## The Elements of Euclid; viz. the first six books, together with the eleventh and twelfth. Also the book of Euclid's Data. By R. Simson. To which is added, A treatise on the construction of the trigonometrical canon [by J. Christison] and A concise account of logarithms [by A. Robertson]. |

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Resultat 1-5 av 69

Side 13

To bisect a given finite straight line , that is , to

To bisect a given finite straight line , that is , to

**divide**it into two equal parts . Let AB be the given straight line ; it is required to**divide**it into two equal parts . € 8. 1 . с a Describe upon it an equilateral triangle ABC ... Side 14

1. to the base DB , and the straight line AB is

1. to the base DB , and the straight line AB is

**divided**into two equal parts in the point D. Which was to be done . с Book I. PROP . XI . PROB . To draw a straight line at right angles to a given straight line , from a given point in ... Side 29

For any rectilineal figure ABCDE , can be

For any rectilineal figure ABCDE , can be

**divided**into as many triangles as the figure has sides , by drawing straight lines from a point F within the figure to A A E a 31. 1 . b 29. 1 . BOOK I. each of its angles . And , by OF EUCLID . Side 43

If there be two straight lines , one of which is

If there be two straight lines , one of which is

**divided**into any number of parts ; the rectangle contained by the two straight lines , is equal to the rectangles contained by the undivided line , and the several parts of the**divided**... Side 44

D E C Let A and BC be two straight lines ; and let BC be

D E C Let A and BC be two straight lines ; and let BC be

**divided**into any parts in the points D , E ; the rectangle contained by the straight lines A , B BC is equal to the rectangle contained by A , BD , together with that contained by ...### Hva folk mener - Skriv en omtale

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The Elements of Euclid; viz. the first six books, together with the eleventh ... Euclides Uten tilgangsbegrensning - 1834 |

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added altitude angle ABC angle BAC arch base Book Book XI centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples 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 logarithm magnitude manner meet multiple 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 Take taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 43 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.

Side 20 - Any two sides of a triangle are together greater than the third side.

Side 30 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 20 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...

Side 310 - 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 8 - DL is equal to DG, and DA, DB, parts of them, are equal ; therefore the remainder AL is equal to the remainder (3. Ax.) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC.

Side 153 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Side 52 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.

Side 3 - 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 165 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.