## 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]. |

### From inside the book

Results 1-5 of 5

Page

among the

is rendered plain and easy . ... Now this Proposition is a Theorem , not a

and not ...

among the

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

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

Page 305

And the

mathematics , depend upon " the accurate mathematical

this : To these we ought principally to attend , as the u doctrine of ratios is more

perfectly ...

And the

**definition**of analogy , which follows , viz . ... and the whole ofmathematics , depend upon " the accurate mathematical

**definitions**which follow “this : To these we ought principally to attend , as the u doctrine of ratios is more

perfectly ...

Page 320

Book VI . by substituting the 5th

the

Book VI . 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 ... Page 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 ...

Page 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...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### Common terms and phrases

added altitude angle ABC angle BAC arch 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 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

### Popular passages

Page 45 - 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.

Page 20 - Any two sides of a triangle are together greater than the third side.

Page 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.

Page 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...

Page 312 - 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.

Page 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.

Page 155 - 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.

Page 54 - 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.

Page 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.

Page 167 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.