## 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]. |

### Inni boken

Resultat 1-5 av 5

Side 61

For , if it be not , let , if possible , G be the

Then , because DA is equal to DB , and DG common to the two triangles ADG ,

BDG , the two sides AD , DG , are equal to the two BD , DG , each to each ; and ...

For , if it be not , let , if possible , G be the

**centre**, and join Book III . GA , GD , GB :Then , because DA is equal to DB , and DG common to the two triangles ADG ,

BDG , the two sides AD , DG , are equal to the two BD , DG , each to each ; and ...

Side 63

If in a circle two straight lines cut one another which do not both pass through the

straight lines in it which cut one another in the point E , and do not both pass ...

If in a circle two straight lines cut one another which do not both pass through the

**centre**, they do not bisect each other . Let ABCD be a circle , and AC , BD twostraight lines in it which cut one another in the point E , and do not both pass ...

Side 69

But K is also the

two circles that cut one another , " % . ... If two circles touch each other internally ,

the straight line which joins their

But K is also the

**centre**of the circle ABC ; therefore the same point is the**centre**oftwo circles that cut one another , " % . ... If two circles touch each other internally ,

the straight line which joins their

**centres**being produced shall pass through ... Side 72

3 . drawn to them from the

distant from the

the

3 . drawn to them from the

**centre**are equalc : Therefore AB , CD must be equallydistant from the

**centre**. Next , if the straight lines AB , CD be equally distant fromthe

**centre**, that is , if FE be equal to EG ; AB is equal to CD : For , the same ... Side 89

If AC , BD pass each of them through the

evident , that AE , EC , BE , ED , being all equal , the rectangle AE , EC is likewise

B equal to the rectangle BE , ED . But let one of them BD pass through the

...

If AC , BD pass each of them through the

**centre**, so that E is the**centre**; it isevident , that AE , EC , BE , ED , being all equal , the rectangle AE , EC is likewise

B equal to the rectangle BE , ED . But let one of them BD pass through the

**centre**...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

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.