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 102
... the second , as the third together with the fourth , is to the fourth . 18th Prop . Book 5 . XVI . Dividendo , by division ; when there are four propor- tionals , and it is inferred , that the excess 102 EUCLID'S ELEMENTS .
... the second , as the third together with the fourth , is to the fourth . 18th Prop . Book 5 . XVI . Dividendo , by division ; when there are four propor- tionals , and it is inferred , that the excess 102 EUCLID'S ELEMENTS .
Page 103
... excess of the third above the fourth , is to the fourth . 17th Prop . Book 5 . XVII . Convertendo , by conversion ; when there are four pro- portionals , and it is inferred , that the first is to its excess above the second , as the ...
... excess of the third above the fourth , is to the fourth . 17th Prop . Book 5 . XVII . Convertendo , by conversion ; when there are four pro- portionals , and it is inferred , that the first is to its excess above the second , as the ...
Page 122
... excess above the second , as the third to its excess above the fourth . Let AB be to BE , as CD to DF : then BA shall be to AE , as DC to CF. Because AB is to BE , as CD to DF , therefore by division * , AE is to EB , as CF to FD ; and ...
... excess above the second , as the third to its excess above the fourth . Let AB be to BE , as CD to DF : then BA shall be to AE , as DC to CF. Because AB is to BE , as CD to DF , therefore by division * , AE is to EB , as CF to FD ; and ...
Page 127
... excess of the first and fifth shall be to the second , as the excess of the third and sixth to the fourth . The de- monstration of this is the same with that of the proposition , if division be used instead of composition . COR . 2 ...
... excess of the first and fifth shall be to the second , as the excess of the third and sixth to the fourth . The de- monstration of this is the same with that of the proposition , if division be used instead of composition . COR . 2 ...
Page 160
... excess of EF above C , and similar and similarly situated to D : then , since D is similar to EF , therefore also KM is similar to EF : let KL be the homologous side to EG , and LM to GF : and because EF is equal to C and KM together ...
... excess of EF above C , and similar and similarly situated to D : then , since D is similar to EF , therefore also KM is similar to EF : let KL be the homologous side to EG , and LM to GF : and because EF is equal to C and KM together ...
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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.