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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Side 228
... prisms , which are their halves , are to one another , as the base AE to the 28. 11. base CF ; that is , as the triangle AEM to the triangle CFG . d PROP . XXXIII . THEOR . SIMILAR solid parallelopipeds are one to another in the ...
... prisms , which are their halves , are to one another , as the base AE to the 28. 11. base CF ; that is , as the triangle AEM to the triangle CFG . d PROP . XXXIII . THEOR . SIMILAR solid parallelopipeds are one to another in the ...
Side 243
... prism GHKLMN . Complete the solids AX , GO ; and because the parallel- ogram AF is double of the triangle GHK ; and ... prism ABCDEF is half of the solid AX ; and the prism GHKLMN half of the solid GO . Therefore the prism ABCDEF is ...
... prism GHKLMN . Complete the solids AX , GO ; and because the parallel- ogram AF is double of the triangle GHK ; and ... prism ABCDEF is half of the solid AX ; and the prism GHKLMN half of the solid GO . Therefore the prism ABCDEF is ...
Side 249
... prisms which together are greater than half of the whole pyramid . Ꭰ 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 . Ꭰ 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 ...
Side 250
... - * 11. 1. rallelogram FBEG is double of the triangle GFC : But when there are two prisms of the same altitude , of which one has a parallelogram for its base , and the other a triangle a * 40. 11 . C that is half of 250 THE ELEMENTS.
... - * 11. 1. rallelogram FBEG is double of the triangle GFC : But when there are two prisms of the same altitude , of which one has a parallelogram for its base , and the other a triangle a * 40. 11 . C that is half of 250 THE ELEMENTS.
Side 251
... prisms are equal to Boox XII . one another ; therefore the prism having the parallelogram EBFG for its base , and the straight line KH opposite to it , is equal to the prism having the triangle GFC for its base , and the triangle HKL ...
... prisms are equal to Boox XII . one another ; therefore the prism having the parallelogram EBFG for its base , and the straight line KH opposite to it , is equal to the prism having the triangle GFC for its base , and the triangle HKL ...
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The Elements of Euclid; viz. the first six books, together with the eleventh ... Euclides Uten tilgangsbegrensning - 1834 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 16 - Any two sides of a triangle are together greater than the third side.
Side 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.
Side 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...
Side 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.
Side 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.
Side 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.
Side 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.
Side 159 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.