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
Page 44
... rectangle contained by the whole and that part , together with the square of the other part . Let the straight line AB be divided into any two parts in the point C : the squares of AB , BC shall be equal to twice the rectangle AB , BC ...
... rectangle contained by the whole and that part , together with the square of the other part . Let the straight line AB be divided into any two parts in the point C : the squares of AB , BC shall be equal to twice the rectangle AB , BC ...
Page 45
... rectangle AB , BC , together with the square of AC , shall be equal to the square of the straight line made up of AB ... contained by AB , BC , for BK , ‡ is equal to BC , therefore four times the rectangle AB , BC , is quadruple of AK ...
... rectangle AB , BC , together with the square of AC , shall be equal to the square of the straight line made up of AB ... contained by AB , BC , for BK , ‡ is equal to BC , therefore four times the rectangle AB , BC , is quadruple of AK ...
Page 48
... rectangle contained by the whole and one of the parts , shall be equal to the square of the other part . Let AB be the given straight line ; it is required to divide it into two parts , so that the rectangle contained by the whole and ...
... rectangle contained by the whole and one of the parts , shall be equal to the square of the other part . Let AB be the given straight line ; it is required to divide it into two parts , so that the rectangle contained by the whole and ...
Page 49
... rectangle CF , FA , together with the square of AE , is equal to the square of EF : but EF is equal to EB ... contained by CF , FA , for FA is equal to FG ; and AD is the square of AB ; therefore FK + 30 Def . is equal † to AD : take away the ...
... rectangle CF , FA , together with the square of AE , is equal to the square of EF : but EF is equal to EB ... contained by CF , FA , for FA is equal to FG ; and AD is the square of AB ; therefore FK + 30 Def . is equal † to AD : take away the ...
Page 50
... rectangle BC , CD : but the square of BA is equal to the squares of BD , DA ... contained by either of these sides , and the straight line intercepted ... rectangle CB , BD . * First , let AD fall within the triangle ABC : and because the ...
... rectangle BC , CD : but the square of BA is equal to the squares of BD , DA ... contained by either of these sides , and the straight line intercepted ... rectangle CB , BD . * First , let AD fall within the triangle ABC : and because the ...
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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.