## 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 7

therefore ca is

and the triangle ABC is therefore equilateral , and it is described upon the given

straight line AB . Which was required to be done . PROP . II . PROB . From a

given ...

therefore ca is

**equal**to CB ; wherefore CA , A B ,**BC**are**equal**to one another ;and the triangle ABC is therefore equilateral , and it is described upon the given

straight line AB . Which was required to be done . PROP . II . PROB . From a

given ...

Side 29

BCA in one ,

side

therefore their other sides shall be

the ...

BCA in one ,

**equal**to two angles BCD , CBD in the other , each to each , and oneside

**bc**common to the two triangles , which is adjacent to their**equal**angles ;therefore their other sides shall be

**equal**, each to each , and the third angle ofthe ...

Side 40

L A into any parts in the points D , E ; the rectangle contained by the straight lines

A ,

contained by A , DE , and that contained by A , EC . From the point B draw ( 1. 11.

) ...

L A into any parts in the points D , E ; the rectangle contained by the straight lines

A ,

**BC is equal**to the B D E С rectangle contained by A , BD , together with thatcontained by A , DE , and that contained by A , EC . From the point B draw ( 1. 11.

) ...

Side 44

to

twice the rectangle AB ,

the square of AC ; therefore the gnomon AKF , together with the squares CK , HF

...

to

**Bc**: Therefore the gnomon D F AKF , together with the square ck , is**equal**totwice the rectangle AB ,

**BC**: To each of these**equals**add HF , which is**equal**tothe square of AC ; therefore the gnomon AKF , together with the squares CK , HF

...

Side 51

than a right angle ; and therefore the square of AB is

squares of AC , CB , and twice the rectangle

square of

twice ...

than a right angle ; and therefore the square of AB is

**equal**( 11. 12. ) to thesquares of AC , CB , and twice the rectangle

**BC**, CD : To these**equals**B add thesquare of

**BC**, and the squares of AB ,**BC**are**equal**to the square of ac , andtwice ...

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The first three books of Euclid's Elements of geometry, with theorems and ... Euclides Uten tilgangsbegrensning - 1851 |

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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.