## 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 26

For , if it be not parallel , AB and CD being produced shall

D , or towards A , C : let them be produced and

therefore GEF is a triangle , and its exterior angle AEF is • 16 . 1 . greater than ...

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 . 1 . greater than ...

Side 201

If two straight lines meeting one another , be pa - See N . rallel to two straight

lines which

the plane which passes through these is parallel to the plane passing through the

...

If two straight lines meeting one another , be pa - See N . rallel to two straight

lines which

**meet**one another , but are not in the same plane with the first two ;the plane which passes through these is parallel to the plane passing through the

...

Side 202

For , if it is not , EF , GH , shall

: First , let them be produced on the side of FH , and

Therefore , since EFK is in the plane AB , every point in EFK is in that plane : and

K is a ...

For , if it is not , EF , GH , shall

**meet**, if produced , either on the side of FH , or EG: First , let them be produced on the side of FH , and

**meet**in the point K :Therefore , since EFK is in the plane AB , every point in EFK is in that plane : and

K is a ...

Side 340

The words at the end of this , " for a straight line can« not

more than one point , ” are left out , as an addition by some unskilful hand ; for

this is to be demonstrated , not assumed . Mr . Thomas Simpson , in his notes at

the ...

The words at the end of this , " for a straight line can« not

**meet**a straight line inmore than one point , ” are left out , as an addition by some unskilful hand ; for

this is to be demonstrated , not assumed . Mr . Thomas Simpson , in his notes at

the ...

Side 341

The thing that should have been demonstrated is , that two · or three straight lines

, that

the enunciation and demonstration are changed into those now put intc the text .

The thing that should have been demonstrated is , that two · or three straight lines

, that

**meet**one another , are in one plane . And as this is not sufficiently done ,the enunciation and demonstration are changed into those now put intc the text .

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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.