## The first three books of Euclid's Elements of geometry, with theorems and problems, by T. Tate |

### Inni boken

Side 59

... the greatest , and FD the least of all the straight lines from F to the

drawn only two equal straight lines from the point F to the

upon each side ...

... the greatest , and FD the least of all the straight lines from F to the

**circumference**; and BF is greater than CF , and CF than GF . Also there can bedrawn only two equal straight lines from the point F to the

**circumference**, oneupon each side ...

Side 61

to the base dB : But , besides DB , there can be no straight line drawn from to the

equal to dn , and also to DB ; therefore DB is equal to Dn , that is , the nearer to

the ...

to the base dB : But , besides DB , there can be no straight line drawn from to the

**circumference**equal to DK : For , if there can , let it be Dn ; and because Dk isequal to dn , and also to DB ; therefore DB is equal to Dn , that is , the nearer to

the ...

Side 74

In equal circles , the angles which stand upon equal

one another , whether they be at the ... when they are at the centre ; therefore the

In equal circles , the angles which stand upon equal

**circumferences**are equal toone another , whether they be at the ... when they are at the centre ; therefore the

**circumference**BK is equal to the**circumference**EF : But EF is equal to BC ... Side 76

K , L the centres of the circles , and join Bk , KC , EL , LF : and because the

bkc is equal ( III . 27. ) to the angle ELF : And because the circles ABC , DEF are

equal ...

K , L the centres of the circles , and join Bk , KC , EL , LF : and because the

**circumference**Bgc is equal to D K L C E B H the**circumference**E H F , the anglebkc is equal ( III . 27. ) to the angle ELF : And because the circles ABC , DEF are

equal ...

Side 105

If from any two points in the

circles , two straight lines be drawn so as to touch the less circle , they shall be

equal to one another . 13. If a quadrilateral rectilineal figure be described about a

...

If from any two points in the

**circumference**of the greater of two given concentriccircles , two straight lines be drawn so as to touch the less circle , they shall be

equal to one another . 13. If a quadrilateral rectilineal figure be described about a

...

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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.