## 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

Side 292

the Greek text , but is as necessary as the other : And that the case left out has

been formerly in the text , appears plainly from this , that the second part of

**PROP**. VII . B . I . There are two cases of this proposition , one of which is not inthe Greek text , but is as necessary as the other : And that the case left out has

been formerly in the text , appears plainly from this , that the second part of

**Prop**. Side 460

subject treated of in the four preceding propositions . • » »

which is

that ...

**PROP**. XXI . XXII . THESE now are added , as being wanting to complete thesubject treated of in the four preceding propositions . • » »

**PROP**. XXIII . This ,which is

**Prop**. 20 . in the Greek text , was separated from**Prop**. 14 . 15 . 16 . in 'that ...

Side 461

is changed into another , wherein the several cases of it are shown , which ,

though necessary , is not done in the Greek .

in ...

**PROP**. XLVII . * This is**Prop**: 44 . in the Greek text ' ; ' but the demonstration of itis changed into another , wherein the several cases of it are shown , which ,

though necessary , is not done in the Greek .

**PROP**. XLVIII . There are two casesin ...

Side 462

The demonstration of the first part of

. Gregory says , that the sentences he has inclosed betwixt two stars are

superfluous , and ought to be cancelled ; but he has not observed , that what

follows ...

The demonstration of the first part of

**Prop**. 73 , in the Greek is grossly vitiated . Dr. Gregory says , that the sentences he has inclosed betwixt two stars are

superfluous , and ought to be cancelled ; but he has not observed , that what

follows ...

Side 463

making use of

. .

a datum , but a theorem premised as a lemma to

making use of

**Prop**. 23 . instead of**Prop**. 22 . of Book 5 . of the Elements . It is X ,. .

**PROP**. LXXVII . This is put in place of**Prop**. 79 . in the Greek text , which is nota datum , but a theorem premised as a lemma to

**Prop**. 80 . in that text : And ...### Hva folk mener - Skriv en omtale

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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.