## 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 2

A plane angle is the inclination of two lines to one another in a plane , which

the inclination of two straight lines to one another , which

not ...

A plane angle is the inclination of two lines to one another in a plane , which

**meet**together , but are not in the same direction . " IX . A plane rectilineal angle isthe inclination of two straight lines to one another , which

**meet**together , but arenot ...

Side 24

For , if it be not parallel , AB and cd being produced , shall

D , or towards A , C ; let them be produced and

therefore GEF is a triangle , and its exterior angle A EF is greater ( 1. 16. ) ...

For , if it be not parallel , AB and cd being produced , shall

**meet**either towards B ,D , or towards A , C ; let them be produced and

**meet**towards B , D in the point g ;therefore GEF is a triangle , and its exterior angle A EF is greater ( 1. 16. ) ...

Side 25

together if continually produced ; therefore the straight lines AB , CD , if produced

far enough , shall

hypothesis ; therefore the angle agh is not unequal to the angle GHD , that is , it is

...

together if continually produced ; therefore the straight lines AB , CD , if produced

far enough , shall

**meet**; but they never**meet**, since they are parallel by thehypothesis ; therefore the angle agh is not unequal to the angle GHD , that is , it is

...

Side 35

if produced far enough : Therefore B , FE shall

in K , and through a draw KL parallel to EA or FH , and produce HA , GB to the

points L , M : Then ALKF is a parallelogram , of which the diameter is hk , and AG

...

if produced far enough : Therefore B , FE shall

**meet**, if produced ; let them**meet**in K , and through a draw KL parallel to EA or FH , and produce HA , GB to the

points L , M : Then ALKF is a parallelogram , of which the diameter is hk , and AG

...

Side 47

EF parallel to AB , and through D draw DF parallel to CE : And because the

straight line EF

Therefore EB , FD shall

and join AG ...

EF parallel to AB , and through D draw DF parallel to CE : And because the

straight line EF

**meets**the parallels EC , FD , the ... if produced far enough :Therefore EB , FD shall

**meet**, if produced towards B , D : Let them**meet**in G ,and join AG ...

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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.