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 4
... Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . I. LET it be granted , that a straight line may be drawn from any one point to any other point ...
... Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . I. LET it be granted , that a straight line may be drawn from any one point to any other point ...
Page 23
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate angles AEF , EFD equal to one another : AB shall be parallel to CD . A E C / F 15 " For if it be not parallel , AB and CD , being ...
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate angles AEF , EFD equal to one another : AB shall be parallel to CD . A E C / F 15 " For if it be not parallel , AB and CD , being ...
Page 24
... parallel to one another : therefore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. * PROPOSITION XXVIII . THEOR . - If a straight line , falling upon two other straight lines , make the exterior angle equal to ...
... parallel to one another : therefore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. * PROPOSITION XXVIII . THEOR . - If a straight line , falling upon two other straight lines , make the exterior angle equal to ...
Page 25
... parallel to the same straight line , are parallel to each other . Let AB , CD be each of them parallel to EF : AB shall be parallel to CD . notes on this propo- sition . 15. 1 . † 1 Ax . +2 Ax . 13. 1 . † 1 Ax . A- B H E F K C- -D 29. 1 ...
... parallel to the same straight line , are parallel to each other . Let AB , CD be each of them parallel to EF : AB shall be parallel to CD . notes on this propo- sition . 15. 1 . † 1 Ax . +2 Ax . 13. 1 . † 1 Ax . A- B H E F K C- -D 29. 1 ...
Page 26
... parallel to the straight line BC . * In BC take any point D , and join AD ; and at the point A , in the straight line AD , make the angle DAE equal to the angle ADC ; and produce the straight line EA to F : EF shall be parallel to BC ...
... parallel to the straight line BC . * In BC take any point D , and join AD ; and at the point A , in the straight line AD , make the angle DAE equal to the angle ADC ; and produce the straight line EA to F : EF shall be parallel to BC ...
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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.