## 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 94

A RECTILINEAL

all the angles of the inscribed See N .

which it is inscribed , each upon each . II . In like manner , a

A RECTILINEAL

**figure**is said to be inscribed in another rectilineal**figure**, whenall the angles of the inscribed See N .

**figure**are upon the sides of the**figure**inwhich it is inscribed , each upon each . II . In like manner , a

**figure**is said to be ... Side 215

SOLID

alike situated , and having none of their ... DE to NO ; and , lastly , FH similar and

equal to PR : The solid

SOLID

**figures**contained by the same number of See N . equal and similar planesalike situated , and having none of their ... DE to NO ; and , lastly , FH similar and

equal to PR : The solid

**figure**AG is equal and similar to the solid**figure**KQ . Side 217

SOLID

alike situated , and having none of their ... DE to NO ; and , lastly , FH similar and

equal to PR : The solid

SOLID

**figures**contained by the same number of Sec N . equal and similar planesalike situated , and having none of their ... DE to NO ; and , lastly , FH similar and

equal to PR : The solid

**figure**AG is equal and similar to the solid**figure**KQ . Side 334

The equxlity of

though it were true , that solid

following is sufficient : Let there be any plane rectilineal

12 .

The equxlity of

**figures**ought not to be defined , but demonstrated : Therefore ,though it were true , that solid

**figures**... can be shown by many examples : Thefollowing is sufficient : Let there be any plane rectilineal

**figure**, as the triangle •12 .

Side 402

And because the si . nilar rectilineal fi . gures AG , F , are described upon the

straight lines AB , CD , which have a given ratio , find their ratio by the 54th dat .

and make the ratio of K to L the same : The

which H ...

And because the si . nilar rectilineal fi . gures AG , F , are described upon the

straight lines AB , CD , which have a given ratio , find their ratio by the 54th dat .

and make the ratio of K to L the same : The

**figure**E has 10 F the same ratiowhich H ...

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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.