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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Página 206
... solid angle at A , are less than four right angles . Next , Let the solid angle at A be contained by any num- ber of plane angles BAC , CAD , DAE , EAF , FAB : these together are less than four right angles . A Let the planes in which ...
... solid angle at A , are less than four right angles . Next , Let the solid angle at A be contained by any num- ber of plane angles BAC , CAD , DAE , EAF , FAB : these together are less than four right angles . A Let the planes in which ...
Página 207
... solid angle at A , are less than four right angles . Therefore every solid angle , & c . Q. E. D. PROP . XXII . THEOR . Ir every two of three plane angles be greater than See N. the third , and if the straight lines which contain them ...
... solid angle at A , are less than four right angles . Therefore every solid angle , & c . Q. E. D. PROP . XXII . THEOR . Ir every two of three plane angles be greater than See N. the third , and if the straight lines which contain them ...
Página 208
... solid angle which shall be contained by three given plane angles , any two of them being greater than the third , and all three together less than four right angles . Let the three given plane angles be ABC , DEF , GHK , any two of ...
... solid angle which shall be contained by three given plane angles , any two of them being greater than the third , and all three together less than four right angles . Let the three given plane angles be ABC , DEF , GHK , any two of ...
Página 212
... solid angle at R , which is contained by three plane angles LRM , MRN , NRL , which are equal to the three given plane angles ABC , DEF , GHK , each to each . Which was to be done . BOOK XI . PROP . A. THEOR . Ir each 212 THE ELEMENTS.
... solid angle at R , which is contained by three plane angles LRM , MRN , NRL , which are equal to the three given plane angles ABC , DEF , GHK , each to each . Which was to be done . BOOK XI . PROP . A. THEOR . Ir each 212 THE ELEMENTS.
Página 213
... solid angles be contained by three See N. plane angles equal to one another , each to each ; the planes in which the equal angles are , have the same inclination to one another . Let there be two solid angles at the points A , B ; and ...
... solid angles be contained by three See N. plane angles equal to one another , each to each ; the planes in which the equal angles are , have the same inclination to one another . Let there be two solid angles at the points A , B ; and ...
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The Elements of Euclid; viz. the first six books, together with the eleventh ... Euclides Visualização integral - 1834 |
Palavras e frases frequentes
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
Passagens conhecidas
Página 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.
Página 16 - Any two sides of a triangle are together greater than the third side.
Página 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.
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.
Página 159 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.