## 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 57

Side 3

... a very few interpolations , explications , and additions , Theon altered nothing in Euclid . ” But , by often considering and comparing together the

... a very few interpolations , explications , and additions , Theon altered nothing in Euclid . ” But , by often considering and comparing together the

**Definitions**and Demonstrations as they are in the Greek editions we now have ... Side 4

Now this Proposition is a Theorem ;. not a

Now this Proposition is a Theorem ;. not a

**Definition**; because the equality of figures of any kind , iust be demonstrated , and not assumed ; and therefore , though this were a true Proposition , it ought to have been demonstrated . Side 5

Now , upon the 10th

Now , upon the 10th

**Definition**of this Book depend the 25th and 28th Propositions of it ; and upon the 25th and 26th depend other eight , viz . the 27th , 31st , 32d , 33d , 34th , 36th , 37th , and 40th of the same Book ; and the 12th ... Side 6

Also the Note on the 29th Proposition , Book Ist , is altered , and made more explicit , and a more general Demonstration is given , instead of that which was in the Note on the 10th

Also the Note on the 29th Proposition , Book Ist , is altered , and made more explicit , and a more general Demonstration is given , instead of that which was in the Note on the 10th

**Definition**of Book 11th ; besides the Translation is ... Side 7

BOOK I.

BOOK I.

**DEFINITIONS**. I. A POINT is that which hath no parts , or which hath no magnitude . * II . A line is length without breadth . III . The extremities of a line are points . IV . A straight line is that which lies evenly between ...### 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

added altitude angle ABC angle BAC base BC is given centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole

### 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.