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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Seite 236
... prisms , which are their halvesd , are to one another as the base AE to the base CF ; that is , as the triangle AEM to the d 28. 11. triangle CFG . PROP . XXXIII . THEOR . SIMILAR solid parallelepipeds are one to another in the ...
... prisms , which are their halvesd , are to one another as the base AE to the base CF ; that is , as the triangle AEM to the d 28. 11. triangle CFG . PROP . XXXIII . THEOR . SIMILAR solid parallelepipeds are one to another in the ...
Seite 251
... prisms of the same al- titude , the base of one of which is a parallelogram , and the base of the other a triangle ; if the parallelo- gram be double of the triangle , the prisms shall be equal to one another . Let the prisms ABCDEF ...
... prisms of the same al- titude , the base of one of which is a parallelogram , and the base of the other a triangle ; if the parallelo- gram be double of the triangle , the prisms shall be equal to one another . Let the prisms ABCDEF ...
Seite 257
... prisms which together are greater than half of the whole pyramid . Let there be a pyramid of which the base is the triangle ABC , and its vertex the point D : the pyramid ABCD may be divided into two equal and similar pyramids having ...
... prisms which together are greater than half of the whole pyramid . Let there be a pyramid of which the base is the triangle ABC , and its vertex the point D : the pyramid ABCD may be divided into two equal and similar pyramids having ...
Seite 258
... prisms of the same alti- tude , of which one has a parallelogram for its base , and the other a triangle that is half of the parallelogram , these prisms are equal a 40. 11. a to one another ; therefore the prism having the ...
... prisms of the same alti- tude , of which one has a parallelogram for its base , and the other a triangle that is half of the parallelogram , these prisms are equal a 40. 11. a to one another ; therefore the prism having the ...
Seite 259
... prisms is greater than either of the pyramids of which the triangles AEG , HKL are the b 15. 11 . bases , and the vertices the points H , D ; because , if EF be join- ed , the prism having the parallelogram EBFG for its base , and KH ...
... prisms is greater than either of the pyramids of which the triangles AEG , HKL are the b 15. 11 . bases , and the vertices the points H , D ; because , if EF be join- ed , the prism having the parallelogram EBFG for its base , and KH ...
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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.