## 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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Side 8

... straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right angle : and the straight line which stands on the other is called a

... straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right angle : and the straight line which stands on the other is called a

**perpendicular**to it . XI . Side 21

To draw a straight line

To draw a straight line

**perpendicular**to a given straight line of an unlimited length , from a given point without it . Let AB be the given straight line , which may be produced to any length both ways , and let C be a point without it ... Side 61

In obtuse angled triangles , if a

In obtuse angled triangles , if a

**perpendicular**be drawn from any of the acute angles to the opposite side produced , the square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse ... Side 62

Let ABC be any triangle , and the angle at B one of its acute angles , and upon BC , one of the sides containing it , let fall the

Let ABC be any triangle , and the angle at B one of its acute angles , and upon BC , one of the sides containing it , let fall the

**perpendicular**( 12. 1. ) AD from the opposite angle : the square of AC , opposite to the angle B ... Side 63

A Lastly , Let the side AC be

A Lastly , Let the side AC be

**perpendicular**. to BC ; then is BC thu straight line between the**perpendicular**and the acute angle at B ; and it is manifest that the square of AB , BC are equal ( 47. 1. ) to the square of AC and twice the ...### 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.