## 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 79

UPON the same straight line , and upon the same see N . side of it , there cannot

be two similar

join CA , DA : And a because the

and ...

UPON the same straight line , and upon the same see N . side of it , there cannot

be two similar

**segments**of circles , not ... and draw the straight line BCD , andjoin CA , DA : And a because the

**segment**ACB is similar to the**segment**ADB ,and ...

Side 80

Therefore the straight line AB coinciding with CD , the

coincide with the

Wherefore similar

drawb DB Jets ...

Therefore the straight line AB coinciding with CD , the

**segment**AEB mustacoincide with the

**segment**CFD , and * 23 . 3 . o therefore is equal to it .Wherefore similar

**segments**, & c . R . E . D . be the given seen it is the sex pdrawb DB Jets ...

Side 81

From the certre E , at the distance of anym of the three AE , EB , EC , describe a

circle , this shall pass " through the other points ; and the circle of which ABC is a

...

From the certre E , at the distance of anym of the three AE , EB , EC , describe a

circle , this shall pass " through the other points ; and the circle of which ABC is a

**segment**is described : And it is evident , that if the angle ABD be greater than the...

Side 88

3 . of contact A cuts the circle , the angle DAB is equal to the angle in the

alternate

therefore also the angle C is equal to the angle in the

Wherefore , upon ...

3 . of contact A cuts the circle , the angle DAB is equal to the angle in the

alternate

**segment**6 32 . 3 . AHB8 : But the angle DAB is equal to the angle C ,therefore also the angle C is equal to the angle in the

**segment**D / AHB :Wherefore , upon ...

Side 450

If a straight line be drawn within a circle given in magnitude , cutting off a

again , and the ...

If a straight line be drawn within a circle given in magnitude , cutting off a

**segment**containing a given angle : If the angle adjacent to the angle in the**segment**be bisected by a straight line produced till it meet the circumferenceagain , and the ...

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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.