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
Results 6-10 of 94
Page 16
... BC be produced to D : the exterior angle ACD shall be greater than either of the interior opposite angles CBA , BAC ... base AB is equal to the base CF , and the triangle AEB to the triangle CEF , and the remaining angles to the re ...
... BC be produced to D : the exterior angle ACD shall be greater than either of the interior opposite angles CBA , BAC ... base AB is equal to the base CF , and the triangle AEB to the triangle CEF , and the remaining angles to the re ...
Page 21
... base BC is equal to the base EG . And be- cause DG is equal to DF , the angle DFG is equal to the angle DGF ; but the angle DGF is greater + than D CE 4.1 . G5.1 . F 9 Ax . the angle EGF ; therefore the angle DFG is greater than EGF ...
... base BC is equal to the base EG . And be- cause DG is equal to DF , the angle DFG is equal to the angle DGF ; but the angle DGF is greater + than D CE 4.1 . G5.1 . F 9 Ax . the angle EGF ; therefore the angle DFG is greater than EGF ...
Page 22
... base BC would be less * than the base EF ; but it ist not ; therefore the angle BAC is not less than the angle EDF : and it was shewn , that it is not equal to it ; therefore the angle BAC is greater than the angle EDF . Wherefore , if ...
... base BC would be less * than the base EF ; but it ist not ; therefore the angle BAC is not less than the angle EDF : and it was shewn , that it is not equal to it ; therefore the angle BAC is greater than the angle EDF . Wherefore , if ...
Page 23
... BC to EF ; and also the third . angle BAC to the third angle EDF . For if BC be not equal to EF , let BC be the ... base AH is equal + to the base DF , and the triangle ABH † 4. 1 . to the triangle DEF , and the other angles to the ...
... BC to EF ; and also the third . angle BAC to the third angle EDF . For if BC be not equal to EF , let BC be the ... base AH is equal + to the base DF , and the triangle ABH † 4. 1 . to the triangle DEF , and the other angles to the ...
Page 28
... BC : and because AB is parallel to CD , and BC meets them , the alternate an- gles * ABC , BCD are equal : and ... base AC is equal to the base BD , and the triangle ABC to the triangle BCD , and the other angles to the other ...
... BC : and because AB is parallel to CD , and BC meets them , the alternate an- gles * ABC , BCD are equal : and ... base AC is equal to the base BD , and the triangle ABC to the triangle BCD , and the other angles to the other ...
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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.