## 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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+ Нур . + Hyp Let ABC , DEF be two triangles , which have the two sides AB , AC equal ... viz . the

+ Нур . + Hyp Let ABC , DEF be two triangles , which have the two sides AB , AC equal ... viz . the

**angle ABC**to the angle DEF , and the angle ACB to DFE . Page 9

A B to D and E : the

A B to D and E : the

**angle ABC**shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F ; and from AE , the greater ... Page 14

The angles which one straight line makes with another upon one side of it ... EBA , add to each of these equals the

The angles which one straight line makes with another upon one side of it ... EBA , add to each of these equals the

**angle ABC**; therefore the angles DBA ... Page 15

DBA ,

DBA ,

**ABC**are equalt to the three**angles**DBE , EBA ,**ABC**: + 2 Ax . but the**angles**CBE , EBD have been demonstrated to be equal to the same three**angles**... Page 17

be demonstrated , that the angle BCG , that is , the angle • • 15. 1 . ACD , is greater than the

be demonstrated , that the angle BCG , that is , the angle • • 15. 1 . ACD , is greater than the

**angle ABC**. Therefore , if one side , & c . Q. E. D. • 16.### What people are saying - Write a review

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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 Euclid 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 manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced Prop proportionals PROPOSITION proved pyramid Q. E. D. PROPOSITION radius reason rectangle rectangle contained remaining right angles segment shewn sides similar sine solid solid angle sphere square square of BC taken third triangle ABC wherefore whole

### Popular passages

Page 32 - To a given straight line, to apply a parallelogram which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle...

Page 138 - 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 39 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Page 22 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...

Page 41 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.

Page 5 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the...

Page 38 - IF a straight line be divided into any two parts, the rectangles contained by the whole and each of the parts, are together equal to the square of the whole line. Let the straight line AB be divided...

Page 262 - 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 89 - PBOR. —To describe an isosceles triangle, having each of the angles at the base, double of the third angle. Take any straight...

Page 165 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.