## 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 27

to two

interior angles of any rectilineal figure , together with four

...

to two

**right angles**; therefore also the angles CBA , BAC , ACB are equal to two**right angles**. Wherefore if a D . side of a triangle , & c . Q . E . D . CoR . 1 . All theinterior angles of any rectilineal figure , together with four

**right angles**, are equal...

Side 36

equal to two

because the straight line ng meets the parallels KM , FG , the alternate angles

MHG , HGF are equal ( 1. 29. ) : Add to each of these the angle HGL : Therefore

the ...

equal to two

**right angles**, ku is in the same straight line ( 1. 14. ) with hm ; andbecause the straight line ng meets the parallels KM , FG , the alternate angles

MHG , HGF are equal ( 1. 29. ) : Add to each of these the angle HGL : Therefore

the ...

Side 37

therefore each of the opposite angles A BE , BED is a

figure ADE B is rectangular , and it has been demonstrated that it is equilateral ; it

is therefore a square ( Def . 30. ) , and it is described upon the given straight ...

therefore each of the opposite angles A BE , BED is a

**right angle**; wherefore thefigure ADE B is rectangular , and it has been demonstrated that it is equilateral ; it

is therefore a square ( Def . 30. ) , and it is described upon the given straight ...

Side 77

F In a circle , the angle in a semicircle is a

greater than a semicircle is less than a

less than a semicircle is greater than a

F In a circle , the angle in a semicircle is a

**right angle**; but the angle in a segmentgreater than a semicircle is less than a

**right angle**; and the angle in a segmentless than a semicircle is greater than a

**right angle**. Let ABCD be a circle , of ... Side 78

greater segment is said to be greater , and the angle of the less segment is said

to be less , than a

same two ; and when the adjacent angles are equal , they are

greater segment is said to be greater , and the angle of the less segment is said

to be less , than a

**right angle**. ... because the angle adjacent to it is equal to thesame two ; and when the adjacent angles are equal , they are

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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.