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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... likewise is of the greatest use in the arts both of peace and war , to many of which geometry is absolutely necessary . This I have endeavoured to do , by taking away the inaccurate and false reasonings which unskilful editors have put ...
... likewise is of the greatest use in the arts both of peace and war , to many of which geometry is absolutely necessary . This I have endeavoured to do , by taking away the inaccurate and false reasonings which unskilful editors have put ...
Page 8
... likewise equal to AD ; whence AE and Care each of them equal to AD ; wherefore the straight * 1 Ax . line AE is equal to C , and from AB , the greater of two straight lines , a part AE has been cut off equal to C the less . Which was to ...
... likewise equal to AD ; whence AE and Care each of them equal to AD ; wherefore the straight * 1 Ax . line AE is equal to C , and from AB , the greater of two straight lines , a part AE has been cut off equal to C the less . Which was to ...
Page 9
... likewise the angles con- tained by those sides equal to one another , their bases shall likewise be equal , and the triangles be equal , and their other angles to which the equal sides are opposite shall be equal , each to each . Which ...
... likewise the angles con- tained by those sides equal to one another , their bases shall likewise be equal , and the triangles be equal , and their other angles to which the equal sides are opposite shall be equal , each to each . Which ...
Page 11
... likewise those which are terminated in the other extremity . If it be possible , let there be two triangles ACB , ADB , upon the same base AB , and upon the same side of it , which have their sides CA , DA terminated in the extremity A ...
... likewise those which are terminated in the other extremity . If it be possible , let there be two triangles ACB , ADB , upon the same base AB , and upon the same side of it , which have their sides CA , DA terminated in the extremity A ...
Page 12
... likewise those which are terminated in the other extremity . Q. E. D. PROP . VIII . THEOR . IF two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal ; the angle ...
... likewise those which are terminated in the other extremity . Q. E. D. PROP . VIII . THEOR . IF two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal ; the angle ...
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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.