## 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 7

Side 105

1 . other sides , and the third angle to the third angle : Therefore the straight line

KC is equal to CL , and the angle FKC to the angle FLC : And because KC is

equal to CL , KL is double of KC ; In the same manner it may be

...

1 . other sides , and the third angle to the third angle : Therefore the straight line

KC is equal to CL , and the angle FKC to the angle FLC : And because KC is

equal to CL , KL is double of KC ; In the same manner it may be

**shown**that HK is...

Side 134

In like manner it may be

be greater than KH : therefore , as has been

because the whole GH is the same multiple of the whole AB , that HK is of BE ...

In like manner it may be

**shown**, that LM is greater than AL NP . ... Next , Let KObe greater than KH : therefore , as has been

**shown**, NP is greater than NM : Andbecause the whole GH is the same multiple of the whole AB , that HK is of BE ...

Side 282

... in the preceding proposition , it was

And AZ is perpendicular to the plane KBOS , and is therefore the shortest of all

the straight lines that can be drawn from A , the centre of the sphere , to that plane

...

... in the preceding proposition , it was

**shown**that KV falls without the circle FGH :And AZ is perpendicular to the plane KBOS , and is therefore the shortest of all

the straight lines that can be drawn from A , the centre of the sphere , to that plane

...

Side 285

... which was

sphere greater than DEF the triplicate ratio of that which BC has to EF : and it was

demonstrated , that nei . ther has it that ratio to any sphere less than DEF .

... which was

**shown**to be impossible : Therefore the sphere ABC has not to anysphere greater than DEF the triplicate ratio of that which BC has to EF : and it was

demonstrated , that nei . ther has it that ratio to any sphere less than DEF .

Side 334

... through the weakness of our minds , we are able to prevent mistakes , even in

the principles of sciences which are justly reckoned amongst the most certain ; for

that the proposition is not universally true , can be

... through the weakness of our minds , we are able to prevent mistakes , even in

the principles of sciences which are justly reckoned amongst the most certain ; for

that the proposition is not universally true , can be

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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.