## 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 8

If two triangles have two sides of the one equal to two sides of the other , each to

each ; and have

another ; they shall

...

If two triangles have two sides of the one equal to two sides of the other , each to

each ; and have

**likewise**theangles contained by those sides equal to oneanother ; they shall

**likewise**have their bases , or third sides , equal ; and the two...

Side 12

1 . equal a to one another : but the angle ECD is greater than the angle BCD ;

wherefore the angle FDC is

angle BDC greater than the angle BCD . Again , because CB is equal to DB , the

...

1 . equal a to one another : but the angle ECD is greater than the angle BCD ;

wherefore the angle FDC is

**likewise**greater than BCD ; much more then is theangle BDC greater than the angle BCD . Again , because CB is equal to DB , the

...

Side 13

side of are termine

coinciding with EF ; Book I . BA and AC shall coincide with ED and DF ; for , if the

base BC coincides with the base EF ; but the sides BA , CA do not coincide with

the ...

side of are termine

**likewise**is impossF . the BC is equal to EF ; therefore BCcoinciding with EF ; Book I . BA and AC shall coincide with ED and DF ; for , if the

base BC coincides with the base EF ; but the sides BA , CA do not coincide with

the ...

Side 134

BL D , Book V . are equimultiples of BE , DF ; and that KH , NM are equimultiples

multiple of the same BE , NP ,

...

BL D , Book V . are equimultiples of BE , DF ; and that KH , NM are equimultiples

**likewise**of BE , DF , if KO , the multiple of BE , be greater than KH , which is amultiple of the same BE , NP ,

**likewise**the multiple of DF , vi shall be greater than...

Side 309

... multiple , or the same part of B , which C is of D : A , B , Bi ' C , D , are

proportionals : This is demonstrated in proposition C . Secondly , if AB contain the

same parts of CĎ that EF does of GH ; in this case

GH .

... multiple , or the same part of B , which C is of D : A , B , Bi ' C , D , are

proportionals : This is demonstrated in proposition C . Secondly , if AB contain the

same parts of CĎ that EF does of GH ; in this case

**likewise**AB is to CD , as EF toGH .

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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.