## 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 5

Side 45

Ira straight line be

whole and one of the parts is equal to the rectangle contained by the two parts ,

together with the square of the aforesaid part . Let the straight line AB be

into ...

Ira straight line be

**divided**into any two parts , the rectangle contained by thewhole and one of the parts is equal to the rectangle contained by the two parts ,

together with the square of the aforesaid part . Let the straight line AB be

**divided**into ...

Side 159

To

into parts that shall have the same ratios to one another which the parts of the

and ...

To

**divide**a given straight line similarly to a given**divided**straight line , that is ,into parts that shall have the same ratios to one another which the parts of the

**divided**given straight line have . Let AB be the straight line given to be**divided**,and ...

Side 252

See N . IF there be two pyramids of the same altitude , upon triangular bases ,

and each of them be

pyramid , and also into two equal prisms ; and if each of these pyramids be

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 wholepyramid , and also into two equal prisms ; and if each of these pyramids be

**divided**in the ... Side 302

This proposition is

construction and demonstration ; therefore it is now

PROP . XXXIII . B . III . This also in the Greek is

, two ...

This proposition is

**divided**into three cases , of which two have the sameconstruction and demonstration ; therefore it is now

**divided**only into two cases .PROP . XXXIII . B . III . This also in the Greek is

**divided**into three cases , of which, two ...

Side 397

And B the ratio of AB to BC is given ; and therefore b the ratio . 9 Dar . of AD to BC

is given . 3 Dat . PROP . LI . RECTILINEAL figures given in species , are

into triangles which are given in species . Let the rectilineal figure ABCDE be ...

And B the ratio of AB to BC is given ; and therefore b the ratio . 9 Dar . of AD to BC

is given . 3 Dat . PROP . LI . RECTILINEAL figures given in species , are

**divided**into triangles which are given in species . Let the rectilineal figure ABCDE be ...

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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.