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 |
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Page 160
... gnomon ERO : but it has been proved that the gnomon ERO is equal to C ; and there- fore also Ts is equal to C. Wherefore the parallelogram TS , equal to the given rectilineal figure C , is applied to the given straight line AB ...
... gnomon ERO : but it has been proved that the gnomon ERO is equal to C ; and there- fore also Ts is equal to C. Wherefore the parallelogram TS , equal to the given rectilineal figure C , is applied to the given straight line AB ...
Page 161
... gnomon NOL , is equal to C. And because AE is equal to EB , the parallelogram AN is equal to the parallelogram NB , that is , to BM * : add NO to each ; there- fore the whole , viz . the parallelogram AX , is equal to the gnomon NOL ...
... gnomon NOL , is equal to C. And because AE is equal to EB , the parallelogram AN is equal to the parallelogram NB , that is , to BM * : add NO to each ; there- fore the whole , viz . the parallelogram AX , is equal to the gnomon NOL ...
Page 389
... gnomon given in magnitude , the sides of the gnomon are given in magnitude . First , let the parallelogram AB given in species and mag- nitude , be increased by the given gnomon ECBDFG : each of the straight lines CE , DF , is given ...
... gnomon given in magnitude , the sides of the gnomon are given in magnitude . First , let the parallelogram AB given in species and mag- nitude , be increased by the given gnomon ECBDFG : each of the straight lines CE , DF , is given ...
Page 390
... gnomon ECBDFG , each of the straight lines CE , DF , is given . Because the parallelogram AG is given , as also its gnomon ECBDFG , the remaining space AB is given in magnitude : but it is also given in species ; because it is similar ...
... gnomon ECBDFG , each of the straight lines CE , DF , is given . Because the parallelogram AG is given , as also its gnomon ECBDFG , the remaining space AB is given in magnitude : but it is also given in species ; because it is similar ...
Page 391
Euclides Robert Simson. nished by the given gnomon ELH , the sides EK , FH of the gnomon are given ; but EK is equal to DC , and FH to BD ; wherefore CD , DB are each of them given . This demonstration is the analysis of the problem in ...
Euclides Robert Simson. nished by the given gnomon ELH , the sides EK , FH of the gnomon are given ; but EK is equal to DC , and FH to BD ; wherefore CD , DB are each of them given . This demonstration is the analysis of the problem in ...
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Common terms and phrases
ABC is given altitude angle ABC angle BAC base BC BC is equal bisected centre circle ABCD 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 plane angles polygon prism Prop proportionals Q. E. D. PROPOSITION radius ratio of AE 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 three plane angles 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.