## 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 6

Side 8

e 15 De Book I . Because the point B is the centre of the circle CGH , BC is

equale to BG ; and because D is the centre of the Det . circle GKL , DL is

DG , and DA , DB , parts of them , are

to * 3 ...

e 15 De Book I . Because the point B is the centre of the circle CGH , BC is

equale to BG ; and because D is the centre of the Det . circle GKL , DL is

**equal**toDG , and DA , DB , parts of them , are

**equal**; therefore the remainder AL is**equal**to * 3 ...

Side 10

Book I .

the angle ABC shall be

BCE . In BD take any point F , and from AE the greater , cut * 3 . 1 . off AG

Book I .

**equal**to AC , and let the straight lines AB , AC be produced w to D and E ,the angle ABC shall be

**equal**to the angle ACB , and the angle CBD to the angleBCE . In BD take any point F , and from AE the greater , cut * 3 . 1 . off AG

**equal**... Side 25

BC to EF , the two sides GB , BC are

each ; and the angle GBC is

equala to the base DF , * 4 . 1 . and the triangle GBC to the triangle DEF , and the

...

BC to EF , the two sides GB , BC are

**equal**to the two DE , Book I . EF , each toeach ; and the angle GBC is

**equal**to the an . gle DEF ; therefore the base GC isequala to the base DF , * 4 . 1 . and the triangle GBC to the triangle DEF , and the

...

Side 219

And Westraight line EDC make KH

Boor XI . gle at A , which is contained by the three plane angles BAL , BAH , HAL ,

is

And Westraight line EDC make KH

**equal**to GF , and join AH : Then the solid an -Boor XI . gle at A , which is contained by the three plane angles BAL , BAH , HAL ,

is

**equal**to the solid angle at D , contained by the three plane angles EDC ... Side 236

11 . makes right angles d with every straight line meeting it in that plane : But BH

meets it in that plane ; therefore ABH is a right angle : For the same reason DEM

is a right angle , and is therefore

11 . makes right angles d with every straight line meeting it in that plane : But BH

meets it in that plane ; therefore ABH is a right angle : For the same reason DEM

is a right angle , and is therefore

**equal**to the angle ABH . And the angle HAB is ...### 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 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples excess figure 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 306 - 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.