## 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 100

Side 5

**Parallel**straight lines , are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . I. LET it be granted that a straight line may be drawn from any one point to any other point . Side 26

For , if it be not

For , if it be not

**parallel**, AB and CD being produced shall meet either towards B , D , or towards A , C : let them be produced and meet towards B , D in the point G ; therefore GEF is a triangle , and its exterior angle AEF is * 16. Side 27

C Because the angle EGB is equal to the angle GHD , and Book I. the angle EGB equala to the angle AGH , the angle AGH is equal to the angle GHD ; and they are the alternate angles ; therefore AB is

C Because the angle EGB is equal to the angle GHD , and Book I. the angle EGB equala to the angle AGH , the angle AGH is equal to the angle GHD ; and they are the alternate angles ; therefore AB is

**parallel**to CD . Side 28

STRAIGHT lines which are

STRAIGHT lines which are

**parallel**to the same straight line are**parallel**to each other . Let AB , CD be each of them**parallel**to EF ; AB is also**parallel**to CD . ALet the straight line GHK cut AB , EF , CD ; and because GHK cuts the ... Side 29

ADC equal to one another , EF is

ADC equal to one another , EF is

**parallel**to BC . There- Book I. fore the straight line EAF is drawn through the given point A**parallel**to the given straight line BC . Which was to be done .. PROP . XXXII . THEOR .### 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.