## 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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Side 189

A

A

**pyramid**is a solid figure contained by planes that are constituted betwixt one plane and one point above it în which they meet . XIII . A prism is a solid figure contained by plane figures , of which two that are opposite are ... Side 249

EVERY

EVERY

**pyramid**having a triangular base , may be see N , divided into two equal and similar**pyramids**having triangular bases , and which are similar to the whole**pyramid**, and into two equal prisms which together are greater than half of ... Side 250

Therefore the

Therefore the

**pyramid**, of which the base is the triangle AEG , and of which the C. 11. vertex is the point H , is equal and similar to the**pyramid**, D K the base of which is the triangle KHL , and vertex the point D. And because HK is ... Side 251

ABC , HKL : And it is manifest that each of these prisms is greater than either of the

ABC , HKL : And it is manifest that each of these prisms is greater than either of the

**pyramids**of which the triangles ... is greater than the**pyramid**of which the base is the triangle EBF , and vertex the point K : But this**pyramid**is ... Side 252

See N. IF there be two

See N. IF there be two

**pyramids**of the same altitude , upon triangular bases , and each of them be divided into two equal**pyramids**similar to the whole**pyramid**, and also into two equal prisms ; and if each of these**pyramids**be divided ...### 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.