## 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

Page 91

...

...

**tangent**DB . D e e 12. 1 . 13. 3 . But if DCA does not pass through the centre of the circle ABC , take the centre E , and draw EF perpendicular to 1.3 . AC , and join EB , EC , ED : And because the straight line EF , which passes ... Page 246

...

...

**tangents*** 41. 1. to the circle , the square EFGH is halfa of the square de- For there is some square equal to the circle ABCD ; let P be the side of it , and to three straight lines BD , FH , and P , there can be a fourth pro ... Page 474

...

...

**Tangent**of the arch AC , or of the angle ABC . VII . The straight line BE between the centre and the extremity of the**tangent**AE , is called the Secant of the arch AC , or angle ABC . COR . to def . 4. 6. 7. The sine ,**tangent**, and ... Page 475

...

...

**tangent**, and BE the secant , of the angle ABG or EBF , from def . 6. 7 . COR . to def . 4. 5. 6. 7. The sine , versed sine ,**tangent**, and Fig . 4 . secant , of any arch which is the measure of any given angle ABC , is to the sine ... Page 476

...

...

**tangent**of the angle opposite to it , and the hypothenuse the secant of the same angle . Let ABC be a right angled triangle : if the hypothenuse BC be made radius , either of the sides AC will be the sine of the angle ABC opposite to it ...### 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.