## 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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Side 162

EQUAL

the other , have their sides about the equal angles ... Complete the

FE ; and because the

EQUAL

**parallelograms**, which have one angle of the one equal to one angle ofthe other , have their sides about the equal angles ... Complete the

**parallelogram**FE ; and because the

**parallelogram**AB is equal to A BC , and that FE is another ... Side 173

5 . rallelogram AC to the

compounded of the ratios of the sides ... THEOR . ' Tue

diameter of any See X .

another .

5 . rallelogram AC to the

**parallelogram**CF : But K has to M the ratio which iscompounded of the ratios of the sides ... THEOR . ' Tue

**parallelograms**about thediameter of any See X .

**parallelogram**, aie siinilar to the whole , and to oneanother .

Side 176

ABCD and AEFG are similar

therefore c as GA to AE , so GA to 110 3 . ... That a

applied to a straight line , when it is described upon it as one of its sides . Ex . gr .

the ...

ABCD and AEFG are similar

**parallelograms**, as DA is to m AB , so is GA to AE ;therefore c as GA to AE , so GA to 110 3 . ... That a

**parallelogram**is said to beapplied to a straight line , when it is described upon it as one of its sides . Ex . gr .

the ...

Side 178

See N . To a given straight line to apply a

rectilineal figure , and deficient by à

applied is to be equal ...

See N . To a given straight line to apply a

**parallelogram**equal to a givenrectilineal figure , and deficient by à

**parallelogram**similar to a given**parallelogram**: But the given rectilineal figure to which the**parallelogram**to beapplied is to be equal ...

Side 435

Because the

43 . 1 . fore AK is given ; and BK is similarb 24 . 6 . - to AC , therefore BK is given

in spe . cies . And since the

...

Because the

**parallelogram**AK is . . equal a ' to BC which is given , there . E C •43 . 1 . fore AK is given ; and BK is similarb 24 . 6 . - to AC , therefore BK is given

in spe . cies . And since the

**parallelogram**H . AK given in magnitude is applied to...

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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 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.