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 |
From inside the book
Results 6-10 of 27
Page 253
... pyramid DEFH equal to one another ; as the prism of which the base is the parallelogram KBXL and opposite side MO ... pyramid ABCG to the two prisms in the pyramid DEFH : And likewise if the pyramids now made , for example , the two OMNG ...
... pyramid DEFH equal to one another ; as the prism of which the base is the parallelogram KBXL and opposite side MO ... pyramid ABCG to the two prisms in the pyramid DEFH : And likewise if the pyramids now made , for example , the two OMNG ...
Page 254
... pyramid OMNG to the two prisms in the pyramid STYH ; and so are all four to all four : And the same thing may be shown of the prisms made by dividing the pyramids AKLO and DPRS , and of all made by the same number of divisions ...
... pyramid OMNG to the two prisms in the pyramid STYH ; and so are all four to all four : And the same thing may be shown of the prisms made by dividing the pyramids AKLO and DPRS , and of all made by the same number of divisions ...
Page 255
... pyramid ABCG to any solid which is less than the pyramid DEFH . In the same manner it may be demonstrated , that the base DEF is not to the base ABC , as the pyramid DEFH to any solid which is less than the pyramid ABCG . Nor can the ...
... pyramid ABCG to any solid which is less than the pyramid DEFH . In the same manner it may be demonstrated , that the base DEF is not to the base ABC , as the pyramid DEFH to any solid which is less than the pyramid ABCG . Nor can the ...
Page 256
... pyramid ABCDEM to the pyra- mid FGHKLN . Divide the base ABCDE into the triangles ABC , ACD , ADE ; and the base ... pyramid ABCM to the pyramid FGHÑ ; and the triangle ACD to the triangle FGH , as the pyramid ACDM to the pyramid M N 5 B ...
... pyramid ABCDEM to the pyra- mid FGHKLN . Divide the base ABCDE into the triangles ABC , ACD , ADE ; and the base ... pyramid ABCM to the pyramid FGHÑ ; and the triangle ACD to the triangle FGH , as the pyramid ACDM to the pyramid M N 5 B ...
Page 257
... pyramid ABCDEM to the pyramid FGHKLN . Therefore pyramids , & c . Q. E.D. € 22. 5 . . PROP . VII . THEOR . EVERY prism having a triangular base may be di- vided into three pyramids that have triangular bases , and are equal to one ...
... pyramid ABCDEM to the pyramid FGHKLN . Therefore pyramids , & c . Q. E.D. € 22. 5 . . PROP . VII . THEOR . EVERY prism having a triangular base may be di- vided into three pyramids that have triangular bases , and are equal to one ...
Other editions - View all
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.