The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthMathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 - 518 Seiten |
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Ergebnisse 6-10 von 76
Seite 214
... solid angle at A , are less than four right angles . Next , let the solid angle at A be contained by any number of plane angles BAC , CAD , DAE , EAF , FAB ; these together are less than four right angles . A F 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 number of plane angles BAC , CAD , DAE , EAF , FAB ; these together are less than four right angles . A F Let the planes in which ...
Seite 215
... solid angle at A , are less than four right angles . Therefore , every solid angle , & c . Q. E. D. PROP . XXII . THEOR . IF 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 . IF every two of three plane angles be greater than See N the third , and if the straight lines which contain them ...
Seite 216
... 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 ...
Seite 220
... solid angle at R , which is contained by three plane an- gles LRM , MRN , NRL , which are equal to the three given plane angles ABC , DEF , GHK , each to each . Which was to be done . d 8. 1 . Book XI . PROP . A. THEOR . IF each 220 THE ...
... solid angle at R , which is contained by three plane an- gles LRM , MRN , NRL , which are equal to the three given plane angles ABC , DEF , GHK , each to each . Which was to be done . d 8. 1 . Book XI . PROP . A. THEOR . IF each 220 THE ...
Seite 221
... 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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altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gnomon greater join less Let ABC meet multiple opposite parallel parallelogram perpendicular point F polygon prisms proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure right angles segment sides BA similar sine solid angle solid parallelepipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
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Seite 30 - Any two sides of a triangle are together greater than the third side.
Seite 64 - 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.
Seite 30 - 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...
Seite 59 - PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Seite 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Seite 165 - 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.
Seite 19 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Seite 191 - In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle.
Seite 39 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Seite 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.