## 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].1814 |

### From inside the book

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Page 63

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**circle**two straight lines cut one another which do not both pass through the centre , they do not bisect each other . Let**ABCD**be a**circle**, and AC , BD two straight lines in it which cut one another in the point E , and do not both ... Page 65

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**ABCD**be a**circle**, and AD its diameter , in which let any point F be taken which is not the centre : Let the centre be E ; of all the straight lines FB , FC , FG , & c . that can be drawn from F to the**circumference**, FA is the greatest ... Page 71

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**circle ABC**in the points A , C , and join AC : Therefore , because the two points A , C are in the circumference of ... ABCD , be equal to one another , they are equally distant from the centre . G Take E the centre of the circle ABDC ... Page 72

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**ABCD**be a**circle**, of which the diameter is AD , and the centre E ; and let BC be nearer to the cen- tre than FG ; AD is greater than any straight line BC , which is not a dia- meter , and BC greater than FG . From the centre draw EH ... Page 77

Euclides Robert Simson. Let

Euclides Robert Simson. Let

**ABC**be a**circle**, and BEC an angle at the centre , Boox III . and BAC an angle at the**circumference**, which have them same**circumference**BC for their base ; the angle BEC is double of the angle BAC . 5. 1 . E ...### Other editions - View all

### Common terms and phrases

ABC is given AC is equal altitude angle ABC angle BAC base BC bisected BOOK XI centre circle ABCD circumference common logarithm cone cylinder demonstrated described diameter drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC logarithm meet multiple opposite parallel parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore

### Popular passages

Page 3-7 - 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 16 - Any two sides of a triangle are together greater than the third side.

Page 26 - 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 16 - 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 304 - 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 4 - 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 147 - 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 3-16 - 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 159 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.