ) ; therefore AF is equal to

FC ...

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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.