## 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 : to this Edition are Also Annexed, Elements of Plane and Spherical Trigonometry |

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Resultat 1-5 av 61

Side 46

To describe a

To describe a

**square**upon a given straight line . Let AB be the given straight line ; it is required to describe a**square**upon AB . From the point A draw ( 11. 1. )**AC**at right angles to AB ; and make ( 3. 1. ) ... Side 47

**squares**GB , HC : and through A draw ( 31. 1. ) AL parallel to BD or CE , and join AD , FC : then , because each of the angles BAC , BAG , is a right angle , G ( 30. def . ) the two straight lines**AC**, AG upon the opposite sides of AB ... Side 48

If the

If the

**square**described upon BC , one of the sides of the triangle ABC , be equal to the**squares**upon the other sides BA ,**AC**, the angle BAC is a right angle . From the point A draw ( 11. 1. ) AD at right angles to**AC**, and make AD ... Side 50

the

the

**square**ADEB , and through C draw ( 31. 1. ) CF , parallel to AD or BE ; then AE is equal to the rectangles AF , CE : and AE is the**square**D of AB : and AF is the rectangle contained by F E $ , BA ,**AC**; for it is contained. Side 51

Let the straight line AB be divided into two parts in the point C ; the rectangle AB , BC is equal to the rectangle

Let the straight line AB be divided into two parts in the point C ; the rectangle AB , BC is equal to the rectangle

**AC**, CB together with the**square**of BC . Upon BC describe ( 46. 1 ; ) the A С B**square**CDEB , and produce ED to F ...### Hva folk mener - Skriv en omtale

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1810 |

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

### Vanlige uttrykk og setninger

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### Populære avsnitt

Side 11 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 155 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...

Side 329 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 20 - To draw a straight line at right angles to a given straight line, from a given point in the same.

Side 9 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Side 55 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Side 53 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Side 318 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Side 21 - The angles which one straight line makes with another upon one tide of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.

Side 27 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.