## 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 66

Also there can be drawn only two equal straight lines from the point F to the

straight c - 93 . 1 . line EF , make c the angle FEH equal to the angle GEF , and

join FH ...

Also there can be drawn only two equal straight lines from the point F to the

**circumference**, one upon each side of the shortest line FD : At the point E in thestraight c - 93 . 1 . line EF , make c the angle FEH equal to the angle GEF , and

join FH ...

Side 183

Take any number of

whatever FM , MN , each equal to EF ... 3 . the

the ...

Take any number of

**circumferences**CK , KL , each equal to BC , and any numberwhatever FM , MN , each equal to EF ... 3 . the

**circumference**BL is of the**circumference**BC , the same - multiple is the angle BGL of the angle BGC : Forthe ...

Side 184

Book VI . be equal to the

the angle EHN ; and if the

the angle BGL is greater thav EHN : and if less , less : There being then four ...

Book VI . be equal to the

**circumference**EN , the angle BGL is also n equala tothe angle EHN ; and if the

**circumference**BL 27 . 3 . be greater than EN , likewisethe angle BGL is greater thav EHN : and if less , less : There being then four ...

Side 185

E ater tre - HF , C1 EN , the sector BGL is equal to the sector EHN ; and if the

E ater tre - HF , C1 EN , the sector BGL is equal to the sector EHN ; and if the

**circumference**BL be greater than ... there are four magnitudes , the two**circumferences**BC , EF , and the two sectors BGC , EHF , and of the**circumference**BC , and ... Side 473

Elem , the angle ABC is to a right angle ABD , as the arch AC to the arch AD ; and

quadrupling the consequents , the angle ABC will be to four right angles , as the

arch AC to four times the arch AD , or to the whole

Elem , the angle ABC is to a right angle ABD , as the arch AC to the arch AD ; and

quadrupling the consequents , the angle ABC will be to four right angles , as the

arch AC to four times the arch AD , or to the whole

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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.