## The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner Corrected |

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Resultat 1-5 av 6

Side 57

Let the straight line AB be divided at the point C into two equal , and at D into two

unequal parts : the squares of AD , DB are together double of the

CD . From the point C draw ( 11. 1. ) CE at right angles to AB , and make it ...

Let the straight line AB be divided at the point C into two equal , and at D into two

unequal parts : the squares of AD , DB are together double of the

**squares of AC**,CD . From the point C draw ( 11. 1. ) CE at right angles to AB , and make it ...

Side 58

of EG , GF ; therefore the square of EF is double of the square of GF ; and GF is

equal ( 34. 1. ) to CD ; therefore the square of EF is double of the square of CD :

but the square of AE is likewise double of the

squares ...

of EG , GF ; therefore the square of EF is double of the square of GF ; and GF is

equal ( 34. 1. ) to CD ; therefore the square of EF is double of the square of CD :

but the square of AE is likewise double of the

**square of AC**: therefore thesquares ...

Side 59

to the squares of EC , CA ; therefore the square of EA is double of the

of FE : and therefore the squares of GF , FE are double of the square of EF : but

the ...

to the squares of EC , CA ; therefore the square of EA is double of the

**square of****AC**: again , because GF is equal to FE , the square of GF is equal to the squareof FE : and therefore the squares of GF , FE are double of the square of EF : but

the ...

Side 62

AD from the opposite angle : the

than the squares of CB , BA , by twice the rectangle CB , BD . First , Let AD fall

within the triangle ABC ; and because the straight line CD is divided into two А

parts ...

AD from the opposite angle : the

**square of AC**, opposite to the angle B , is lessthan the squares of CB , BA , by twice the rectangle CB , BD . First , Let AD fall

within the triangle ABC ; and because the straight line CD is divided into two А

parts ...

Side 446

to AEB , as AC to CB , so is AB to BE ; therefore the rectangle AC , BE is equal to

AB , BC ; and the rectangle AB , BC is given , wherefore AC , BE is given : and

because the sum of the squares of AB , BC is given , the

to AEB , as AC to CB , so is AB to BE ; therefore the rectangle AC , BE is equal to

AB , BC ; and the rectangle AB , BC is given , wherefore AC , BE is given : and

because the sum of the squares of AB , BC is given , the

**square of AC**which is ...### Hva folk mener - Skriv en omtale

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1825 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Euclid,Robert Simson Uten tilgangsbegrensning - 1838 |

### Vanlige uttrykk og setninger

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### Populære avsnitt

Side 9 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 81 - The angles in the same segment of a circle are equal to one another.

Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Side 96 - 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 155 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Side 22 - ANY two angles of a triangle are together less than two right angles.

Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.

Side 24 - Any two sides of a triangle are together greater than the third side.