## 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 4

... aru similar solid figures are those which are : cantained : by similar

... aru similar solid figures are those which are : cantained : by similar

**planes**of the same number and • magnitude ? ... by no more than three**plane**angles ; for in other cases , two solid figures may be contained by similar**planes**of ... Side 5

...

...

**plane**figures , which are not similar to one another , in the true sense of similarity received by all geometers ; and all these Propositions have , for these reasons , been insufficiently demonstrated since Theon's time hitherto . Side 6

... besides the Translation is much amended by the friendly assistance of a learned gentleman , To which are also added , the Elements of

... besides the Translation is much amended by the friendly assistance of a learned gentleman , To which are also added , the Elements of

**Plane**and Spherical Trigonometry , which are commonly taught after the Elements of Euclid . Side 7

A

A

**plane**superficies is that in which any two points being taken , * the straight line between them lies wholly in that superficies . VIII . “ A**plane**angle is the inclination of two lines to one another * in a**plane**, which meet ... Side 8

XIII . “ A term or boundary is the extremity of any thing . " XIV . A figure is that which is inclosed by one or more boundaries . XV . A circle is a

XIII . “ A term or boundary is the extremity of any thing . " XIV . A figure is that which is inclosed by one or more boundaries . XV . A circle is a

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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.