## 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]. |

### Inni boken

Resultat 1-5 av 5

Side 254

Book XII . so are the two prisms in the

made by dividing the

number of ...

Book XII . so are the two prisms in the

**pyramid**ABCG to the two prisms in the**pyramid**DEFH ; and so are the two prisms in ... may be shown of tbe prismsmade by dividing the

**pyramids**AKLO and DPRS , and of all made by the samenumber of ...

Side 255

ABC is not to the base DEF , as the

the

DEF is not to the base ABC , as the

...

ABC is not to the base DEF , as the

**pyramid**ABCG to any solid which is less thanthe

**pyramid**DEFH . In the same manner it may be demonstrated , that the baseDEF is not to the base ABC , as the

**pyramid**DEFH to any solid which is less than...

Side 256

See N .

to one another as their bases . ... N , be of the same altitude : As the base ABCDE

to the base FGHKL , so is the

See N .

**PYRAMIDS**of the same altitude which have polygons for their bases , areto one another as their bases . ... N , be of the same altitude : As the base ABCDE

to the base FGHKL , so is the

**pyramid**ABCDEM to the pyra . mid FGHKLN . Side 257

ABCDE to the base FGHKL , so the

FGHKLN . Therefore

prism having a triangular base may be divided into three

ABCDE to the base FGHKL , so the

**pyramid**ABCDEM to De 22 . 5 . the**pyramid**FGHKLN . Therefore

**pyramids**, & c , Q . E . D . er . PROP . VII . THEOR . Everyprism having a triangular base may be divided into three

**pyramids**that have ... Side 351

6 . the

points M , N for their vertices , are ... 11 . the solids themselves are contained by

the same number of• . similar planes : In the same manner the

may ...

6 . the

**pyramids**which have the triangles EAB , LFG , for their bases , and thepoints M , N for their vertices , are ... 11 . the solids themselves are contained by

the same number of• . similar planes : In the same manner the

**pyramid**EBCMmay ...

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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.