## 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 12

To bisect a given rectilineal angle , that is , to

BAC be the given rectilineal angle , it is ... the base Ad is equal to the base ( 1 . 4 .

) DB , and the straight line A B is

To bisect a given rectilineal angle , that is , to

**divide**it into two equal angles . LetBAC be the given rectilineal angle , it is ... the base Ad is equal to the base ( 1 . 4 .

) DB , and the straight line A B is

**divided**into two equal parts in the point d . Side 39

If there be two straight lines , one of which

rectangle contained by the two straight lines , is equal to the rectangles contained

by the undivided line , and the several parts of the

If there be two straight lines , one of which

**divided**into any number of parts ; therectangle contained by the two straight lines , is equal to the rectangles contained

by the undivided line , and the several parts of the

**divided**line . Let A and Bc be ... Side 40

If a straight line be

whole and each of the parts are together equal to the square of the whole line .

Let the straight line AB be

...

If a straight line be

**divided**into any two parts , the rectangles contained by thewhole and each of the parts are together equal to the square of the whole line .

Let the straight line AB be

**divided**into any two parts in the point c ; the rectangle...

Side 41

If a straight line be

whole and one of the parts is equal with the rectangle contained by the two parts ,

together with the square of the aforesaid part . Let the straight line AB be

...

If a straight line be

**divided**into any two parts , the rectangle contained by thewhole and one of the parts is equal with the rectangle contained by the two parts ,

together with the square of the aforesaid part . Let the straight line AB be

**divided**...

Side 49

To

the whole , and one of the parts , shall be equal to the square of ... the square

FGHA ; AB is

AH .

To

**divide**a given straight line into two parts , so that the rectangle contained bythe whole , and one of the parts , shall be equal to the square of ... the square

FGHA ; AB is

**divided**in H , so that the rectangle AB , Bh is equal to the square ofAH .

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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.