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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Results 6-10 of 62
Page 48
... half a right angle , and is therefore equal to the angle DBG ; wherefore also the side BD is equal to the side DG . Again , because EGF is half a right angle , and that the angle at F is a right angle , because it is equal to the op ...
... half a right angle , and is therefore equal to the angle DBG ; wherefore also the side BD is equal to the side DG . Again , because EGF is half a right angle , and that the angle at F is a right angle , because it is equal to the op ...
Page 74
... half + of the angle BGC , and the angle at D half of the angle EHF ; therefore the angle at A is equal t to the angle at D. Wherefore , in equal circles , & c . Q. E. D. , PROPOSITION XXVIII . THEOR . - In equal circles , equal straight ...
... half + of the angle BGC , and the angle at D half of the angle EHF ; therefore the angle at A is equal t to the angle at D. Wherefore , in equal circles , & c . Q. E. D. , PROPOSITION XXVIII . THEOR . - In equal circles , equal straight ...
Page 90
... half of AD , and AF the half of AB , AE is equal to AF ; wherefore the sides op- posite to these are equal , viz . FG to GE : in the same manner it may be demonstrated , that GH , GK are each of them equal to FG or GE ; therefore the ...
... half of AD , and AF the half of AB , AE is equal to AF ; wherefore the sides op- posite to these are equal , viz . FG to GE : in the same manner it may be demonstrated , that GH , GK are each of them equal to FG or GE ; therefore the ...
Page 91
... half of DAB , and EBA the half of ABC , the angle EAB is equal to the angle EBA ; wherefore the side EA is equal to the side EB : in the same manner it may be demonstrated , that the straight lines EC , ED are each of them equal to EA ...
... half of DAB , and EBA the half of ABC , the angle EAB is equal to the angle EBA ; wherefore the side EA is equal to the side EB : in the same manner it may be demonstrated , that the straight lines EC , ED are each of them equal to EA ...
Page 96
... half of the angle BCD , and CDF the half of CDE , therefore the angle FCD is equal FDC ; wherefore the side CF is equal to the side FD : in like manner it may be demonstrated , that FB , FA , FE , are each of them equal to FC or FD ...
... half of the angle BCD , and CDF the half of CDE , therefore the angle FCD is equal FDC ; wherefore the side CF is equal to the side FD : in like manner it may be demonstrated , that FB , FA , FE , are each of them equal to FC or FD ...
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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.