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 17
... triangle are together less than two right angles . Let ABC be any triangle : any two of its angles together shall be less than two right angles . * 16. 1 . B † 4 Ax . Produce BC to D : and because ACD is the exterior angle of the ...
... triangle are together less than two right angles . Let ABC be any triangle : any two of its angles together shall be less than two right angles . * 16. 1 . B † 4 Ax . Produce BC to D : and because ACD is the exterior angle of the ...
Page 18
... ABC would be equal to the angle CAB ; but it * is not ; therefore AC is not equal to AB : neither is it less ... triangle are together greater than the third side . Let ABC be a triangle : any two sides of it together shall be greater ...
... ABC would be equal to the angle CAB ; but it * is not ; therefore AC is not equal to AB : neither is it less ... triangle are together greater than the third side . Let ABC be a triangle : any two sides of it together shall be greater ...
Page 22
... ABC , DEF be two triangles , which have the angles ABC , BCA equal to the angles DEF , EFD , each to each , viz ... triangle GBC to the triangle DEF , and the other angles to the other angles , each to each , to which the equal sides are ...
... ABC , DEF be two triangles , which have the angles ABC , BCA equal to the angles DEF , EFD , each to each , viz ... triangle GBC to the triangle DEF , and the other angles to the other angles , each to each , to which the equal sides are ...
Page 26
... triangle are equal to two right angles . Let ABC be a triangle , and let one of its sides BC be pro- duced to D ; the exterior angle ACD shall be equal to the two interior and opposite angles CAB , ABC ; and the three interior angles of ...
... triangle are equal to two right angles . Let ABC be a triangle , and let one of its sides BC be pro- duced to D ; the exterior angle ACD shall be equal to the two interior and opposite angles CAB , ABC ; and the three interior angles of ...
Page 27
... ABC : to each of these equals add the angle ACB ; and the angles ACD , ACB ... triangle , & c . Q. E. D. * COR . 1. All the interior angles of any ... ABC , with its adjacent exterior ABD , is equal to two right angles , there- fore all ...
... ABC : to each of these equals add the angle ACB ; and the angles ACD , ACB ... triangle , & c . Q. E. D. * COR . 1. All the interior angles of any ... ABC , with its adjacent exterior ABD , is equal to two right angles , there- fore all ...
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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.