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 188
... solid is a superficies . III . A straight line is perpendicular , or at right angles , to a plane , when it makes ... angle con- tained by two straight lines drawn from any the same point of their common section at right angles to it ...
... solid is a superficies . III . A straight line is perpendicular , or at right angles , to a plane , when it makes ... angle con- tained by two straight lines drawn from any the same point of their common section at right angles to it ...
Page 189
... angles of inclination are equal to one another . VIII . Parallel planes are such which do not meet one another though produced . IX . BOOK XI . A solid angle is that which is made by the meeting of more See N. than two plane angles ...
... angles of inclination are equal to one another . VIII . Parallel planes are such which do not meet one another though produced . IX . BOOK XI . A solid angle is that which is made by the meeting of more See N. than two plane angles ...
Page 190
... angled cone . XIX . The axis of a cone is the fixed straight line about which the triangle revolves . XX . The base of a cone is the circle described by that side con- taining the right angle , which revolves . XXI . A cylinder is a solid ...
... angled cone . XIX . The axis of a cone is the fixed straight line about which the triangle revolves . XX . The base of a cone is the circle described by that side con- taining the right angle , which revolves . XXI . A cylinder is a solid ...
Page 205
... solid angle be contained by three plane angles , See N. any two of them are greater than the third . Let the solid angle at A be contained by the three plane angles , BAC , CAD , DAB . Any two of them are greater than the third . a If the ...
... solid angle be contained by three plane angles , See N. any two of them are greater than the third . Let the solid angle at A be contained by the three plane angles , BAC , CAD , DAB . Any two of them are greater than the third . a If the ...
Page 206
... angles . Take in each of the straight lines AB , AC , AD any points B , C , D , and join BC , CD , DB : Then because the solid angle at B is contained by the three plane angles CBA , a 20. 11. ABD , DBC , any two of them are greater ...
... angles . Take in each of the straight lines AB , AC , AD any points B , C , D , and join BC , CD , DB : Then because the solid angle at B is contained by the three plane angles CBA , a 20. 11. ABD , DBC , any two of them are greater ...
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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.