## 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

among the

is rendered plain and easy . ... not a

of any kind must be demonstrated , and not assumed ; and therefore , though ...

among the

**Definitions**of the 5th Book , by which the doctrine of compound ratiosis rendered plain and easy . ... not a

**Definition**; because the equality of figures ' ,of any kind must be demonstrated , and not assumed ; and therefore , though ...

Side 305

And the

the accurate mathematical

principally to attend , as the “ doctrine of ratios is more perfectly explained by

them ...

And the

**definition**of analogy , which follows , viz . ... mathematics , depend upon “the accurate mathematical

**definitions**which follow “ this : To these we oughtprincipally to attend , as the “ doctrine of ratios is more perfectly explained by

them ...

Side 320

Boor VL by substituting the 5th

the

...

Boor VL by substituting the 5th

**definition**of the 6th book in place of the right**definition**, which without doubt Eudoxus or Euclid gave , in its proper place , afterthe

**definition**of triplicate ratio , & c . in the 5th book . Theon ' s**definition**is this ; a...

Side 321

book , as appears from Hervagius ' s edition : But Zambertus Boox VI . and

Commandine , in their Latin translations , subjoin the same to these

Neither Campanus , nor , as it seems , the Arabic manuscripts from which he

made his ...

book , as appears from Hervagius ' s edition : But Zambertus Boox VI . and

Commandine , in their Latin translations , subjoin the same to these

**definitions**.Neither Campanus , nor , as it seems , the Arabic manuscripts from which he

made his ...

Side 333

The similitude of plane figures is

the proportionality of the sides about the ... that are neither similar por equal , as

shall be demonstrated after the notes on the 10th

...

The similitude of plane figures is

**defined**from the equality of their angles , andthe proportionality of the sides about the ... that are neither similar por equal , as

shall be demonstrated after the notes on the 10th

**definition**: Upon this account it...

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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.