## 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].1834 |

### From inside the book

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Page 39

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**Gnomon**. Thus the parallelogram HG , together with the complements AF , FC , is the gno- 11 mon , which is more briefly expressed by the letters AGK , or EHC , which are at the opposite angles of the parallelograms which make the**gnomon**... Page 43

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**gnomon**CMG ; therefore the**gnomon**CMG is equal to the rectangle AD , DB : to each of these add LG , which is equal to the square of CD ; therefore the**gnomon**CMG , together with LG is equal to the rectangle AD , DB , together with ... Page 44

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**gnomon**CMG and LG make up the whole figure CEFD , which is the square of CD ; therefore the rectangle AD , DB ...**gnomon**AKF , to- gether with the square CK ; therefore the**gnomon**AKF , together with the square CK , ist double of ... Page 45

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**gnomon**AOH was demonstrated to be quadruple of AK ; therefore four times the rectangle AB , BC , is equal to the**gnomon**AOH : to each of these add XH , which is equal to the square of AC ; therefore four times the rectangle AB , BC ... Page 159

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**gnomon**CHL : therefore CE or the parallelogram AD , is greater than the parallelogram AF . A G FM H L D E 34. 1 . • 36. 1 . AKC B • 43. 1 . Next , let AK the base of AF , be less than AC : then , the same construction being made ...### Other editions - View all

### Common terms and phrases

ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circle EFGH circumference common logarithm cone Constr cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali 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 multiple parallel parallelogram perpendicular point F polygon prism Prop proportionals Q. E. D. PROPOSITION radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment shewn sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR.-If tiple triangle ABC vertex wherefore

### 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.