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].1814 |
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Page 9
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles to which the equal sides B are opposite , shall be CE equal each to each , viz . the angle ABC to ...
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles to which the equal sides B are opposite , shall be CE equal each to each , viz . the angle ABC to ...
Page 10
... angles , each to each , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG : And , since it has been demonstrated , that the ... angle ABC equal 10 THE ELEMENTS.
... angles , each to each , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG : And , since it has been demonstrated , that the ... angle ABC equal 10 THE ELEMENTS.
Page 11
Euclides Robert Simson. Let ABC be a triangle having the angle ABC equal to the angle ACB ; the side AB is also equal ... angles , & c . Q. E. D. B C COR . Hence every equiangular triangle is also equila- teral . PROP . VII . THEOR . b 4 ...
Euclides Robert Simson. Let ABC be a triangle having the angle ABC equal to the angle ACB ; the side AB is also equal ... angles , & c . Q. E. D. B C COR . Hence every equiangular triangle is also equila- teral . PROP . VII . THEOR . b 4 ...
Page 13
... equal angles . Let BAC be the given rectilineal angle , it is required to bisect it . b 1.1 . Take any point D in AB , and from AC cut off AE equal . 3. 1 . to AD ; join DE , and upon it describeb an equilateral triangle DEF ; then join ...
... equal angles . Let BAC be the given rectilineal angle , it is required to bisect it . b 1.1 . Take any point D in AB , and from AC cut off AE equal . 3. 1 . to AD ; join DE , and upon it describeb an equilateral triangle DEF ; then join ...
Page 14
... angles to the given straight line AB . с AD F E B Because DC is equal to CE , and FC common to the two triangles DCF , ECF ; the two sides DC , CF , are equal to the two EC , CF , each to each ; and the base DF is equal to the base EF ...
... angles to the given straight line AB . с AD F E B Because DC is equal to CE , and FC common to the two triangles DCF , ECF ; the two sides DC , CF , are equal to the two EC , CF , each to each ; and the base DF is equal to the base EF ...
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Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected BOOK XI centre circle ABCD circumference common logarithm cone cylinder demonstrated described diameter drawn equal angles equiangular equimultiples Euclid 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 meet multiple opposite parallel parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Popular passages
Page 3-7 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 16 - Any two sides of a triangle are together greater than the third side.
Page 26 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 16 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Page 304 - 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 4 - DL is equal to DG, and DA, DB, parts of them, are equal ; therefore the remainder AL is equal to the remainder (3. Ax.) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC.
Page 147 - 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 3-16 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Page 159 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.