## 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 |

### Inni boken

Side 11

Parallel

produced ever so far both ways, do not meet. ... And that a

which are equal to the same are equal to one another.

equals, the wholes ...

Parallel

**straight lines**, are such as are in the same plane, and which beingproduced ever so far both ways, do not meet. ... And that a

**circle may**be**described**from**any centre**, at**any distance**from that**centre**.**AXIOMS**. I. Thingswhich are equal to the same are equal to one another.

**II**. If equals be added toequals, the wholes ...

Side 299

Viz. the First Six Books, Together with the Eleventh and Twelfth : the Errors by

which Theon, Or Others, Have

be increased without necessity, asitraust be if these propositions be not

demonstrated. ... from the determination he has given, viz. that

the Elements, as not to perceive that the

Viz. the First Six Books, Together with the Eleventh and Twelfth : the Errors by

which Theon, Or Others, Have

**Long**Ago ... that the number of**axioms**oughtnot tobe increased without necessity, asitraust be if these propositions be not

demonstrated. ... from the determination he has given, viz. that

**any**two of the**straight lines**DF, FG, GH must be greater than**the third**: for ... beginning to learnthe Elements, as not to perceive that the

**circle described**from the**centre**F, at the**distance**d M FD, ... Side 300

Viz. the First Six Books, Together with the Eleventh and Twelfth : the Errors by

which Theon, Or Others, Have

must meet one another, because FD and GH are together greater than FG? and

this ... that he

is that

D, atthe

EF, ...

Viz. the First Six Books, Together with the Eleventh and Twelfth : the Errors by

which Theon, Or Others, Have

**Long**Ago Vitiated ... and G; and that these**circles**must meet one another, because FD and GH are together greater than FG? and

this ... that he

**may**supply the omission he blames Euclid for; which determinationis that

**any**of the**three straight lines**must be ... acircle**described**from the**centre**D, atthe

**distance**DF, and must be in <hat part of it which isabovethe**straight line**EF, ...

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The Elements of Euclid: Viz. The First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1793 |

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.